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TABLES

 

Débutants

Général

Premiers

 

Glossaire

Général

 

INDEX

Tables

Premiers

Longs

Sommes

Partition

 

Sommaire de cette page

>>> Liste

>>> Statistiques

>>> Développement décimal

 

 

 

Nombres têtus

Nombres premiers longs

Nombres à permutation circulaire

 

 

Définition

Nombre premier dont l'inverse a un développement décimal périodique de période maximale.
La longueur de la période est égale au nombre considéré moins 1.
                                           L = P – 1

 

Voir Nombres premiers longs – Développements
            Nombres premiers longs – Critère de détection

Anglais: Full Reptend Prime

 

 

 

NOMBRES PREMIERS LONGS

Liste jusqu'à 3000

 

           7            17         19         23         29         47         59         61         97         109

              113       131       149       167       179       181       193       223       229       233

              257       263       269       313       337       367       379       383       389       419

              433       461       487       491       499       503       509       541       571       577

              593       619       647       659       701       709       727       743       811       821

              823       857       863       887       937       941       953       971       977       983

              1019     1021     1033     1051     1063     1069     1087     1091     1097     1103

              1109     1153     1171     1181     1193     1217     1223     1229     1259     1291

              1297     1301     1303     1327     1367     1381     1429     1433     1447     1487

              1531     1543     1549     1553     1567     1571     1579     1583     1607     1619

              1621     1663     1697     1709     1741     1777     1783     1789     1811     1823

              1847     1861     1873     1913     1949     1979     2017     2029     2063     2069

              2099     2113     2137     2141     2143     2153     2179     2207     2221     2251

              2269     2273     2297     2309     2339     2341     2371     2383     2389     2411

              2417     2423     2447     2459     2473     2539     2543     2549     2579     2593

              2617     2621     2633     2657     2663     2687     2699     2713     2731     2741

              2753     2767     2777     2789     2819     2833     2851     2861     2887     2897

              2903     2909     2927     2939     2971     3011     3019     3023     3137    

 

*      En rouge, les premiers logs jumeaux.

Voir Analyse dichotomique des quelques premiers longs

 

 

 

STATISTIQUE

 

                 N             Quantité                                           Cumul                                   

                                de premiers    de P. longs    %       de premiers    de P. longs    %

                 100         25                    9                     36%  25                    9                     36,0%

                 200         21                    8                     38%  46                    17                   37,0%

                 300         16                    6                     38%  62                    23                   37,1%

                 400         16                    6                     38%  78                    29                   37,2%

                 500         17                    6                     35%  95                    35                   36,8%

                 600         14                    6                     43%  109                  41                   37,6%

                 700         16                    3                     19%  125                  44                   35,2%

                 800         14                    4                     29%  139                  48                   34,5%

                 900         15                    6                     40%  154                  54                   35,1%

                 1000       14                    6                     43%  168                  60                   35,7%

 

                 2000       135                  56                   41%  303                  116                38,3%

                 3000       127                  59                   46%  430                  175                40,7%

                 4000       120                  43                   36%  550                  218                39,6%

                 5000       119                  40                   34%  669                  258                38,6%

                 6000       114                  44                   39%  783                  302                38,6%

                 7000       117                  47                   40%  900                  349                38,8%

                 8000       107                  41                   38%  1007                390                38,7%

                 9000       110                  41                   37%  1117                431                38,6%

                 10000    112                  36                   32%  1229                467                38,0%

 

Lecture: pour N de 0 à 100, il y a 25 nombres premiers et 9 premiers longs. Pour N de 100 à 200, il y a 21 nombres premiers et 9 premiers longs. Soit un cumul pour N de 0 à 200 de 46 premiers et 17 longs.

 

 

 

 

Table des périodes de 7 à 100

 

*      La période est donnée entre crochets.
En rouge les périodes pour les nombres premiers longs.

*      Exemple de lecture: 1 / 7 = 142857 142857 … Cette ligne est en rouge car la longueur de la période est 6 qui vaut 7 – 1.

