NOMBRES - Curiosités, théorie et usages

 

Accueil                           DicoNombre            Rubriques           Nouveautés      Édition du: 06/08/2018

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Barre de recherche          DicoCulture              Index alphabétique          Brèves de Maths                   

     

Tables de nombres

 

Débutants

Général

Partition des nombres

en somme de nombres premiers distincts

 

Glossaire

Général

INDEX

Partitions

2 à 29

30 à 49

50 à 59

60 à 69

70 à 79

80 à 89

90 à 99

100

 

 

NOMBRES

somme de Premiers distincts

 

Table de partitions pour tous les nombres de 2 à 100

Voir Développements sur les nombres premiers / Somme de premiers consécutifs

 

 

Légende

*  Qté: Quantité de termes dans la partition; en rouge la quantité minimale.

*  N: Le nombre partitionné.

*  somme: les termes de la somme.

 

 

TABLE pour N de 60 à 69

Voir Nombre 60

 

 

Qté N        Somme

 

7    60        2     + 3     + 5     + 7     + 11     + 13                 + 19                                                                                                                          

4    60                                            + 11     + 13     + 17     + 19                                                                                                                          

5    60        2                         + 7     + 11                 + 17                 + 23                                                                                                              

5    60        2               + 5                           + 13     + 17                 + 23                                                                                                              

4    60                                   + 7                 + 13     + 17                 + 23                                                                                                              

5    60        2               + 5               + 11                             + 19     + 23                                                                                                              

4    60                                   + 7     + 11                             + 19     + 23                                                                                                              

5    60        2     + 3                                    + 13                 + 19     + 23                                                                                                              

4    60                         + 5                           + 13                 + 19     + 23                                                                                                              

5    60        2               + 5               + 11     + 13                                        + 29                                                                                                   

4    60                                   + 7     + 11     + 13                                        + 29                                                                                                   

5    60        2               + 5     + 7                            + 17                            + 29                                                                                                   

4    60               + 3                        + 11                 + 17                            + 29                                                                                                   

5    60        2     + 3               + 7                                        + 19                + 29                                                                                                   

4    60                         + 5     + 7                                        + 19                + 29                                                                                                   

4    60               + 3     + 5                                                              + 23     + 29                                                                                                   

5    60        2     + 3                        + 11     + 13                                                    + 31                                                                                       

4    60                         + 5               + 11     + 13                                                    + 31                                                                                       

5    60        2     + 3               + 7                            + 17                                        + 31                                                                                       

4    60                         + 5     + 7                            + 17                                        + 31                                                                                       

5    60        2     + 3     + 5                                                  + 19                            + 31                                                                                       

4    60               + 3               + 7                                        + 19                            + 31                                                                                       

2    60                                                                                                       + 29     + 31                                                                                       

5    60        2     + 3               + 7     + 11                                                                            + 37                                                                           

4    60                         + 5     + 7     + 11                                                                            + 37                                                                           

5    60        2     + 3     + 5                           + 13                                                                + 37                                                                           

4    60               + 3               + 7                 + 13                                                                + 37                                                                           

2    60                                                                                            + 23                            + 37                                                                           

4    60               + 3     + 5               + 11                                                                                        + 41                                                               

3    60        2                                                          + 17                                                                + 41                                                               

2    60                                                                                + 19                                                    + 41                                                               

5    60        2     + 3     + 5     + 7                                                                                                               + 43                                                   

2    60                                                                    + 17                                                                            + 43                                                   

3    60        2                                  + 11                                                                                                               + 47                                       

2    60                                                        + 13                                                                                                   + 47                                       

3    60        2               + 5                                                                                                                                                 + 53                            

2    60                                   + 7                                                                                                                                       + 53                            

6    61        2               + 5     + 7     + 11                 + 17     + 19                                                                                                                          

6    61        2     + 3               + 7                 + 13     + 17     + 19                                                                                                                          

5    61                         + 5     + 7                 + 13     + 17     + 19                                                                                                                          

6    61        2               + 5     + 7     + 11     + 13                            + 23                                                                                                              

6    61        2     + 3     + 5               + 11                 + 17                 + 23                                                                                                              

5    61               + 3               + 7     + 11                 + 17                 + 23                                                                                                              

5    61               + 3     + 5                           + 13     + 17                 + 23                                                                                                              

5    61               + 3     + 5               + 11                             + 19     + 23                                                                                                              

