Problème GR comme base d’une énigme en une ligne de code C

Ma première question pour "[Concours]La ligne de code la moins interprétable" sur OpenClassrooms.
Quelle valeur vaudra x à la fin du code suivant ?
for(srand(time(NULL)),_^=_,x|=rand();__=Break=_++<=x;x=Break*010*(1|!(x&1)<<1))while((__+=(1<<1))<=x)Break+=(__)*!/*__*/(x%__);
La valeur de x vaudra 96, quelque soit la valeur (aux 227 exceptions près listées ci-dessous) de départ (qui est aléatoire) tenant sur 32 bits.
Le processus itère le calcul de la fonction GR (OEIS A000118, le nombre de représentations du nombre en somme de 4 carrés) calculé à partir de la somme des diviseurs impairs. Ce processus selon ma conjecture mathématique (problème GR) aboutit toujours à 96.
Usage des exécutables (sources complètes gr32_check.tar.gz) :
Exceptions : (attention, ce ne sont pas des exceptions à la conjecture mathématique, ces exceptions surgissent dans l’arithmétique modulo 232)
1. x = 341 310 837 = 3 × 7 × 31 × 524 287 : GR(x) = 4 294 967 296 mais GR(x) modulo 232 = 0
2. x = 349 566 357 = 3 × 7 × 127 × 131 071 : GR(x) = 4 294 967 296 mais GR(x) modulo 232 = 0
3. x = 466 091 143 = 7 × 127 × 524 287 : GR(x) = 4 294 967 296 mais GR(x) modulo 232 = 0
4. x = 516 026 527 = 31 × 127 × 131 071 : GR(x) = 4 294 967 296 mais GR(x) modulo 232 = 0
5. x = 677 207 307 = 3 × 7 × 31 × 127 × 8 191 : GR(x) = 8 589 934 592 mais GR(x) modulo 232 = 0
6. x = 682 621 674 = 2 × 3 × 7 × 31 × 524 287 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
7. x = 699 132 714 = 2 × 3 × 7 × 127 × 131 071 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
8. x = 932 182 286 = 2 × 7 × 127 × 524 287 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
9. x = 938 599 431 = 3 × 7 × 11 × 31 × 131 071 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
10. x = 998 766 735 = 3 × 5 × 127 × 524 287 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
11. x = 1 018 477 131 = 3 × 7 × 31 × 191 × 8 191 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
12. x = 1 026 733 659 = 3 × 7 × 47 × 127 × 8 191 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
13. x = 1 032 053 054 = 2 × 31 × 127 × 131 071 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
14. x = 1 054 204 053 = 3 × 7 × 383 × 131 071 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
15. x = 1 056 663 573 = 3 × 7 × 6 143 × 8 191 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
16. x = 1 064 182 911 = 3 × 11 × 31 × 127 × 8 191 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
17. x = 1 073 602 561 = 8 191 × 131 071 : GR(x) = 8 589 934 592 mais GR(x) modulo 232 = 0
18. x = 1 121 449 893 = 3 × 23 × 31 × 524 287 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
19. x = 1 128 678 845 = 5 × 7 × 31 × 127 × 8 191 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
20. x = 1 148 575 173 = 3 × 23 × 127 × 131 071 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
21. x = 1 195 255 293 = 3 × 127 × 383 × 8 191 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
22. x = 1 251 473 069 = 7 × 11 × 31 × 524 287 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
23. x = 1 281 743 309 = 7 × 11 × 127 × 131 071 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
24. x = 1 336 793 129 = 7 × 31 × 47 × 131 071 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
25. x = 1 354 414 614 = 2 × 3 × 7 × 31 × 127 × 8 191 : GR(x) = 25 769 803 776 mais GR(x) modulo 232 = 0
