论坛 › 数学欣赏 › 只以2^k为底的强伪素数

mathematica 发表于 2019-1-26 14:14:21

只以2^k为底的强伪素数

本帖最后由 mathematica 于 2019-1-26 15:04 编辑

Clear["Global`*"];(*Clear all variables*)
n=26816952863;
m=n-1;s=0;
While==0,m=m/2;s=s+1];
Do;
    k=0;
    If;Continue[]];
    t2=t1;
    While];
    If[t2==n-1,
      Print[{a,k,t2-n,prime}],
      Print[{a,k,composite}]
    ],
{a,2,100}]

这个伪素数是26816952863=18287*1466449=(41*446+1)*(3288*446+1)
运行结果
{2,0,1,prime}
{3,0,composite}
{4,0,1,prime}
{5,0,composite}
{6,0,composite}
{7,0,composite}
{8,0,1,prime}
{9,0,composite}
{10,0,composite}
{11,0,composite}
{12,0,composite}
{13,0,composite}
{14,0,composite}
{15,0,composite}
{16,0,1,prime}
{17,0,composite}
{18,0,composite}
{19,0,composite}
{20,0,composite}
{21,0,composite}
{22,0,composite}
{23,0,composite}
{24,0,composite}
{25,0,composite}
{26,0,composite}
{27,0,composite}
{28,0,composite}
{29,0,composite}
{30,0,composite}
{31,0,composite}
{32,0,1,prime}
{33,0,composite}
{34,0,composite}
{35,0,composite}
{36,0,composite}
{37,0,composite}
{38,0,composite}
{39,0,composite}
{40,0,composite}
{41,0,composite}
{42,0,composite}
{43,0,composite}
{44,0,composite}
{45,0,composite}
{46,0,composite}
{47,0,composite}
{48,0,composite}
{49,0,composite}
{50,0,composite}
{51,0,composite}
{52,0,composite}
{53,0,composite}
{54,0,composite}
{55,0,composite}
{56,0,composite}
{57,0,composite}
{58,0,composite}
{59,0,composite}
{60,0,composite}
{61,0,composite}
{62,0,composite}
{63,0,composite}
{64,0,1,prime}
{65,0,composite}
{66,0,composite}
{67,0,composite}
{68,0,composite}
{69,0,composite}
{70,0,composite}
{71,0,composite}
{72,0,composite}
{73,0,composite}
{74,0,composite}
{75,0,composite}
{76,0,composite}
{77,0,composite}
{78,0,composite}
{79,0,composite}
{80,0,composite}
{81,0,composite}
{82,0,composite}
{83,0,composite}
{84,0,composite}
{85,0,composite}
{86,0,composite}
{87,0,composite}
{88,0,composite}
{89,0,composite}
{90,0,composite}
{91,0,composite}
{92,0,composite}
{93,0,composite}
{94,0,composite}
{95,0,composite}
{96,0,composite}
{97,0,composite}
{98,0,composite}
{99,0,composite}
{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",
别的数都证明他是伪素数!

mathematica 发表于 2019-1-26 14:30:18

26880359551=(4*4822+1)(289*4822+1)

mathematica 发表于 2019-1-29 11:58:36

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

nyy 发表于 2022-10-11 11:37:26

262144
最小的反例！

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