4    61        2                                                          + 17     + 19     + 23                                                                                                              

5    61               + 3     + 5               + 11     + 13                                        + 29                                                                                                   

5    61               + 3     + 5     + 7                            + 17                            + 29                                                                                                   

4    61        2                                              + 13     + 17                            + 29                                                                                                   

4    61        2                                  + 11                             + 19                + 29                                                                                                   

3    61                                                        + 13                 + 19                + 29                                                                                                   

4    61        2                         + 7                                                    + 23     + 29                                                                                                   

6    61        2     + 3     + 5     + 7                 + 13                                                    + 31                                                                                       

4    61        2                                  + 11                 + 17                                        + 31                                                                                       

3    61                                                        + 13     + 17                                        + 31                                                                                       

3    61                                            + 11                             + 19                            + 31                                                                                       

4    61        2               + 5                                                              + 23                 + 31                                                                                       

3    61                                   + 7                                                    + 23                 + 31                                                                                       

3    61                                            + 11     + 13                                                                + 37                                                                           

4    61        2               + 5                                      + 17                                                    + 37                                                                           

3    61                                   + 7                            + 17                                                    + 37                                                                           

4    61        2     + 3                                                            + 19                                        + 37                                                                           

3    61                         + 5                                                  + 19                                        + 37                                                                           

4    61        2                         + 7     + 11                                                                                        + 41                                                               

4    61        2               + 5                           + 13                                                                            + 41                                                               

3    61                                   + 7                 + 13                                                                            + 41                                                               

3    61               + 3                                                + 17                                                                + 41                                                               

4    61        2               + 5               + 11                                                                                                   + 43                                                   

3    61                                   + 7     + 11                                                                                                   + 43                                                   

4    61        2     + 3                                    + 13                                                                                       + 43                                                   

3    61                         + 5                           + 13                                                                                       + 43                                                   

4    61        2               + 5     + 7                                                                                                                           + 47                                       

3    61               + 3                        + 11                                                                                                               + 47                                       

3    61               + 3     + 5                                                                                                                                                 + 53                            

2    61        2                                                                                                                                                                                + 59                

1    61                                                                                                                                                                                                      + 61    

6    62               + 3     + 5     + 7     + 11                 + 17     + 19                                                                                                                          

5    62        2                                  + 11     + 13     + 17     + 19                                                                                                                          

6    62               + 3     + 5     + 7     + 11     + 13                            + 23                                                                                                              

5    62        2                         + 7                 + 13     + 17                 + 23                                                                                                              

5    62        2                         + 7     + 11                             + 19     + 23                                                                                                              

5    62        2               + 5                           + 13                 + 19     + 23                                                                                                              

4    62                                   + 7                 + 13                 + 19     + 23                                                                                                              

4    62               + 3                                                + 17     + 19     + 23                                                                                                              

5    62        2                         + 7     + 11     + 13                                        + 29                                                                                                   

5    62        2     + 3                        + 11                 + 17                            + 29                                                                                                   

4    62                         + 5               + 11                 + 17                            + 29                                                                                                   

4    62               + 3                                    + 13     + 17                            + 29                                                                                                   

5    62        2               + 5     + 7                                        + 19                + 29                                                                                                   

4    62               + 3                        + 11                             + 19                + 29                                                                                                   

5    62        2     + 3     + 5                                                              + 23     + 29                                                                                                   

4    62               + 3               + 7                                                    + 23     + 29                                                                                                   

5    62        2               + 5               + 11     + 13                                                    + 31                                                                                       

4    62                                   + 7     + 11     + 13                                                    + 31                                                                                       

5    62        2               + 5     + 7                            + 17                                        + 31                                                                                       

4    62               + 3                        + 11                 + 17                                        + 31                                                                                       

5    62        2     + 3               + 7                                        + 19                            + 31                                                                                       

4    62                         + 5     + 7                                        + 19                            + 31                                                                                       

4    62               + 3     + 5                                                              + 23                 + 31                                                                                       

3    62        2                                                                                             + 29     + 31                                                                                       

5    62        2               + 5     + 7     + 11                                                                            + 37                                                                           

5    62        2     + 3               + 7                 + 13                                                                + 37                                                                           

4    62                         + 5     + 7                 + 13                                                                + 37                                                                           

4    62               + 3     + 5                                      + 17                                                    + 37                                                                           

3    62        2                                                                                  + 23                            + 37                                                                           