26. x = 1 365 243 348 = 2 × 3 × 7 × 31 × 524 287 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
27. x = 1 390 823 609 = 7 × 127 × 191 × 8 191 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
28. x = 1 398 265 428 = 2 × 3 × 7 × 127 × 131 071 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
29. x = 1 398 273 429 = 3 × 7 × 127 × 524 287 : GR(x) = 17 179 869 184 mais GR(x) modulo 232 = 0
30. x = 1 405 613 447 = 7 × 383 × 524 287 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
31. x = 1 515 654 449 = 31 × 47 × 127 × 8 191 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
32. x = 1 531 442 327 = 23 × 127 × 524 287 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
33. x = 1 548 079 581 = 3 × 31 × 127 × 131 071 : GR(x) = 17 179 869 184 mais GR(x) modulo 232 = 0
34. x = 1 556 205 983 = 31 × 383 × 131 071 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
35. x = 1 559 836 703 = 31 × 6 143 × 8 191 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
36. x = 1 621 217 199 = 3 × 7 × 19 × 31 × 131 071 : GR(x) = 21 474 836 480 mais GR(x) modulo 232 = 0
37. x = 1 693 142 283 = 3 × 7 × 31 × 127 × 20 479 : GR(x) = 21 474 836 480 mais GR(x) modulo 232 = 0
38. x = 1 706 554 185 = 3 × 5 × 7 × 31 × 524 287 : GR(x) = 25 769 803 776 mais GR(x) modulo 232 = 0
39. x = 1 725 786 363 = 3 × 7 × 79 × 127 × 8 191 : GR(x) = 21 474 836 480 mais GR(x) modulo 232 = 0
40. x = 1 747 831 785 = 3 × 5 × 7 × 127 × 131 071 : GR(x) = 25 769 803 776 mais GR(x) modulo 232 = 0
41. x = 1 797 780 123 = 3 × 127 × 524 287 : GR(x) = 21 474 836 480 mais GR(x) modulo 232 = 0
42. x = 1 838 134 119 = 3 × 19 × 31 × 127 × 8 191 : GR(x) = 21 474 836 480 mais GR(x) modulo 232 = 0
43. x = 1 864 364 572 = 2 × 7 × 127 × 524 287 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
44. x = 1 877 198 862 = 2 × 3 × 7 × 11 × 31 × 131 071 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
45. x = 1 962 526 083 = 3 × 7 × 23 × 31 × 131 071 : GR(x) = 25 769 803 776 mais GR(x) modulo 232 = 0
46. x = 1 997 533 470 = 2 × 3 × 5 × 127 × 524 287 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
47. x = 2 011 689 219 = 3 × 1 279 × 524 287 : GR(x) = 21 474 836 480 mais GR(x) modulo 232 = 0
48. x = 2 012 857 347 = 3 × 5 119 × 131 071 : GR(x) = 21 474 836 480 mais GR(x) modulo 232 = 0
49. x = 2 012 995 587 = 3 × 8 191 × 81 919 : GR(x) = 21 474 836 480 mais GR(x) modulo 232 = 0
50. x = 2 036 954 262 = 2 × 3 × 7 × 31 × 191 × 8 191 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
51. x = 2 042 286 603 = 3 × 7 × 31 × 383 × 8 191 : GR(x) = 25 769 803 776 mais GR(x) modulo 232 = 0
52. x = 2 053 467 318 = 2 × 3 × 7 × 47 × 127 × 8 191 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
53. x = 2 064 106 108 = 2 × 31 × 127 × 131 071 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
54. x = 2 064 117 919 = 31 × 127 × 524 287 : GR(x) = 17 179 869 184 mais GR(x) modulo 232 = 0
55. x = 2 097 411 477 = 3 × 7 × 127 × 786 431 : GR(x) = 25 769 803 776 mais GR(x) modulo 232 = 0
56. x = 2 102 915 157 = 3 × 7 × 191 × 524 287 : GR(x) = 25 769 803 776 mais GR(x) modulo 232 = 0
57. x = 2 108 408 106 = 2 × 3 × 7 × 383 × 131 071 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
58. x = 2 113 327 146 = 2 × 3 × 7 × 6 143 × 8 191 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
59. x = 2 128 365 822 = 2 × 3 × 11 × 31 × 127 × 8 191 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
