帐号 自动登录 找回密码 密码 欢迎注册
 搜索

# [分享] 只以2^k为底的强伪素数

### 马上注册，结交更多好友，享用更多功能，让你轻松玩转社区。

x

1. Clear["Global`*"];(*Clear all variables*)
2. n=26816952863;
3. m=n-1;s=0;
4. While[Mod[m,2]==0,m=m/2;s=s+1];
5. Do[t1=PowerMod[a,m,n];
6.     k=0;
7.     If[t1==1,Print[{a,k,t1,prime}];Continue[]];
8.     t2=t1;
9.     While[k<s-1&&t2!=n-1,k=k+1;t2=Mod[t2*t2,n]];
10.     If[t2==n-1,
11.         Print[{a,k,t2-n,prime}],
12.         Print[{a,k,composite}]
13.     ],
14. {a,2,100}]

1. {2,0,1,prime}
2. {3,0,composite}
3. {4,0,1,prime}
4. {5,0,composite}
5. {6,0,composite}
6. {7,0,composite}
7. {8,0,1,prime}
8. {9,0,composite}
9. {10,0,composite}
10. {11,0,composite}
11. {12,0,composite}
12. {13,0,composite}
13. {14,0,composite}
14. {15,0,composite}
15. {16,0,1,prime}
16. {17,0,composite}
17. {18,0,composite}
18. {19,0,composite}
19. {20,0,composite}
20. {21,0,composite}
21. {22,0,composite}
22. {23,0,composite}
23. {24,0,composite}
24. {25,0,composite}
25. {26,0,composite}
26. {27,0,composite}
27. {28,0,composite}
28. {29,0,composite}
29. {30,0,composite}
30. {31,0,composite}
31. {32,0,1,prime}
32. {33,0,composite}
33. {34,0,composite}
34. {35,0,composite}
35. {36,0,composite}
36. {37,0,composite}
37. {38,0,composite}
38. {39,0,composite}
39. {40,0,composite}
40. {41,0,composite}
41. {42,0,composite}
42. {43,0,composite}
43. {44,0,composite}
44. {45,0,composite}
45. {46,0,composite}
46. {47,0,composite}
47. {48,0,composite}
48. {49,0,composite}
49. {50,0,composite}
50. {51,0,composite}
51. {52,0,composite}
52. {53,0,composite}
53. {54,0,composite}
54. {55,0,composite}
55. {56,0,composite}
56. {57,0,composite}
57. {58,0,composite}
58. {59,0,composite}
59. {60,0,composite}
60. {61,0,composite}
61. {62,0,composite}
62. {63,0,composite}
63. {64,0,1,prime}
64. {65,0,composite}
65. {66,0,composite}
66. {67,0,composite}
67. {68,0,composite}
68. {69,0,composite}
69. {70,0,composite}
70. {71,0,composite}
71. {72,0,composite}
72. {73,0,composite}
73. {74,0,composite}
74. {75,0,composite}
75. {76,0,composite}
76. {77,0,composite}
77. {78,0,composite}
78. {79,0,composite}
79. {80,0,composite}
80. {81,0,composite}
81. {82,0,composite}
82. {83,0,composite}
83. {84,0,composite}
84. {85,0,composite}
85. {86,0,composite}
86. {87,0,composite}
87. {88,0,composite}
88. {89,0,composite}
89. {90,0,composite}
90. {91,0,composite}
91. {92,0,composite}
92. {93,0,composite}
93. {94,0,composite}
94. {95,0,composite}
95. {96,0,composite}
96. {97,0,composite}
97. {98,0,composite}
98. {99,0,composite}
99. {100,0,composite}

n^0.5以下,似乎只有1 2 4 8 16 32 64 128 256"证明它是素数",

楼主| 发表于 2019-1-26 14:30:18 | 显示全部楼层
 26880359551=(4*4822+1)(289*4822+1)

楼主| 发表于 2019-1-29 11:58:36 | 显示全部楼层
 mathematica 发表于 2019-1-26 14:30 26880359551=(4*4822+1)(289*4822+1) 我发现第5个费马数似乎也是这样,2^(2^5)+1也是只以2 4 8 16 32为伪素数,不知道为什么

 您需要登录后才可以回帖 登录 | 欢迎注册 本版积分规则 回帖后跳转到最后一页

GMT+8, 2021-9-27 12:27 , Processed in 0.136226 second(s), 16 queries .