5    62        2     + 3     + 5               + 11                                                                                        + 41                                                               

4    62               + 3               + 7     + 11                                                                                        + 41                                                               

4    62               + 3     + 5                           + 13                                                                            + 41                                                               

3    62        2                                                                      + 19                                                    + 41                                                               

4    62               + 3     + 5               + 11                                                                                                   + 43                                                   

3    62        2                                                          + 17                                                                            + 43                                                   

2    62                                                                                + 19                                                                + 43                                                   

4    62               + 3     + 5     + 7                                                                                                                           + 47                                       

3    62        2                                              + 13                                                                                                   + 47                                       

3    62        2                         + 7                                                                                                                                       + 53                            

2    62               + 3                                                                                                                                                                      + 59                

6    63        2               + 5     + 7                 + 13     + 17     + 19                                                                                                                          

5    63               + 3                        + 11     + 13     + 17     + 19                                                                                                                          

6    63        2     + 3               + 7     + 11                 + 17                 + 23                                                                                                              

5    63                         + 5     + 7     + 11                 + 17                 + 23                                                                                                              

6    63        2     + 3     + 5                           + 13     + 17                 + 23                                                                                                              

5    63               + 3               + 7                 + 13     + 17                 + 23                                                                                                              

6    63        2     + 3     + 5               + 11                             + 19     + 23                                                                                                              

5    63               + 3               + 7     + 11                             + 19     + 23                                                                                                              

5    63               + 3     + 5                           + 13                 + 19     + 23                                                                                                              

6    63        2     + 3     + 5               + 11     + 13                                        + 29                                                                                                   

5    63               + 3               + 7     + 11     + 13                                        + 29                                                                                                   

6    63        2     + 3     + 5     + 7                            + 17                            + 29                                                                                                   

5    63               + 3     + 5     + 7                                        + 19                + 29                                                                                                   

4    63        2                                              + 13                 + 19                + 29                                                                                                   

3    63                                            + 11                                        + 23     + 29                                                                                                   

5    63               + 3     + 5               + 11     + 13                                                    + 31                                                                                       

5    63               + 3     + 5     + 7                            + 17                                        + 31                                                                                       

4    63        2                                              + 13     + 17                                        + 31                                                                                       

4    63        2                                  + 11                             + 19                            + 31                                                                                       

3    63                                                        + 13                 + 19                            + 31                                                                                       

4    63        2                         + 7                                                    + 23                 + 31                                                                                       

3    63               + 3                                                                                   + 29     + 31                                                                                       

5    63               + 3     + 5     + 7     + 11                                                                            + 37                                                                           

4    63        2                                  + 11     + 13                                                                + 37                                                                           

4    63        2                         + 7                            + 17                                                    + 37                                                                           

4    63        2               + 5                                                  + 19                                        + 37                                                                           

3    63                                   + 7                                        + 19                                        + 37                                                                           

3    63               + 3                                                                        + 23                            + 37                                                                           

4    63        2                         + 7                 + 13                                                                            + 41                                                               

4    63        2     + 3                                                + 17                                                                + 41                                                               

3    63                         + 5                                      + 17                                                                + 41                                                               

3    63               + 3                                                            + 19                                                    + 41                                                               

4    63        2                         + 7     + 11                                                                                                   + 43                                                   

4    63        2               + 5                           + 13                                                                                       + 43                                                   

3    63                                   + 7                 + 13                                                                                       + 43                                                   

3    63               + 3                                                + 17                                                                            + 43                                                   

4    63        2     + 3                        + 11                                                                                                               + 47                                       

3    63                         + 5               + 11                                                                                                               + 47                                       

3    63               + 3                                    + 13                                                                                                   + 47                                       

4    63        2     + 3     + 5                                                                                                                                                 + 53                            

3    63               + 3               + 7                                                                                                                                       + 53                            

2    63        2                                                                                                                                                                                            + 61    

7    64        2     + 3     + 5     + 7     + 11                 + 17     + 19                                                                                                                          

6    64               + 3     + 5     + 7                 + 13     + 17     + 19                                                                                                                          

7    64        2     + 3     + 5     + 7     + 11     + 13                            + 23                                                                                                              

4    64                                            + 11     + 13     + 17                 + 23                                                                                                              

5    64        2                         + 7                 + 13                 + 19     + 23                                                                                                              

5    64        2     + 3                                                + 17     + 19     + 23                                                                                                              

