数学研发论坛

 找回密码
 欢迎注册
查看: 119|回复: 2

[分享] 只以2^k为底的强伪素数

[复制链接]
发表于 2019-1-26 14:14:21 | 显示全部楼层 |阅读模式

马上注册,结交更多好友,享用更多功能,让你轻松玩转社区。

您需要 登录 才可以下载或查看,没有帐号?欢迎注册

x
本帖最后由 mathematica 于 2019-1-26 15:04 编辑
  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}]
复制代码

这个伪素数是26816952863=18287*1466449=(41*446+1)*(3288*446+1)
运行结果
  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}
复制代码

n^0.5以下,似乎只有1 2 4 8 16 32 64 128 256"证明它是素数",
别的数都证明他是伪素数!
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2019-1-26 14:30:18 | 显示全部楼层
26880359551=(4*4822+1)(289*4822+1)
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 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
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
您需要登录后才可以回帖 登录 | 欢迎注册

本版积分规则

小黑屋|手机版|数学研发网 ( 苏ICP备07505100号 )

GMT+8, 2019-2-24 11:11 , Processed in 0.050898 second(s), 16 queries .

Powered by Discuz! X3.4

© 2001-2017 Comsenz Inc.

快速回复 返回顶部 返回列表