60. x = 2 147 205 122 = 2 × 8 191 × 131 071 : GR(x) = 25 769 803 776 mais GR(x) modulo 232 = 0
61. x = 2 147 483 647 = : GR(x) = 17 179 869 184 mais GR(x) modulo 232 = 0
62. x = 2 161 635 301 = 7 × 19 × 31 × 524 287 : GR(x) = 21 474 836 480 mais GR(x) modulo 232 = 0
63. x = 2 197 286 817 = 3 × 11 × 127 × 524 287 : GR(x) = 25 769 803 776 mais GR(x) modulo 232 = 0
64. x = 2 213 920 261 = 7 × 19 × 127 × 131 071 : GR(x) = 21 474 836 480 mais GR(x) modulo 232 = 0
65. x = 2 225 109 723 = 3 × 23 × 31 × 127 × 8 191 : GR(x) = 25 769 803 776 mais GR(x) modulo 232 = 0
66. x = 2 242 899 786 = 2 × 3 × 23 × 31 × 524 287 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
67. x = 2 246 950 153 = 7 × 31 × 79 × 131 071 : GR(x) = 21 474 836 480 mais GR(x) modulo 232 = 0
68. x = 2 257 357 690 = 2 × 5 × 7 × 31 × 127 × 8 191 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
69. x = 2 257 605 721 = 7 × 31 × 127 × 81 919 : GR(x) = 21 474 836 480 mais GR(x) modulo 232 = 0
70. x = 2 273 354 713 = 7 × 31 × 1 279 × 8 191 : GR(x) = 21 474 836 480 mais GR(x) modulo 232 = 0
71. x = 2 291 658 477 = 3 × 31 × 47 × 524 287 : GR(x) = 25 769 803 776 mais GR(x) modulo 232 = 0
72. x = 2 297 150 346 = 2 × 3 × 23 × 127 × 131 071 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
73. x = 2 328 214 173 = 3 × 31 × 191 × 131 071 : GR(x) = 25 769 803 776 mais GR(x) modulo 232 = 0
74. x = 2 330 455 715 = 5 × 7 × 127 × 524 287 : GR(x) = 25 769 803 776 mais GR(x) modulo 232 = 0
75. x = 2 347 088 397 = 3 × 47 × 127 × 131 071 : GR(x) = 25 769 803 776 mais GR(x) modulo 232 = 0
76. x = 2 390 510 586 = 2 × 3 × 127 × 383 × 8 191 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
77. x = 2 415 507 459 = 3 × 6 143 × 131 071 : GR(x) = 25 769 803 776 mais GR(x) modulo 232 = 0
78. x = 2 446 980 501 = 3 × 7 × 127 × 917 503 : GR(x) = 30 064 771 072 mais GR(x) modulo 232 = 0
79. x = 2 455 236 021 = 3 × 7 × 223 × 524 287 : GR(x) = 30 064 771 072 mais GR(x) modulo 232 = 0
80. x = 2 483 093 459 = 7 × 11 × 31 × 127 × 8 191 : GR(x) = 25 769 803 776 mais GR(x) modulo 232 = 0
81. x = 2 502 946 138 = 2 × 7 × 11 × 31 × 524 287 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
82. x = 2 512 220 655 = 3 × 5 × 7 × 23 × 127 × 8 191 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
83. x = 2 539 424 055 = 3 × 5 × 7 × 31 × 127 × 6 143 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
84. x = 2 547 589 393 = 31 × 79 × 127 × 8 191 : GR(x) = 21 474 836 480 mais GR(x) modulo 232 = 0
85. x = 2 559 832 905 = 3 × 5 × 7 × 31 × 786 431 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
86. x = 2 563 486 618 = 2 × 7 × 11 × 127 × 131 071 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
87. x = 2 580 132 635 = 5 × 31 × 127 × 131 071 : GR(x) = 25 769 803 776 mais GR(x) modulo 232 = 0
88. x = 2 587 356 345 = 3 × 5 × 7 × 47 × 524 287 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
89. x = 2 596 793 511 = 3 × 13 × 127 × 524 287 : GR(x) = 30 064 771 072 mais GR(x) modulo 232 = 0
90. x = 2 616 716 417 = 7 × 23 × 31 × 524 287 : GR(x) = 25 769 803 776 mais GR(x) modulo 232 = 0
91. x = 2 628 628 905 = 3 × 5 × 7 × 191 × 131 071 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
92. x = 2 673 586 258 = 2 × 7 × 31 × 47 × 131 071 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
93. x = 2 680 008 737 = 7 × 23 × 127 × 131 071 : GR(x) = 25 769 803 776 mais GR(x) modulo 232 = 0
94. x = 2 681 728 005 = 3 × 5 × 11 × 31 × 524 287 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