4    64                         + 5                                      + 17     + 19     + 23                                                                                                              

5    64        2               + 5               + 11                 + 17                            + 29                                                                                                   

4    64                                   + 7     + 11                 + 17                            + 29                                                                                                   

5    64        2     + 3                                    + 13     + 17                            + 29                                                                                                   

4    64                         + 5                           + 13     + 17                            + 29                                                                                                   

5    64        2     + 3                        + 11                             + 19                + 29                                                                                                   

4    64                         + 5               + 11                             + 19                + 29                                                                                                   

4    64               + 3                                    + 13                 + 19                + 29                                                                                                   

5    64        2     + 3               + 7                                                    + 23     + 29                                                                                                   

4    64                         + 5     + 7                                                    + 23     + 29                                                                                                   

5    64        2                         + 7     + 11     + 13                                                    + 31                                                                                       

5    64        2     + 3                        + 11                 + 17                                        + 31                                                                                       

4    64                         + 5               + 11                 + 17                                        + 31                                                                                       

4    64               + 3                                    + 13     + 17                                        + 31                                                                                       

5    64        2               + 5     + 7                                        + 19                            + 31                                                                                       

4    64               + 3                        + 11                             + 19                            + 31                                                                                       

5    64        2     + 3     + 5                                                              + 23                 + 31                                                                                       

4    64               + 3               + 7                                                    + 23                 + 31                                                                                       

5    64        2               + 5     + 7                 + 13                                                                + 37                                                                           

4    64               + 3                        + 11     + 13                                                                + 37                                                                           

5    64        2     + 3     + 5                                      + 17                                                    + 37                                                                           

4    64               + 3               + 7                            + 17                                                    + 37                                                                           

4    64               + 3     + 5                                                  + 19                                        + 37                                                                           

5    64        2     + 3               + 7     + 11                                                                                        + 41                                                               

4    64                         + 5     + 7     + 11                                                                                        + 41                                                               

5    64        2     + 3     + 5                           + 13                                                                            + 41                                                               

4    64               + 3               + 7                 + 13                                                                            + 41                                                               

2    64                                                                                            + 23                                        + 41                                                               

5    64        2     + 3     + 5               + 11                                                                                                   + 43                                                   

4    64               + 3               + 7     + 11                                                                                                   + 43                                                   

4    64               + 3     + 5                           + 13                                                                                       + 43                                                   

3    64        2                                                                      + 19                                                                + 43                                                   

5    64        2     + 3     + 5     + 7                                                                                                                           + 47                                       

2    64                                                                    + 17                                                                                        + 47                                       

2    64                                            + 11                                                                                                                           + 53                            

3    64        2     + 3                                                                                                                                                                      + 59                

2    64                         + 5                                                                                                                                                             + 59                

2    64               + 3                                                                                                                                                                                  + 61    

6    65        2     + 3                        + 11     + 13     + 17     + 19                                                                                                                          

5    65                         + 5               + 11     + 13     + 17     + 19                                                                                                                          

6    65        2               + 5     + 7     + 11                 + 17                 + 23                                                                                                              

6    65        2     + 3               + 7                 + 13     + 17                 + 23                                                                                                              

5    65                         + 5     + 7                 + 13     + 17                 + 23                                                                                                              

6    65        2     + 3               + 7     + 11                             + 19     + 23                                                                                                              

5    65                         + 5     + 7     + 11                             + 19     + 23                                                                                                              

6    65        2     + 3     + 5                           + 13                 + 19     + 23                                                                                                              

5    65               + 3               + 7                 + 13                 + 19     + 23                                                                                                              

6    65        2     + 3               + 7     + 11     + 13                                        + 29                                                                                                   

5    65                         + 5     + 7     + 11     + 13                                        + 29                                                                                                   

5    65               + 3     + 5               + 11                 + 17                            + 29                                                                                                   

6    65        2     + 3     + 5     + 7                                        + 19                + 29                                                                                                   

3    65                                                                    + 17     + 19                + 29                                                                                                   

4    65        2                                  + 11                                        + 23     + 29                                                                                                   

3    65                                                        + 13                            + 23     + 29                                                                                                   

6    65        2     + 3     + 5               + 11     + 13                                                    + 31                                                                                       

5    65               + 3               + 7     + 11     + 13                                                    + 31                                                                                       

6    65        2     + 3     + 5     + 7                            + 17                                        + 31                                                                                       

