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TABLES de NOMBRES

 

Glossaire

Nombre

 

 

 

PARTITIONS

par des nombres premiers

 

Table donnant la partition des nombres avec des nombres premiers.

Voir Table des sommes de premiers consécutifs

 

 

 

 

Partitions avec des nombres premiers

 

 

Table indiquant la quantité de partitions avec de nombres premiers tous différents

P2 indique la quantité de partitions à deux termes; P3 à trois termes; etc.

 

 

Le nombre 5 est le plus petit nombre ayant une partition avec deux premiers différents: 5 = 2 + 3.

 

Le nombre 10 est le plus petit ayant une partition à deux termes et une partition à trois termes: 10 = 3 + 7 = 2 + 3 + 5

 

Le nombre 21 est le plus petit ayant, au moins, une partition à deux termes,   une partition à trois termes et une partition à quatre termes:
21 = 2 + 19

         = 3 + 5 + 13 = 3 + 7 + 11

         = 2 + 3 + 5 + 11

 

Le nombre 25 est le plus petit ayant, au moins, une partition à 2, 3, 4 et 5 termes:
25 = 2 + 23
     = 3 + 5 + 17 = 5 + 7 + 13
     = 2 + 3 + 7 + 13 = 2 + 5 + 7 + 11
     = 2 + 3 + 5 + 7 + 8


 

 

 

Les premières partitions

 

5 = 2 + 3

7 = 2 + 5

8 = 3 + 5

9 = 2 + 7

10 = 3 + 7 = 2 + 3 + 5

12 = 5 + 7 = 2 + 3 + 7

14 = 3 + 11 = 2 + 5 + 7

15 = 2 + 13 = 3 + 5 + 7

 

 

16 = 3 + 13 = 5 + 11 = 2 + 3 + 11

18 = 5 + 13 = 7 + 11 = 2 + 3 + 13 = 2 + 5 + 11

19 = 2 + 17 = 3 + 5 + 11

20 = 3 + 17 = 7 + 13 = 2 + 5 + 13 = 2 + 7 + 11

21 = 2 + 19 = 3 + 5 + 13 = 3 + 7 + 11= 2 + 3 + 5 + 11

22 = 3 + 19 = 5 + 17 = 2 + 3 + 17 = 2 + 7 + 13

24 = 5 + 19 = 7 + 17 = 11 + 13 = 2 + 3 + 19 = 2 + 5 + 17

 

 

 

Nombres avec partitions de 2, 3, 4 et 5 termes

Exemple avec 25, le plus petit nombre à présenter une partition avec 2, 3, 4 et 5 termes.

On donne le nombre suivi de la quantité de partitions à 2, 3, 4 et 5 termes; puis les partitions.

25 =

2 + 23                  => 1 fois

3 + 5 + 17

5 + 7 + 13            => 2 fois

2 + 3 + 7 + 13

2 + 5 + 7 + 11      => 2 fois

2 + 3 + 5 + 7 + 8  => 1 fois

25, 1, 2, 2, 1,
[[2, 23]], [[3, 5, 17], [5, 7, 13]], [[2, 3, 7, 13], [2, 5, 7, 11]], [[2, 3, 5, 7, 8]]

 

26, 2, 3, 1, 1,
[[3, 23], [7, 19]], [[2, 5, 19], [2, 7, 17], [2, 11, 13]], [[3, 5, 7, 11]], [[2, 3, 5, 7, 9]]

 

28, 2, 2, 1, 1,
[[5, 23], [11, 17]], [[2, 3, 23], [2, 7, 19]], [[3, 5, 7, 13]], [[2, 3, 5, 7, 11]]

 

31, 1, 4, 3, 1,
[[2, 29]], [[3, 5, 23], [3, 11, 17], [5, 7, 19], [7, 11, 13]], [[2, 3, 7, 19], [2, 5, 7, 17], [2, 5, 11, 13]], [[2, 3, 5, 7, 14]]

 

32, 2, 3, 2, 1,
[[3, 29], [13, 19]], [[2, 7, 23], [2, 11, 19], [2, 13, 17]], [[3, 5, 7, 17], [3, 5, 11, 13]], [[2, 3, 5, 7, 15]]

 

33, 1, 4, 4, 2,
[[2, 31]], [[3, 7, 23], [3, 11, 19], [3, 13, 17], [5, 11, 17]], [[2, 3, 5, 23], [2, 3, 11, 17], [2, 5, 7, 19], [2, 7, 11, 13]], [[2, 3, 5, 7, 16], [2, 3, 5, 11, 12]]

 

34, 3, 2, 2, 2,
[[3, 31], [5, 29], [11, 23]], [[2, 3, 29], [2, 13, 19]], [[3, 5, 7, 19], [3, 7, 11, 13]], [[2, 3, 5, 7, 17], [2, 3, 5, 11, 13]]

 