95. x = 2 683 825 153 = 5 119 × 524 287 : GR(x) = 21 474 836 480 mais GR(x) modulo 232 = 0
96. x = 2 684 203 009 = 20 479 × 131 071 : GR(x) = 21 474 836 480 mais GR(x) modulo 232 = 0
97. x = 2 708 829 228 = 2 × 3 × 7 × 31 × 127 × 8 191 : GR(x) = 25 769 803 776 mais GR(x) modulo 232 = 0
98. x = 2 718 281 469 = 3 × 31 × 223 × 131 071 : GR(x) = 30 064 771 072 mais GR(x) modulo 232 = 0
99. x = 2 729 396 829 = 3 × 31 × 3 583 × 8 191 : GR(x) = 30 064 771 072 mais GR(x) modulo 232 = 0
100. x = 2 730 486 696 = 2 × 3 × 7 × 31 × 524 287 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
101. x = 2 746 592 805 = 3 × 5 × 11 × 127 × 131 071 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
102. x = 2 756 820 297 = 3 × 7 × 11 × 31 × 47 × 8 191 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
103. x = 2 781 647 218 = 2 × 7 × 127 × 191 × 8 191 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
104. x = 2 785 536 831 = 3 × 7 × 11 × 23 × 524 287 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
105. x = 2 788 929 017 = 7 × 127 × 383 × 8 191 : GR(x) = 25 769 803 776 mais GR(x) modulo 232 = 0
106. x = 2 796 530 856 = 2 × 3 × 7 × 127 × 131 071 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
107. x = 2 796 546 858 = 2 × 3 × 7 × 127 × 524 287 : GR(x) = 51 539 607 552 mais GR(x) modulo 232 = 0
108. x = 2 811 226 894 = 2 × 7 × 383 × 524 287 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
109. x = 2 864 556 705 = 3 × 5 × 31 × 47 × 131 071 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
110. x = 2 934 564 997 = 7 × 13 × 31 × 127 × 8 191 : GR(x) = 30 064 771 072 mais GR(x) modulo 232 = 0
111. x = 2 975 442 771 = 3 × 7 × 23 × 47 × 131 071 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
112. x = 2 980 336 305 = 3 × 5 × 127 × 191 × 8 191 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
113. x = 3 012 028 815 = 3 × 5 × 383 × 524 287 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
114. x = 3 031 308 898 = 2 × 31 × 47 × 127 × 8 191 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
115. x = 3 062 884 654 = 2 × 23 × 127 × 524 287 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
116. x = 3 071 797 533 = 3 × 7 × 31 × 524 287 : GR(x) = 42 949 672 960 mais GR(x) modulo 232 = 0
117. x = 3 083 969 559 = 3 × 11 × 23 × 31 × 131 071 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
118. x = 3 096 159 162 = 2 × 3 × 31 × 127 × 131 071 : GR(x) = 51 539 607 552 mais GR(x) modulo 232 = 0
119. x = 3 096 178 847 = 31 × 127 × 786 431 : GR(x) = 25 769 803 776 mais GR(x) modulo 232 = 0
120. x = 3 096 370 011 = 3 × 7 × 47 × 383 × 8 191 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
121. x = 3 104 303 327 = 31 × 191 × 524 287 : GR(x) = 25 769 803 776 mais GR(x) modulo 232 = 0
122. x = 3 112 411 966 = 2 × 31 × 383 × 131 071 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
123. x = 3 119 673 406 = 2 × 31 × 6 143 × 8 191 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
124. x = 3 129 225 771 = 3 × 7 × 127 × 191 × 6 143 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
125. x = 3 129 469 103 = 47 × 127 × 524 287 : GR(x) = 25 769 803 776 mais GR(x) modulo 232 = 0
126. x = 3 146 097 213 = 3 × 7 × 127 × 131 071 : GR(x) = 42 949 672 960 mais GR(x) modulo 232 = 0
127. x = 3 154 374 741 = 3 × 7 × 191 × 786 431 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