 

  7,  [1, 4, 2, 8, 5, 7]

11, [0, 9])

13, [0, 7, 6, 9, 2, 3]

17, [0, 5, 8, 8, 2, 3, 5, 2, 9, 4, 1, 1, 7, 6, 4, 7]

19, [0, 5, 2, 6, 3, 1, 5, 7, 8, 9, 4, 7, 3, 6, 8, 4, 2, 1]

23, [0, 4, 3, 4, 7, 8, 2, 6, 0, 8, 6, 9, 5, 6, 5, 2, 1, 7, 3, 9, 1, 3]

29, [0, 3, 4, 4, 8, 2, 7, 5, 8, 6, 2, 0, 6, 8, 9, 6, 5, 5, 1, 7, 2, 4, 1, 3, 7, 9, 3, 1]

31, [0, 3, 2, 2, 5, 8, 0, 6, 4, 5, 1, 6, 1, 2, 9]

37, [0, 2, 7]

41, [0, 2, 4, 3, 9]

43, [0, 2, 3, 2, 5, 5, 8, 1, 3, 9, 5, 3, 4, 8, 8, 3, 7, 2, 0, 9, 3]

47, [0, 2, 1, 2, 7, 6, 5, 9, 5, 7, 4, 4, 6, 8, 0, 8, 5, 1, 0, 6, 3, 8, 2, 9, 7, 8, 7, 2, 3, 4, 0, 4, 2, 5, 5, 3, 1, 9, 1, 4, 8, 9, 3, 6, 1, 7]

53, [0, 1, 8, 8, 6, 7, 9, 2, 4, 5, 2, 8, 3]

59, [0, 1, 6, 9, 4, 9, 1, 5, 2, 5, 4, 2, 3, 7, 2, 8, 8, 1, 3, 5, 5, 9, 3, 2, 2, 0, 3, 3, 8, 9, 8, 3, 0, 5, 0, 8, 4, 7, 4, 5, 7, 6, 2, 7, 1, 1, 8, 6, 4, 4, 0, 6, 7, 7, 9, 6, 6, 1]

61, [0, 1, 6, 3, 9, 3, 4, 4, 2, 6, 2, 2, 9, 5, 0, 8, 1, 9, 6, 7, 2, 1, 3, 1, 1, 4, 7, 5, 4, 0, 9, 8, 3, 6, 0, 6, 5, 5, 7, 3, 7, 7, 0, 4, 9, 1, 8, 0, 3, 2, 7, 8, 6, 8, 8, 5, 2, 4, 5, 9]

67, [0, 1, 4, 9, 2, 5, 3, 7, 3, 1, 3, 4, 3, 2, 8, 3, 5, 8, 2, 0, 8, 9, 5, 5, 2, 2, 3, 8, 8, 0, 5, 9, 7]

71, [0, 1, 4, 0, 8, 4, 5, 0, 7, 0, 4, 2, 2, 5, 3, 5, 2, 1, 1, 2, 6, 7, 6, 0, 5, 6, 3, 3, 8, 0, 2, 8, 1, 6, 9]

73, [0, 1, 3, 6, 9, 8, 6, 3]

79, [0, 1, 2, 6, 5, 8, 2, 2, 7, 8, 4, 8, 1]

83, [0, 1, 2, 0, 4, 8, 1, 9, 2, 7, 7, 1, 0, 8, 4, 3, 3, 7, 3, 4, 9, 3, 9, 7, 5, 9, 0, 3, 6, 1, 4, 4, 5, 7, 8, 3, 1, 3, 2, 5, 3]

89, [0, 1, 1, 2, 3, 5, 9, 5, 5, 0, 5, 6, 1, 7, 9, 7, 7, 5, 2, 8, 0, 8, 9, 8, 8, 7, 6, 4, 0, 4, 4, 9, 4, 3, 8, 2, 0, 2, 2, 4, 7, 1, 9, 1]