5    65               + 3     + 5     + 7                                        + 19                            + 31                                                                                       

4    65        2                                              + 13                 + 19                            + 31                                                                                       

3    65                                            + 11                                        + 23                 + 31                                                                                       

4    65        2     + 3                                                                                   + 29     + 31                                                                                       

3    65                         + 5                                                                          + 29     + 31                                                                                       

6    65        2     + 3     + 5     + 7     + 11                                                                            + 37                                                                           

5    65               + 3     + 5     + 7                 + 13                                                                + 37                                                                           

3    65                                            + 11                 + 17                                                    + 37                                                                           

4    65        2                         + 7                                        + 19                                        + 37                                                                           

4    65        2     + 3                                                                        + 23                            + 37                                                                           

3    65                         + 5                                                              + 23                            + 37                                                                           

3    65                                            + 11     + 13                                                                            + 41                                                               

4    65        2               + 5                                      + 17                                                                + 41                                                               

3    65                                   + 7                            + 17                                                                + 41                                                               

4    65        2     + 3                                                            + 19                                                    + 41                                                               

3    65                         + 5                                                  + 19                                                    + 41                                                               

4    65        2                         + 7                 + 13                                                                                       + 43                                                   

4    65        2     + 3                                                + 17                                                                            + 43                                                   

3    65                         + 5                                      + 17                                                                            + 43                                                   

3    65               + 3                                                            + 19                                                                + 43                                                   

4    65        2               + 5               + 11                                                                                                               + 47                                       

3    65                                   + 7     + 11                                                                                                               + 47                                       

4    65        2     + 3                                    + 13                                                                                                   + 47                                       

3    65                         + 5                           + 13                                                                                                   + 47                                       

4    65        2     + 3               + 7                                                                                                                                       + 53                            

3    65                         + 5     + 7                                                                                                                                       + 53                            

7    66        2     + 3     + 5     + 7                 + 13     + 17     + 19                                                                                                                          

6    66               + 3     + 5     + 7     + 11                 + 17                 + 23                                                                                                              

5    66        2                                  + 11     + 13     + 17                 + 23                                                                                                              

4    66                                            + 11     + 13                 + 19     + 23                                                                                                              

5    66        2               + 5                                      + 17     + 19     + 23                                                                                                              

4    66                                   + 7                            + 17     + 19     + 23                                                                                                              

5    66        2                         + 7     + 11                 + 17                            + 29                                                                                                   

5    66        2               + 5                           + 13     + 17                            + 29                                                                                                   

4    66                                   + 7                 + 13     + 17                            + 29                                                                                                   

5    66        2               + 5               + 11                             + 19                + 29                                                                                                   

4    66                                   + 7     + 11                             + 19                + 29                                                                                                   

5    66        2     + 3                                    + 13                 + 19                + 29                                                                                                   

4    66                         + 5                           + 13                 + 19                + 29                                                                                                   

5    66        2               + 5     + 7                                                    + 23     + 29                                                                                                   

4    66               + 3                        + 11                                        + 23     + 29                                                                                                   

5    66        2               + 5               + 11                 + 17                                        + 31                                                                                       

4    66                                   + 7     + 11                 + 17                                        + 31                                                                                       

5    66        2     + 3                                    + 13     + 17                                        + 31                                                                                       

4    66                         + 5                           + 13     + 17                                        + 31                                                                                       

5    66        2     + 3                        + 11                             + 19                            + 31                                                                                       

4    66                         + 5               + 11                             + 19                            + 31                                                                                       

4    66               + 3                                    + 13                 + 19                            + 31                                                                                       

5    66        2     + 3               + 7                                                    + 23                 + 31                                                                                       

4    66                         + 5     + 7                                                    + 23                 + 31                                                                                       

5    66        2     + 3                        + 11     + 13                                                                + 37                                                                           

4    66                         + 5               + 11     + 13                                                                + 37                                                                           

5    66        2     + 3               + 7                            + 17                                                    + 37                                                                           

4    66                         + 5     + 7                            + 17                                                    + 37                                                                           

5    66        2     + 3     + 5                                                  + 19                                        + 37                                                                           

4    66               + 3               + 7                                        + 19                                        + 37                                                                           

2    66                                                                                                       + 29                 + 37                                                                           

5    66        2               + 5     + 7     + 11                                                                                        + 41                                                               

5    66        2     + 3               + 7                 + 13                                                                            + 41                                                               