128. x = 3 168 117 141 = 3 × 7 × 1 151 × 131 071 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
129. x = 3 179 389 247 = 127 × 191 × 131 071 : GR(x) = 25 769 803 776 mais GR(x) modulo 232 = 0
130. x = 3 185 573 671 = 7 × 31 × 14 680 063 : GR(x) = 30 064 771 072 mais GR(x) modulo 232 = 0
131. x = 3 209 307 519 = 3 × 11 × 31 × 383 × 8 191 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
132. x = 3 220 695 041 = 6 143 × 524 287 : GR(x) = 25 769 803 776 mais GR(x) modulo 232 = 0
133. x = 3 220 807 683 = 3 × 8 191 × 131 071 : GR(x) = 34 359 738 368 mais GR(x) modulo 232 = 0
134. x = 3 242 434 398 = 2 × 3 × 7 × 19 × 31 × 131 071 : GR(x) = 64 424 509 440 mais GR(x) modulo 232 = 0
135. x = 3 270 876 805 = 5 × 7 × 23 × 31 × 131 071 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
136. x = 3 287 391 751 = 7 × 3 583 × 131 071 : GR(x) = 30 064 771 072 mais GR(x) modulo 232 = 0
137. x = 3 295 932 321 = 3 × 11 × 127 × 786 431 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
138. x = 3 304 580 961 = 3 × 11 × 191 × 524 287 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
139. x = 3 346 424 859 = 3 × 23 × 31 × 191 × 8 191 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
140. x = 3 373 553 451 = 3 × 23 × 47 × 127 × 8 191 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
141. x = 3 386 036 535 = 3 × 5 × 7 × 31 × 127 × 8 191 : GR(x) = 51 539 607 552 mais GR(x) modulo 232 = 0
142. x = 3 386 284 566 = 2 × 3 × 7 × 31 × 127 × 20 479 : GR(x) = 64 424 509 440 mais GR(x) modulo 232 = 0
143. x = 3 395 806 899 = 3 × 17 × 127 × 524 287 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
144. x = 3 403 811 005 = 5 × 7 × 31 × 383 × 8 191 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
145. x = 3 410 083 731 = 3 × 31 × 47 × 127 × 6 143 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
146. x = 3 413 108 370 = 2 × 3 × 5 × 7 × 31 × 524 287 : GR(x) = 77 309 411 328 mais GR(x) modulo 232 = 0
147. x = 3 437 489 901 = 3 × 31 × 47 × 786 431 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
148. x = 3 451 572 726 = 2 × 3 × 7 × 79 × 127 × 8 191 : GR(x) = 64 424 509 440 mais GR(x) modulo 232 = 0
149. x = 3 461 867 061 = 3 × 31 × 71 × 524 287 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
150. x = 3 463 813 317 = 3 × 23 × 383 × 131 071 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
151. x = 3 471 894 597 = 3 × 23 × 6 143 × 8 191 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
152. x = 3 483 193 821 = 3 × 31 × 127 × 294 911 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
153. x = 3 495 663 570 = 2 × 3 × 5 × 7 × 127 × 131 071 : GR(x) = 77 309 411 328 mais GR(x) modulo 232 = 0
154. x = 3 495 685 795 = 5 × 7 × 127 × 786 431 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
155. x = 3 495 687 573 = 3 × 7 × 127 × 1 310 719 : GR(x) = 42 949 672 960 mais GR(x) modulo 232 = 0
156. x = 3 504 858 595 = 5 × 7 × 191 × 524 287 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
157. x = 3 520 435 989 = 3 × 7 × 1 279 × 131 071 : GR(x) = 42 949 672 960 mais GR(x) modulo 232 = 0
158. x = 3 522 613 269 = 3 × 7 × 8 191 × 20 479 : GR(x) = 42 949 672 960 mais GR(x) modulo 232 = 0
159. x = 3 529 873 101 = 3 × 47 × 191 × 131 071 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
160. x = 3 545 601 621 = 3 × 71 × 127 × 131 071 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
161. x = 3 592 007 421 = 3 × 127 × 1 151 × 8 191 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