97, [0, 1, 0, 3, 0, 9, 2, 7, 8, 3, 5, 0, 5, 1, 5, 4, 6, 3, 9, 1, 7, 5, 2, 5, 7, 7, 3, 1, 9, 5, 8, 7, 6, 2, 8, 8, 6, 5, 9, 7, 9, 3, 8, 1, 4, 4, 3, 2, 9, 8, 9, 6, 9, 0, 7, 2, 1, 6, 4, 9, 4, 8, 4, 5, 3, 6, 0, 8, 2, 4, 7, 4, 2, 2, 6, 8, 0, 4, 1, 2, 3, 7, 1, 1, 3, 4, 0, 2, 0, 6, 1, 8, 5, 5, 6, 7]

 

 

 

 

SUITE de 100 à 200

 

101, [0, 0, 9, 9]

103, [0, 0, 9, 7, 0, 8, 7, 3, 7, 8, 6, 4, 0, 7, 7, 6, 6, 9, 9, 0, 2, 9, 1, 2, 6, 2, 1, 3, 5, 9, 2, 2, 3, 3]

107, [0, 0, 9, 3, 4, 5, 7, 9, 4, 3, 9, 2, 5, 2, 3, 3, 6, 4, 4, 8, 5, 9, 8, 1, 3, 0, 8, 4, 1, 1, 2, 1, 4, 9, 5, 3, 2, 7, 1, 0, 2, 8, 0, 3, 7, 3, 8, 3, 1, 7, 7, 5, 7]

109, [0, 0, 9, 1, 7, 4, 3, 1, 1, 9, 2, 6, 6, 0, 5, 5, 0, 4, 5, 8, 7, 1, 5, 5, 9, 6, 3, 3, 0, 2, 7, 5, 2, 2, 9, 3, 5, 7, 7, 9, 8, 1, 6, 5, 1, 3, 7, 6, 1, 4, 6, 7, 8, 8, 9, 9, 0, 8, 2, 5, 6, 8, 8, 0, 7, 3, 3, 9, 4, 4, 9, 5, 4, 1, 2, 8, 4, 4, 0, 3, 6, 6, 9, 7, 2, 4, 7, 7, 0, 6, 4, 2, 2, 0, 1, 8, 3, 4, 8, 6, 2, 3, 8, 5, 3, 2, 1, 1]

113, [0, 0, 8, 8, 4, 9, 5, 5, 7, 5, 2, 2, 1, 2, 3, 8, 9, 3, 8, 0, 5, 3, 0, 9, 7, 3, 4, 5, 1, 3, 2, 7, 4, 3, 3, 6, 2, 8, 3, 1, 8, 5, 8, 4, 0, 7, 0, 7, 9, 6, 4, 6, 0, 1, 7, 6, 9, 9, 1, 1, 5, 0, 4, 4, 2, 4, 7, 7, 8, 7, 6, 1, 0, 6, 1, 9, 4, 6, 9, 0, 2, 6, 5, 4, 8, 6, 7, 2, 5, 6, 6, 3, 7, 1, 6, 8, 1, 4, 1, 5, 9, 2, 9, 2, 0, 3, 5, 3, 9, 8, 2, 3]

127, [0, 0, 7, 8, 7, 4, 0, 1, 5, 7, 4, 8, 0, 3, 1, 4, 9, 6, 0, 6, 2, 9, 9, 2, 1, 2, 5, 9, 8, 4, 2, 5, 1, 9, 6, 8, 5, 0, 3, 9, 3, 7]

131, [0, 0, 7, 6, 3, 3, 5, 8, 7, 7, 8, 6, 2, 5, 9, 5, 4, 1, 9, 8, 4, 7, 3, 2, 8, 2, 4, 4, 2, 7, 4, 8, 0, 9, 1, 6, 0, 3, 0, 5, 3, 4, 3, 5, 1, 1, 4, 5, 0, 3, 8, 1, 6, 7, 9, 3, 8, 9, 3, 1, 2, 9, 7, 7, 0, 9, 9, 2, 3, 6, 6, 4, 1, 2, 2, 1, 3, 7, 4, 0, 4, 5, 8, 0, 1, 5, 2, 6, 7, 1, 7, 5, 5, 7, 2, 5, 1, 9, 0, 8, 3, 9, 6, 9, 4, 6, 5, 6, 4, 8, 8, 5, 4, 9, 6, 1, 8, 3, 2, 0, 6, 1, 0, 6, 8, 7, 0, 2, 2, 9]