4    66                         + 5     + 7                 + 13                                                                            + 41                                                               

4    66               + 3     + 5                                      + 17                                                                + 41                                                               

3    66        2                                                                                  + 23                                        + 41                                                               

5    66        2     + 3               + 7     + 11                                                                                                   + 43                                                   

4    66                         + 5     + 7     + 11                                                                                                   + 43                                                   

5    66        2     + 3     + 5                           + 13                                                                                       + 43                                                   

4    66               + 3               + 7                 + 13                                                                                       + 43                                                   

2    66                                                                                            + 23                                                    + 43                                                   

4    66               + 3     + 5               + 11                                                                                                               + 47                                       

3    66        2                                                          + 17                                                                                        + 47                                       

2    66                                                                                + 19                                                                            + 47                                       

3    66        2                                  + 11                                                                                                                           + 53                            

2    66                                                        + 13                                                                                                               + 53                            

3    66        2               + 5                                                                                                                                                             + 59                

2    66                                   + 7                                                                                                                                                   + 59                

3    66        2     + 3                                                                                                                                                                                  + 61    

2    66                         + 5                                                                                                                                                                        + 61    

6    67        2               + 5               + 11     + 13     + 17     + 19                                                                                                                          

5    67                                   + 7     + 11     + 13     + 17     + 19                                                                                                                          

6    67        2               + 5     + 7                 + 13     + 17                 + 23                                                                                                               

5    67               + 3                        + 11     + 13     + 17                 + 23                                                                                                              

6    67        2               + 5     + 7     + 11                             + 19     + 23                                                                                                              

6    67        2     + 3               + 7                 + 13                 + 19     + 23                                                                                                              

5    67                         + 5     + 7                 + 13                 + 19     + 23                                                                                                              

5    67               + 3     + 5                                      + 17     + 19     + 23                                                                                                              

6    67        2               + 5     + 7     + 11     + 13                                        + 29                                                                                                   

6    67        2     + 3     + 5               + 11                 + 17                            + 29                                                                                                   

5    67               + 3               + 7     + 11                 + 17                            + 29                                                                                                   

5    67               + 3     + 5                           + 13     + 17                            + 29                                                                                                   

5    67               + 3     + 5               + 11                             + 19                + 29                                                                                                   

4    67        2                                                          + 17     + 19                + 29                                                                                                   

5    67               + 3     + 5     + 7                                                    + 23     + 29                                                                                                   

4    67        2                                              + 13                            + 23     + 29                                                                                                   

6    67        2     + 3               + 7     + 11     + 13                                                    + 31                                                                                       

5    67                         + 5     + 7     + 11     + 13                                                    + 31                                                                                       

5    67               + 3     + 5               + 11                 + 17                                        + 31                                                                                       

6    67        2     + 3     + 5     + 7                                        + 19                            + 31                                                                                       

3    67                                                                    + 17     + 19                            + 31                                                                                       

4    67        2                                  + 11                                        + 23                 + 31                                                                                       

3    67                                                        + 13                            + 23                 + 31                                                                                       

4    67        2               + 5                                                                          + 29     + 31                                                                                       

3    67                                   + 7                                                                + 29     + 31                                                                                       

6    67        2     + 3     + 5     + 7                 + 13                                                                + 37                                                                           

4    67        2                                  + 11                 + 17                                                    + 37                                                                           

3    67                                                        + 13     + 17                                                    + 37                                                                           

3    67                                            + 11                             + 19                                        + 37                                                                           

4    67        2               + 5                                                              + 23                            + 37                                                                           

3    67                                   + 7                                                    + 23                            + 37                                                                           

5    67               + 3     + 5     + 7     + 11                                                                                        + 41                                                               

4    67        2                                  + 11     + 13                                                                            + 41                                                               

4    67        2                         + 7                            + 17                                                                + 41                                                               

4    67        2               + 5                                                  + 19                                                    + 41                                                               

3    67                                   + 7                                        + 19                                                    + 41                                                               

3    67               + 3                                                                        + 23                                        + 41                                                               

3    67                                            + 11     + 13                                                                                       + 43                                                   

4    67        2               + 5                                      + 17                                                                            + 43                                                   

3    67                                   + 7                            + 17                                                                            + 43                                                   

4    67        2     + 3                                                            + 19                                                                + 43                                                   

3    67                         + 5                                                  + 19                                                                + 43                                                   

