NOMBRES - Curiosités, théorie et usages

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ORIENTATION GÉNÉRALE  - M'écrire - Édition du: 10/06/2010

 

Débutants

Nombres

- Ý -  TABLE DE NOMBRES

Glossaire

Nombres

§  Partition des nombres en somme de nombres premiers distincts

2 à 29

30 à 49

50 à 59

60 à 69

70 à 79

80 à 89

90 à 99

100

 

Voir Développements sur les nombres premiers / Somme de premiers consécutifs


 

NOMBRES

somme de Premiers distincts

 

Table de partition pour tous les nombres de 2 à 100

 

 

Légende

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

§  N: Le nombre partitionné; en rouge les nombres premiers

§  somme: les termes de la somme

 

 

TABLE pour N de 2 à 29

 

 

Qté   N      =      somme

 

1      2        =      2                                                                               

1      3        =            3                                                                         

0      4        =                                                                                       

2      5        =      2    + 3                                                                      

1      5        =                    5                                                                 

0      6        =                                                                                       

2      7        =      2            + 5                                                              

1      7        =                            7                                                         

2      8        =            3      + 5                                                              

2      9        =      2                    + 7                                                      

3      10      =      2    + 3   + 5                                                              

2      10      =            3              + 7                                                      

1      11      =                                    11                                               

3      12      =      2    + 3           + 7                                                      

2      12      =                    5      + 7                                                      

2      13      =      2                            + 11                                           

1      13      =                                               13                                    

3      14      =      2            + 5   + 7                                                      

2      14      =            3                      + 11                                           

3      15      =            3      + 5   + 7                                                      

2      15      =      2                                       + 13                                 

3      16      =      2    + 3                   + 11                                           

2      16      =                    5              + 11                                           

2      16      =            3                                 + 13                                 

4      17      =      2    + 3   + 5   + 7                                                      

1      17      =                                                         17                          

3      18      =      2            + 5           + 11                                           

2      18      =                            7      + 11                                           

3      18      =      2    + 3                              + 13                                 

2      18      =                    5                         + 13                                 

3      19      =            3      + 5           + 11                                           

2      19      =      2                                                 + 17                       

1      19      =                                                                   19               

3      20      =      2                    + 7   + 11                                           

3      20      =      2            + 5                     + 13                                 

2      20      =                            7                 + 13                                 

2      20      =            3                                           + 17                       

4      21      =      2    + 3   + 5           + 11                                           

3      21      =            3              + 7   + 11                                           

3      21      =            3      + 5                     + 13                                 

2      21      =      2                                                           + 19             

3      22      =      2                    + 7             + 13                                 

3      22      =      2    + 3                                        + 17                       

2      22      =                    5                                   + 17                       

2      22      =            3                                                      + 19            

4      23      =      2    + 3           + 7   + 11                                           

3      23      =                    5      + 7   + 11                                           

4      23      =      2    + 3   + 5                     + 13                                 

3      23      =            3              + 7             + 13                                 

1      23      =                                                                              23     

2      24      =                                    11      + 13                                 

3      24      =      2            + 5                                + 17                       

2      24      =                            7                           + 17                       

3      24      =      2    + 3                                                  + 19            

2      24      =                    5                                             + 19            

4      25      =      2            + 5   + 7   + 11                                           

4      25      =      2    + 3           + 7             + 13                                 

3      25      =                    5      + 7             + 13                                 

3      25      =            3      + 5                                + 17                       

2      25      =      2                                                                      + 23  

4      26      =            3      + 5   + 7   + 11                                           

3      26      =      2                            + 11   + 13                                 

3      26      =      2                    + 7                        + 17                       

3      26      =      2            + 5                                          + 19            

2      26      =                            7                                     + 19            

2      26      =            3                                                                + 23  

4      27      =      2            + 5   + 7             + 13                                 

3      27      =            3                      + 11   + 13                                 

4      27      =      2    + 3   + 5                                + 17                       

3      27      =            + 3           + 7                        + 17                       

3      27      =            3      + 5                                          + 19            

5      28      =      2    + 3   + 5   + 7   + 11                                           

4      28      =            3      + 5   + 7             + 13                                 

2      28      =                                    + 11             + 17                       

3      28      =      2                    + 7                                  + 19            

3      28      =      2    + 3                                                             + 23  

2      28      =                    5                                                        + 23  

4      29      =      2    + 3                   + 11   + 13                                 

3      29      =                    5              + 11   + 13                                 

4      29      =      2    + 3           + 7                        + 17                       

3      29      =                    + 5   + 7                        + 17                       

4      29      =      2    + 3   + 5                                          + 19            

3      29      =            3              + 7                                  + 19            

1      29      =                                                                                        29

 

 

 

Remarques

§  Pas de partition possible pour les seuls nombres 4 et 6

§  Partition triviale en un seul terme pour les nombres premiers

 

Hors ces partitions triviales:

§  Premier partition d'un nombre premier pour N = 13 = 11 + 2

§  Première partition double pour N  = 10 = 3 + 7 = 2 + 3 + 5 

§  Première partition triple    pour N  = 16 = 3 + 13 = 5 + 11 = 2 + 3 + 11

§  La quantité de partition en nombres premiers distincts croit rapidement

 


 

-Ý-

Voir

§  Orientation vers tous les nombres du dictionnaire

§  Liste des tables de nombres