137, [0, 0, 7, 2, 9, 9, 2, 7]

139, [0, 0, 7, 1, 9, 4, 2, 4, 4, 6, 0, 4, 3, 1, 6, 5, 4, 6, 7, 6, 2, 5, 8, 9, 9, 2, 8, 0, 5, 7, 5, 5, 3, 9, 5, 6, 8, 3, 4, 5, 3, 2, 3, 7, 4, 1]

149, [0, 0, 6, 7, 1, 1, 4, 0, 9, 3, 9, 5, 9, 7, 3, 1, 5, 4, 3, 6, 2, 4, 1, 6, 1, 0, 7, 3, 8, 2, 5, 5, 0, 3, 3, 5, 5, 7, 0, 4, 6, 9, 7, 9, 8, 6, 5, 7, 7, 1, 8, 1, 2, 0, 8, 0, 5, 3, 6, 9, 1, 2, 7, 5, 1, 6, 7, 7, 8, 5, 2, 3, 4, 8, 9, 9, 3, 2, 8, 8, 5, 9, 0, 6, 0, 4, 0, 2, 6, 8, 4, 5, 6, 3, 7, 5, 8, 3, 8, 9, 2, 6, 1, 7, 4, 4, 9, 6, 6, 4, 4, 2, 9, 5, 3, 0, 2, 0, 1, 3, 4, 2, 2, 8, 1, 8, 7, 9, 1, 9, 4, 6, 3, 0, 8, 7, 2, 4, 8, 3, 2, 2, 1, 4, 7, 6, 5, 1]

151, [0, 0, 6, 6, 2, 2, 5, 1, 6, 5, 5, 6, 2, 9, 1, 3, 9, 0, 7, 2, 8, 4, 7, 6, 8, 2, 1, 1, 9, 2, 0, 5, 2, 9, 8, 0, 1, 3, 2, 4, 5, 0, 3, 3, 1, 1, 2, 5, 8, 2, 7, 8, 1, 4, 5, 6, 9, 5, 3, 6, 4, 2, 3, 8, 4, 1, 0, 5, 9, 6, 0, 2, 6, 4, 9]

157, [0, 0, 6, 3, 6, 9, 4, 2, 6, 7, 5, 1, 5, 9, 2, 3, 5, 6, 6, 8, 7, 8, 9, 8, 0, 8, 9, 1, 7, 1, 9, 7, 4, 5, 2, 2, 2, 9, 2, 9, 9, 3, 6, 3, 0, 5, 7, 3, 2, 4, 8, 4, 0, 7, 6, 4, 3, 3, 1, 2, 1, 0, 1, 9, 1, 0, 8, 2, 8, 0, 2, 5, 4, 7, 7, 7, 0, 7]

163, [0, 0, 6, 1, 3, 4, 9, 6, 9, 3, 2, 5, 1, 5, 3, 3, 7, 4, 2, 3, 3, 1, 2, 8, 8, 3, 4, 3, 5, 5, 8, 2, 8, 2, 2, 0, 8, 5, 8, 8, 9, 5, 7, 0, 5, 5, 2, 1, 4, 7, 2, 3, 9, 2, 6, 3, 8, 0, 3, 6, 8, 0, 9, 8, 1, 5, 9, 5, 0, 9, 2, 0, 2, 4, 5, 3, 9, 8, 7, 7, 3]