36, 4, 3, 2, 3,
[[5, 31], [7, 29], [13, 23], [17, 19]], [[2, 3, 31], [2, 5, 29], [2, 11, 23]], [[3, 5, 11, 17], [5, 7, 11, 13]], [[2, 3, 5, 7, 19], [2, 3, 5, 11, 15], [2, 3, 7, 11, 13]]

 

38, 1, 4, 4, 6,
[[7, 31]], [[2, 5, 31], [2, 7, 29], [2, 13, 23], [2, 17, 19]], [[3, 5, 7, 23], [3, 5, 11, 19], [3, 5, 13, 17], [3, 7, 11, 17]], [[2, 3, 5, 7, 21], [2, 3, 5, 11, 17], [2, 3, 5, 13, 15], [2, 3, 7, 11, 15], [2, 5, 7, 11, 13], [3, 5, 7, 11, 12]]

 

39, 1, 6, 5, 7,
[[2, 37]], [[3, 5, 31], [3, 7, 29], [3, 13, 23], [3, 17, 19], [5, 11, 23], [7, 13, 19]], [[2, 3, 5, 29], [2, 3, 11, 23], [2, 5, 13, 19], [2, 7, 11, 19], [2, 7, 13, 17]], [[2, 3, 5, 7, 22], [2, 3, 5, 11, 18], [2, 3, 5, 13, 16], [2, 3, 7, 11, 16], [2, 3, 7, 13, 14], [2, 5, 7, 11, 14], [3, 5, 7, 11, 13]]

 

40, 3, 1, 4, 7,
[[3, 37], [11, 29], [17, 23]], [[2, 7, 31]], [[3, 5, 13, 19], [3, 7, 11, 19], [3, 7, 13, 17], [5, 7, 11, 17]], [[2, 3, 5, 7, 23], [2, 3, 5, 11, 19], [2, 3, 5, 13, 17], [2, 3, 7, 11, 17], [2, 3, 7, 13, 15], [2, 5, 7, 11, 15], [3, 5, 7, 11, 14]]

 

42, 4, 3, 4, 9,
[[5, 37], [11, 31], [13, 29], [19, 23]], [[2, 3, 37], [2, 11, 29], [2, 17, 23]], [[3, 5, 11, 23], [3, 7, 13, 19], [5, 7, 11, 19], [5, 7, 13, 17]], [[2, 3, 5, 7, 25], [2, 3, 5, 11, 21], [2, 3, 5, 13, 19], [2, 3, 7, 11, 19], [2, 3, 7, 13, 17], [2, 5, 7, 11, 17], [2, 5, 7, 13, 15], [3, 5, 7, 11, 16], [3, 5, 7, 13, 14]]

 

43, 1, 6, 6, 10,
[[2, 41]], [[3, 11, 29], [3, 17, 23], [5, 7, 31], [7, 13, 23], [7, 17, 19], [11, 13, 19]], [[2, 3, 7, 31], [2, 5, 7, 29], [2, 5, 13, 23], [2, 5, 17, 19], [2, 7, 11, 23], [2, 11, 13, 17]], [[2, 3, 5, 7, 26], [2, 3, 5, 11, 22], [2, 3, 5, 13, 20], [2, 3, 7, 11, 20], [2, 3, 7, 13, 18], [2, 3, 11, 13, 14], [2, 5, 7, 11, 18], [2, 5, 7, 13, 16], [3, 5, 7, 11, 17], [3, 5, 7, 13, 15]]

 

44, 3, 4, 6, 10,
[[3, 41], [7, 37], [13, 31]], [[2, 5, 37], [2, 11, 31], [2, 13, 29], [2, 19, 23]], [[3, 5, 7, 29], [3, 5, 13, 23], [3, 5, 17, 19], [3, 7, 11, 23], [3, 11, 13, 17], [5, 7, 13, 19]], [[2, 3, 5, 7, 27], [2, 3, 5, 11, 23], [2, 3, 5, 13, 21], [2, 3, 7, 11, 21], [2, 3, 7, 13, 19], [2, 3, 11, 13, 15], [2, 5, 7, 11, 19], [2, 5, 7, 13, 17], [3, 5, 7, 11, 18], [3, 5, 7, 13, 16]]

 

45, 1, 6, 6, 12,
[[2, 43]], [[3, 5, 37], [3, 11, 31], [3, 13, 29], [3, 19, 23], [5, 11, 29], [5, 17, 23]], [[2, 3, 11, 29], [2, 3, 17, 23], [2, 5, 7, 31], [2, 7, 13, 23], [2, 7, 17, 19], [2, 11, 13, 19]], [[2, 3, 5, 7, 28], [2, 3, 5, 11, 24], [2, 3, 5, 13, 22], [2, 3, 5, 17, 18], [2, 3, 7, 11, 22], [2, 3, 7, 13, 20], [2, 3, 11, 13, 16], [2, 5, 7, 11, 20], [2, 5, 7, 13, 18], [2, 5, 11, 13, 14], [3, 5, 7, 11, 19], [3, 5, 7, 13, 17]]