4    67        2                         + 7     + 11                                                                                                               + 47                                       

4    67        2               + 5                           + 13                                                                                                   + 47                                       

3    67                                   + 7                 + 13                                                                                                   + 47                                       

3    67               + 3                                                + 17                                                                                        + 47                                       

4    67        2               + 5     + 7                                                                                                                                       + 53                            

3    67               + 3                        + 11                                                                                                                           + 53                            

3    67               + 3     + 5                                                                                                                                                             + 59                

1    67                                                                                                                                                                                                                  + 67

6    68               + 3     + 5               + 11     + 13     + 17     + 19                                                                                                                          

7    68        2     + 3     + 5     + 7     + 11                 + 17                 + 23                                                                                                              

6    68               + 3     + 5     + 7                 + 13     + 17                 + 23                                                                                                              

6    68               + 3     + 5     + 7     + 11                             + 19     + 23                                                                                                              

5    68        2                                  + 11     + 13                 + 19     + 23                                                                                                              

5    68        2                         + 7                            + 17     + 19     + 23                                                                                                               

6    68               + 3     + 5     + 7     + 11     + 13                                        + 29                                                                                                   

5    68        2                         + 7                 + 13     + 17                            + 29                                                                                                   

5    68        2                         + 7     + 11                             + 19                + 29                                                                                                   

5    68        2               + 5                           + 13                 + 19                + 29                                                                                                   

4    68                                   + 7                 + 13                 + 19                + 29                                                                                                   

4    68               + 3                                                + 17     + 19                + 29                                                                                                   

5    68        2     + 3                        + 11                                        + 23     + 29                                                                                                   

4    68                         + 5               + 11                                        + 23     + 29                                                                                                   

4    68               + 3                                    + 13                            + 23     + 29                                                                                                   

5    68        2                         + 7     + 11                 + 17                                        + 31                                                                                       

5    68        2               + 5                           + 13     + 17                                        + 31                                                                                       

4    68                                   + 7                 + 13     + 17                                        + 31                                                                                       

5    68        2               + 5               + 11                             + 19                            + 31                                                                                       

4    68                                   + 7     + 11                             + 19                            + 31                                                                                       

5    68        2     + 3                                    + 13                 + 19                            + 31                                                                                       

4    68                         + 5                           + 13                 + 19                            + 31                                                                                       

5    68        2               + 5     + 7                                                    + 23                 + 31                                                                                       

4    68               + 3                        + 11                                        + 23                 + 31                                                                                       

4    68               + 3     + 5                                                                          + 29     + 31                                                                                       

5    68        2               + 5               + 11     + 13                                                                + 37                                                                           

4    68                                   + 7     + 11     + 13                                                                + 37                                                                           

5    68        2               + 5     + 7                            + 17                                                    + 37                                                                           

4    68               + 3                        + 11                 + 17                                                    + 37                                                                           

5    68        2     + 3               + 7                                        + 19                                        + 37                                                                           

4    68                         + 5     + 7                                        + 19                                        + 37                                                                           

4    68               + 3     + 5                                                              + 23                             + 37                                                                           

3    68        2                                                                                             + 29                 + 37                                                                           

2    68                                                                                                                   + 31     + 37                                                                           

5    68        2               + 5     + 7                 + 13                                                                            + 41                                                               

4    68               + 3                        + 11     + 13                                                                            + 41                                                               

5    68        2     + 3     + 5                                      + 17                                                                + 41                                                               

4    68               + 3               + 7                            + 17                                                                + 41                                                               

4    68               + 3     + 5                                                  + 19                                                    + 41                                                               

5    68        2               + 5     + 7     + 11                                                                                                   + 43                                                   

5    68        2     + 3               + 7                 + 13                                                                                       + 43                                                   

4    68                         + 5     + 7                 + 13                                                                                       + 43                                                   

4    68               + 3     + 5                                      + 17                                                                            + 43                                                   

3    68        2                                                                                  + 23                                                    + 43                                                   

5    68        2     + 3     + 5               + 11                                                                                                               + 47                                       

4    68               + 3               + 7     + 11                                                                                                               + 47                                       

4    68               + 3     + 5                           + 13                                                                                                   + 47                                       

3    68        2                                                                      + 19                                                                            + 47                                       

4    68               + 3     + 5     + 7                                                                                                                                       + 53                            

3    68        2                                              + 13                                                                                                               + 53                            