167, [0, 0, 5, 9, 8, 8, 0, 2, 3, 9, 5, 2, 0, 9, 5, 8, 0, 8, 3, 8, 3, 2, 3, 3, 5, 3, 2, 9, 3, 4, 1, 3, 1, 7, 3, 6, 5, 2, 6, 9, 4, 6, 1, 0, 7, 7, 8, 4, 4, 3, 1, 1, 3, 7, 7, 2, 4, 5, 5, 0, 8, 9, 8, 2, 0, 3, 5, 9, 2, 8, 1, 4, 3, 7, 1, 2, 5, 7, 4, 8, 5, 0, 2, 9, 9, 4, 0, 1, 1, 9, 7, 6, 0, 4, 7, 9, 0, 4, 1, 9, 1, 6, 1, 6, 7, 6, 6, 4, 6, 7, 0, 6, 5, 8, 6, 8, 2, 6, 3, 4, 7, 3, 0, 5, 3, 8, 9, 2, 2, 1, 5, 5, 6, 8, 8, 6, 2, 2, 7, 5, 4, 4, 9, 1, 0, 1, 7, 9, 6, 4, 0, 7, 1, 8, 5, 6, 2, 8, 7, 4, 2, 5, 1, 4, 9, 7]

173, [0, 0, 5, 7, 8, 0, 3, 4, 6, 8, 2, 0, 8, 0, 9, 2, 4, 8, 5, 5, 4, 9, 1, 3, 2, 9, 4, 7, 9, 7, 6, 8, 7, 8, 6, 1, 2, 7, 1, 6, 7, 6, 3]

179, [0, 0, 5, 5, 8, 6, 5, 9, 2, 1, 7, 8, 7, 7, 0, 9, 4, 9, 7, 2, 0, 6, 7, 0, 3, 9, 1, 0, 6, 1, 4, 5, 2, 5, 1, 3, 9, 6, 6, 4, 8, 0, 4, 4, 6, 9, 2, 7, 3, 7, 4, 3, 0, 1, 6, 7, 5, 9, 7, 7, 6, 5, 3, 6, 3, 1, 2, 8, 4, 9, 1, 6, 2, 0, 1, 1, 1, 7, 3, 1, 8, 4, 3, 5, 7, 5, 4, 1, 8, 9, 9, 4, 4, 1, 3, 4, 0, 7, 8, 2, 1, 2, 2, 9, 0, 5, 0, 2, 7, 9, 3, 2, 9, 6, 0, 8, 9, 3, 8, 5, 4, 7, 4, 8, 6, 0, 3, 3, 5, 1, 9, 5, 5, 3, 0, 7, 2, 6, 2, 5, 6, 9, 8, 3, 2, 4, 0, 2, 2, 3, 4, 6, 3, 6, 8, 7, 1, 5, 0, 8, 3, 7, 9, 8, 8, 8, 2, 6, 8, 1, 5, 6, 4, 2, 4, 5, 8, 1]

181, [0, 0, 5, 5, 2, 4, 8, 6, 1, 8, 7, 8, 4, 5, 3, 0, 3, 8, 6, 7, 4, 0, 3, 3, 1, 4, 9, 1, 7, 1, 2, 7, 0, 7, 1, 8, 2, 3, 2, 0, 4, 4, 1, 9, 8, 8, 9, 5, 0, 2, 7, 6, 2, 4, 3, 0, 9, 3, 9, 2, 2, 6, 5, 1, 9, 3, 3, 7, 0, 1, 6, 5, 7, 4, 5, 8, 5, 6, 3, 5, 3, 5, 9, 1, 1, 6, 0, 2, 2, 0, 9, 9, 4, 4, 7, 5, 1, 3, 8, 1, 2, 1, 5, 4, 6, 9, 6, 1, 3, 2, 5, 9, 6, 6, 8, 5, 0, 8, 2, 8, 7, 2, 9, 2, 8, 1, 7, 6, 7, 9, 5, 5, 8, 0, 1, 1, 0, 4, 9, 7, 2, 3, 7, 5, 6, 9, 0, 6, 0, 7, 7, 3, 4, 8, 0, 6, 6, 2, 9, 8, 3, 4, 2, 5, 4, 1, 4, 3, 6, 4, 6, 4, 0, 8, 8, 3, 9, 7, 7, 9]