 

46, 3, 3, 6, 13,
[[3, 43], [5, 41], [17, 29]], [[2, 3, 41], [2, 7, 37], [2, 13, 31]], [[3, 5, 7, 31], [3, 7, 13, 23], [3, 7, 17, 19], [3, 11, 13, 19], [5, 7, 11, 23], [5, 11, 13, 17]], [[2, 3, 5, 7, 29], [2, 3, 5, 11, 25], [2, 3, 5, 13, 23], [2, 3, 5, 17, 19], [2, 3, 7, 11, 23], [2, 3, 7, 13, 21], [2, 3, 11, 13, 17], [2, 5, 7, 11, 21], [2, 5, 7, 13, 19], [2, 5, 11, 13, 15], [3, 5, 7, 11, 20], [3, 5, 7, 13, 18], [3, 5, 11, 13, 14]]

 

48, 5, 3, 6, 16,
[[5, 43], [7, 41], [11, 37], [17, 31], [19, 29]], [[2, 3, 43], [2, 5, 41], [2, 17, 29]], [[3, 5, 11, 29], [3, 5, 17, 23], [5, 7, 13, 23], [5, 7, 17, 19], [5, 11, 13, 19], [7, 11, 13, 17]], [[2, 3, 5, 7, 31], [2, 3, 5, 11, 27], [2, 3, 5, 13, 25], [2, 3, 5, 17, 21], [2, 3, 7, 11, 25], [2, 3, 7, 13, 23], [2, 3, 7, 17, 19], [2, 3, 11, 13, 19], [2, 5, 7, 11, 23], [2, 5, 7, 13, 21], [2, 5, 11, 13, 17], [2, 7, 11, 13, 15], [3, 5, 7, 11, 22], [3, 5, 7, 13, 20], [3, 5, 11, 13, 16], [3, 7, 11, 13, 14]]

 

49, 1, 8, 9, 18,
[[2, 47]], [[3, 5, 41], [3, 17, 29], [5, 7, 37], [5, 13, 31], [7, 11, 31], [7, 13, 29], [7, 19, 23], [13, 17, 19]], [[2, 3, 7, 37], [2, 3, 13, 31], [2, 5, 11, 31], [2, 5, 13, 29], [2, 5, 19, 23], [2, 7, 11, 29], [2, 7, 17, 23], [2, 11, 13, 23], [2, 11, 17, 19]], [[2, 3, 5, 7, 32], [2, 3, 5, 11, 28], [2, 3, 5, 13, 26], [2, 3, 5, 17, 22], [2, 3, 5, 19, 20], [2, 3, 7, 11, 26], [2, 3, 7, 13, 24], [2, 3, 7, 17, 20], [2, 3, 11, 13, 20], [2, 5, 7, 11, 24], [2, 5, 7, 13, 22], [2, 5, 7, 17, 18], [2, 5, 11, 13, 18], [2, 7, 11, 13, 16], [3, 5, 7, 11, 23], [3, 5, 7, 13, 21], [3, 5, 11, 13, 17], [3, 7, 11, 13, 15]]

 

50, 4, 5, 8, 20,
[[3, 47], [7, 43], [13, 37], [19, 31]], [[2, 5, 43], [2, 7, 41], [2, 11, 37], [2, 17, 31], [2, 19, 29]], [[3, 5, 11, 31], [3, 5, 13, 29], [3, 5, 19, 23], [3, 7, 11, 29], [3, 7, 17, 23], [3, 11, 13, 23], [3, 11, 17, 19], [7, 11, 13, 19]], [[2, 3, 5, 7, 33], [2, 3, 5, 11, 29], [2, 3, 5, 13, 27], [2, 3, 5, 17, 23], [2, 3, 5, 19, 21], [2, 3, 7, 11, 27], [2, 3, 7, 13, 25], [2, 3, 7, 17, 21], [2, 3, 11, 13, 21], [2, 5, 7, 11, 25], [2, 5, 7, 13, 23], [2, 5, 7, 17, 19], [2, 5, 11, 13, 19], [2, 7, 11, 13, 17], [3, 5, 7, 11, 24], [3, 5, 7, 13, 22], [3, 5, 7, 17, 18], [3, 5, 11, 13, 18], [3, 7, 11, 13, 16], [5, 7, 11, 13, 14]]

 

 

 

 

 

 

 

Voir

*    Développements sur les nombres premiers

*    Liste des tables de nombres Index

*    Nombres premiersIndex

*    Orientation vers tous les nombres du dictionnaire

*    Somme de cubes

*    Somme de premiers distincts

Sites

*    OEIS A007504 - Sum of first n primes

*    OEIS A045345 - Numbers n such that n divides sum of first n primes

Cette page

http://villemin.gerard.free.fr/TABLES/PartPrem.htm