162. x = 3 595 560 246 = 2 × 3 × 127 × 524 287 : GR(x) = 64 424 509 440 mais GR(x) modulo 232 = 0
163. x = 3 612 185 689 = 7 × 31 × 127 × 131 071 : GR(x) = 34 359 738 368 mais GR(x) modulo 232 = 0
164. x = 3 612 209 311 = 31 × 127 × 917 503 : GR(x) = 30 064 771 072 mais GR(x) modulo 232 = 0
165. x = 3 624 396 031 = 31 × 223 × 524 287 : GR(x) = 30 064 771 072 mais GR(x) modulo 232 = 0
166. x = 3 662 144 695 = 5 × 11 × 127 × 524 287 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
167. x = 3 669 070 503 = 3 × 7 × 31 × 43 × 131 071 : GR(x) = 47 244 640 256 mais GR(x) modulo 232 = 0
168. x = 3 676 268 238 = 2 × 3 × 19 × 31 × 127 × 8 191 : GR(x) = 64 424 509 440 mais GR(x) modulo 232 = 0
169. x = 3 708 516 205 = 5 × 23 × 31 × 127 × 8 191 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
170. x = 3 712 061 791 = 127 × 223 × 131 071 : GR(x) = 30 064 771 072 mais GR(x) modulo 232 = 0
171. x = 3 727 240 831 = 127 × 3 583 × 8 191 : GR(x) = 30 064 771 072 mais GR(x) modulo 232 = 0
172. x = 3 728 729 144 = 2 × 7 × 127 × 524 287 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
173. x = 3 734 416 147 = 7 × 11 × 31 × 191 × 8 191 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
174. x = 3 754 397 724 = 2 × 3 × 7 × 11 × 31 × 131 071 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
175. x = 3 754 419 207 = 3 × 7 × 11 × 31 × 524 287 : GR(x) = 51 539 607 552 mais GR(x) modulo 232 = 0
176. x = 3 758 096 383 = : GR(x) = 30 064 771 072 mais GR(x) modulo 232 = 0
177. x = 3 764 690 083 = 7 × 11 × 47 × 127 × 8 191 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
178. x = 3 795 313 593 = 3 × 19 × 127 × 524 287 : GR(x) = 42 949 672 960 mais GR(x) modulo 232 = 0
179. x = 3 819 430 795 = 5 × 31 × 47 × 524 287 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
180. x = 3 837 508 073 = 7 × 17 × 31 × 127 × 8 191 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
181. x = 3 839 724 945 = 3 × 5 × 7 × 31 × 131 071 : GR(x) = 64 424 509 440 mais GR(x) modulo 232 = 0
182. x = 3 845 229 927 = 3 × 7 × 11 × 127 × 131 071 : GR(x) = 51 539 607 552 mais GR(x) modulo 232 = 0
183. x = 3 851 936 589 = 3 × 31 × 79 × 524 287 : GR(x) = 42 949 672 960 mais GR(x) modulo 232 = 0
184. x = 3 865 414 861 = 7 × 11 × 383 × 131 071 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
185. x = 3 874 433 101 = 7 × 11 × 6 143 × 8 191 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
186. x = 3 880 356 955 = 5 × 31 × 191 × 131 071 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
187. x = 3 893 783 551 = 7 × 23 × 31 × 127 × 6 143 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
188. x = 3 899 464 797 = 3 × 31 × 5 119 × 8 191 : GR(x) = 42 949 672 960 mais GR(x) modulo 232 = 0
189. x = 3 911 813 995 = 5 × 47 × 127 × 131 071 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
190. x = 3 925 052 166 = 2 × 3 × 7 × 23 × 31 × 131 071 : GR(x) = 77 309 411 328 mais GR(x) modulo 232 = 0
191. x = 3 925 077 121 = 7 × 23 × 31 × 786 431 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
192. x = 3 945 106 029 = 3 × 79 × 127 × 131 071 : GR(x) = 42 949 672 960 mais GR(x) modulo 232 = 0
193. x = 3 967 279 729 = 7 × 23 × 47 × 524 287 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
194. x = 3 991 466 109 = 3 × 127 × 1 279 × 8 191 : GR(x) = 42 949 672 960 mais GR(x) modulo 232 = 0
195. x = 3 995 066 940 = 2 × 3 × 5 × 127 × 524 287 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