191, [0, 0, 5, 2, 3, 5, 6, 0, 2, 0, 9, 4, 2, 4, 0, 8, 3, 7, 6, 9, 6, 3, 3, 5, 0, 7, 8, 5, 3, 4, 0, 3, 1, 4, 1, 3, 6, 1, 2, 5, 6, 5, 4, 4, 5, 0, 2, 6, 1, 7, 8, 0, 1, 0, 4, 7, 1, 2, 0, 4, 1, 8, 8, 4, 8, 1, 6, 7, 5, 3, 9, 2, 6, 7, 0, 1, 5, 7, 0, 6, 8, 0, 6, 2, 8, 2, 7, 2, 2, 5, 1, 3, 0, 8, 9])

193, [0, 0, 5, 1, 8, 1, 3, 4, 7, 1, 5, 0, 2, 5, 9, 0, 6, 7, 3, 5, 7, 5, 1, 2, 9, 5, 3, 3, 6, 7, 8, 7, 5, 6, 4, 7, 6, 6, 8, 3, 9, 3, 7, 8, 2, 3, 8, 3, 4, 1, 9, 6, 8, 9, 1, 1, 9, 1, 7, 0, 9, 8, 4, 4, 5, 5, 9, 5, 8, 5, 4, 9, 2, 2, 2, 7, 9, 7, 9, 2, 7, 4, 6, 1, 1, 3, 9, 8, 9, 6, 3, 7, 3, 0, 5, 6, 9, 9, 4, 8, 1, 8, 6, 5, 2, 8, 4, 9, 7, 4, 0, 9, 3, 2, 6, 4, 2, 4, 8, 7, 0, 4, 6, 6, 3, 2, 1, 2, 4, 3, 5, 2, 3, 3, 1, 6, 0, 6, 2, 1, 7, 6, 1, 6, 5, 8, 0, 3, 1, 0, 8, 8, 0, 8, 2, 9, 0, 1, 5, 5, 4, 4, 0, 4, 1, 4, 5, 0, 7, 7, 7, 2, 0, 2, 0, 7, 2, 5, 3, 8, 8, 6, 0, 1, 0, 3, 6, 2, 6, 9, 4, 3]

197, [0, 0, 5, 0, 7, 6, 1, 4, 2, 1, 3, 1, 9, 7, 9, 6, 9, 5, 4, 3, 1, 4, 7, 2, 0, 8, 1, 2, 1, 8, 2, 7, 4, 1, 1, 1, 6, 7, 5, 1, 2, 6, 9, 0, 3, 5, 5, 3, 2, 9, 9, 4, 9, 2, 3, 8, 5, 7, 8, 6, 8, 0, 2, 0, 3, 0, 4, 5, 6, 8, 5, 2, 7, 9, 1, 8, 7, 8, 1, 7, 2, 5, 8, 8, 8, 3, 2, 4, 8, 7, 3, 0, 9, 6, 4, 4, 6, 7]

199, [0, 0, 5, 0, 2, 5, 1, 2, 5, 6, 2, 8, 1, 4, 0, 7, 0, 3, 5, 1, 7, 5, 8, 7, 9, 3, 9, 6, 9, 8, 4, 9, 2, 4, 6, 2, 3, 1, 1, 5, 5, 7, 7, 8, 8, 9, 4, 4, 7, 2, 3, 6, 1, 8, 0, 9, 0, 4, 5, 2, 2, 6, 1, 3, 0, 6, 5, 3, 2, 6, 6, 3, 3, 1, 6, 5, 8, 2, 9, 1, 4, 5, 7, 2, 8, 6, 4, 3, 2, 1, 6, 0, 8, 0, 4, 0, 2, 0, 1]

 

 

 

Voir

*    Nombres premiers longs

*    Nombre magique 142857

*    Nombre périodiques

Aussi

*    Nombres premiers

*    Nombres premiers – Tous les types

Sites

*    OEIS A001913 - Full reptend primes: primes with primitive root 10.

*    Full Reptend Prime – Wolfram MathWorld

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