3    68        2                         + 7                                                                                                                                                   + 59                

3    68        2               + 5                                                                                                                                                                        + 61    

2    68                                   + 7                                                                                                                                                              + 61    

6    69        2                         + 7     + 11     + 13     + 17     + 19                                                                                                                          

6    69        2     + 3                        + 11     + 13     + 17                 + 23                                                                                                              

5    69                         + 5               + 11     + 13     + 17                 + 23                                                                                                              

6    69        2               + 5     + 7                 + 13                 + 19     + 23                                                                                                              

5    69               + 3                        + 11     + 13                 + 19     + 23                                                                                                              

6    69        2     + 3     + 5                                      + 17     + 19     + 23                                                                                                              

5    69               + 3               + 7                            + 17     + 19     + 23                                                                                                              

6    69        2     + 3               + 7     + 11                 + 17                            + 29                                                                                                   

5    69                         + 5     + 7     + 11                 + 17                            + 29                                                                                                   

6    69        2     + 3     + 5                           + 13     + 17                            + 29                                                                                                   

5    69               + 3               + 7                 + 13     + 17                            + 29                                                                                                   

6    69        2     + 3     + 5               + 11                             + 19                + 29                                                                                                   

5    69               + 3               + 7     + 11                             + 19                + 29                                                                                                   

5    69               + 3     + 5                           + 13                 + 19                + 29                                                                                                   

6    69        2     + 3     + 5     + 7                                                    + 23     + 29                                                                                                   

3    69                                                                    + 17                 + 23     + 29                                                                                                   

6    69        2               + 5     + 7     + 11     + 13                                                    + 31                                                                                       

6    69        2     + 3     + 5               + 11                 + 17                                        + 31                                                                                       

5    69               + 3               + 7     + 11                 + 17                                        + 31                                                                                       

5    69               + 3     + 5                           + 13     + 17                                        + 31                                                                                       

5    69               + 3     + 5               + 11                             + 19                            + 31                                                                                       

4    69        2                                                          + 17     + 19                            + 31                                                                                       

5    69               + 3     + 5     + 7                                                    + 23                 + 31                                                                                       

4    69        2                                              + 13                            + 23                 + 31                                                                                       

4    69        2                         + 7                                                               + 29     + 31                                                                                       

5    69               + 3     + 5               + 11     + 13                                                                + 37                                                                           

5    69               + 3     + 5     + 7                            + 17                                                    + 37                                                                           

4    69        2                                              + 13     + 17                                                    + 37                                                                           

4    69        2                                  + 11                             + 19                                        + 37                                                                           

3    69                                                        + 13                 + 19                                        + 37                                                                           

4    69        2                         + 7                                                    + 23                            + 37                                                                           

3    69               + 3                                                                                   + 29                 + 37                                                                           

6    69        2     + 3     + 5     + 7     + 11                                                                                        + 41                                                               

5    69               + 3     + 5     + 7                 + 13                                                                            + 41                                                               

3    69                                            + 11                 + 17                                                                + 41                                                               

4    69        2                         + 7                                        + 19                                                    + 41                                                               

4    69        2     + 3                                                                        + 23                                        + 41                                                               

3    69                         + 5                                                              + 23                                        + 41                                                               

5    69               + 3     + 5     + 7     + 11                                                                                                   + 43                                                   

4    69        2                                  + 11     + 13                                                                                       + 43                                                   

4    69        2                         + 7                            + 17                                                                            + 43                                                   

4    69        2               + 5                                                  + 19                                                                + 43                                                   

3    69                                   + 7                                        + 19                                                                + 43                                                   

3    69               + 3                                                                        + 23                                                    + 43                                                   

4    69        2                         + 7                 + 13                                                                                                   + 47                                       

4    69        2     + 3                                                + 17                                                                                        + 47                                       

3    69                         + 5                                      + 17                                                                                        + 47                                       

3    69               + 3                                                            + 19                                                                            + 47                                       

4    69        2     + 3                        + 11                                                                                                                           + 53                            

3    69                         + 5               + 11                                                                                                                           + 53                            

3    69               + 3                                    + 13                                                                                                               + 53                            

4    69        2     + 3     + 5                                                                                                                                                             + 59                

3    69               + 3               + 7                                                                                                                                                   + 59                

3    69               + 3     + 5                                                                                                                                                                        + 61    

2    69        2                                                                                                                                                                                                        + 67

 

 

 

 

 

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