196. x = 4 010 379 387 = 3 × 7 × 31 × 47 × 131 071 : GR(x) = 51 539 607 552 mais GR(x) modulo 232 = 0
197. x = 4 023 378 438 = 2 × 3 × 1 279 × 524 287 : GR(x) = 64 424 509 440 mais GR(x) modulo 232 = 0
198. x = 4 025 714 694 = 2 × 3 × 5 119 × 131 071 : GR(x) = 64 424 509 440 mais GR(x) modulo 232 = 0
199. x = 4 025 845 765 = 5 × 6 143 × 131 071 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
200. x = 4 025 991 174 = 2 × 3 × 8 191 × 81 919 : GR(x) = 64 424 509 440 mais GR(x) modulo 232 = 0
201. x = 4 030 564 321 = 7 × 23 × 191 × 131 071 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
202. x = 4 073 908 524 = 2 × 3 × 7 × 31 × 191 × 8 191 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
203. x = 4 084 573 206 = 2 × 3 × 7 × 31 × 383 × 8 191 : GR(x) = 77 309 411 328 mais GR(x) modulo 232 = 0
204. x = 4 095 737 639 = 7 × 31 × 18 874 367 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
205. x = 4 106 934 636 = 2 × 3 × 7 × 47 × 127 × 8 191 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
206. x = 4 111 982 941 = 11 × 23 × 31 × 524 287 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
207. x = 4 128 212 216 = 2 × 31 × 127 × 131 071 : GR(x) = 12 884 901 888 mais GR(x) modulo 232 = 0
208. x = 4 128 235 838 = 2 × 31 × 127 × 524 287 : GR(x) = 51 539 607 552 mais GR(x) modulo 232 = 0
209. x = 4 159 987 743 = 3 × 31 × 43 × 127 × 8 191 : GR(x) = 47 244 640 256 mais GR(x) modulo 232 = 0
210. x = 4 172 470 827 = 3 × 7 × 127 × 191 × 8 191 : GR(x) = 51 539 607 552 mais GR(x) modulo 232 = 0
211. x = 4 194 373 561 = 7 × 191 × 383 × 8 191 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
212. x = 4 194 820 287 = 3 × 7 × 127 × 524 287 : GR(x) = 55 834 574 848 mais GR(x) modulo 232 = 0
213. x = 4 194 822 954 = 2 × 3 × 7 × 127 × 786 431 : GR(x) = 77 309 411 328 mais GR(x) modulo 232 = 0
214. x = 4 205 830 314 = 2 × 3 × 7 × 191 × 524 287 : GR(x) = 77 309 411 328 mais GR(x) modulo 232 = 0
215. x = 4 211 442 301 = 11 × 23 × 127 × 131 071 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
216. x = 4 216 816 212 = 2 × 3 × 7 × 383 × 131 071 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
217. x = 4 216 840 341 = 3 × 7 × 383 × 524 287 : GR(x) = 51 539 607 552 mais GR(x) modulo 232 = 0
218. x = 4 224 180 359 = 7 × 1 151 × 524 287 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
219. x = 4 226 654 292 = 2 × 3 × 7 × 6 143 × 8 191 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
220. x = 4 227 284 999 = 7 × 8 191 × 73 727 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
221. x = 4 256 731 644 = 2 × 3 × 11 × 31 × 127 × 8 191 : GR(x) = 38 654 705 664 mais GR(x) modulo 232 = 0
222. x = 4 266 390 345 = 3 × 5 × 7 × 31 × 1 310 719 : GR(x) = 64 424 509 440 mais GR(x) modulo 232 = 0
223. x = 4 288 979 611 = 7 × 19 × 31 × 127 × 8 191 : GR(x) = 42 949 672 960 mais GR(x) modulo 232 = 0
224. x = 4 294 410 244 = 2 × 8 191 × 131 071 : GR(x) = 25 769 803 776 mais GR(x) modulo 232 = 0
225. x = 4 294 434 817 = 8 191 × 524 287 : GR(x) = 34 359 738 368 mais GR(x) modulo 232 = 0
226. x = 4 294 967 294 = 2 × 2 147 483 647 : GR(x) = 51 539 607 552 mais GR(x) modulo 232 = 0
227. x = 4 294 967 295 = 3 × 5 × 17 × 257 × 65 537 : GR(x) = 58 436 826 624
  GR(x) modulo 232 = 2 602 251 776
  et son itération aboutirait à 96,
  mais le code de l’énigme tombe dans une boucle infinie
dimanche 16 mars 2014

© Olivier Pirson
http://www.opimedia.be/
olivier_pirson_opi@yahoo.fr