yyh2004 在 2004-9-20 12:00 AM 发表:
自己建立了一个小小的公式,可以验证前面几项都是梅森素数。但这个数列发散的厉害,下一个数就是2147483647,它肯定是个素数,但是不是梅森素数无法判定。
2,147,483,647 是第 8 个(p=31)梅森素数
到目前为止,梅森素数已经发现 41 个。前 15 个梅森素数是:
1:(p=2) 3
2:(p=3) 7
3:(p=5) 31
4:(p=7) 127
5:(p=13) 8,191
6:(p=17) 131,071
7:(p=19) 524,287
8:(p=31) 2,147,483,647
9:(p=61) 2,305,843,009,213,693,951
10:(p=89) 618,970,019,642,690,137,449,562,111
11:(p=107) 162,259,276,829,213,363,391,578,010,288,127
12:(p=127) 170,141,183,460,469,231,731,687,303,715,884,105,727
13:(p=521) 6,864,797,660,130,609,714,981,900,799,081,393,217,269,435,300,143,305,409,394,463,459,185,543,183,397,656,052,122,559,640,661,454,554,977,296,311,391,480,858,037,121,987,999,716,643,812,574,028,291,115,057,151
14:(p=607) 531,137,992,816,767,098,689,588,206,552,468,627,329,593,117,727,031,923,199,444,138,200,403,559,860,852,242,739,162,502,265,229,285,668,889,329,486,246,501,015,346,579,337,652,707,239,409,519,978,766,587,351,943,831,270,835,393,219,031,728,127
15:(p=1,279) 10,407,932,194,664,399,081,925,240,327,364,085,538,615,262,247,266,704,805,319,112,350,403,608,059,673,360,298,012,239,441,732,324,184,842,421,613,954,281,007,791,383,566,248,323,464,908,139,906,605,677,320,762,924,129,509,389,220,345,773,183,349,661,583,550,472,959,420,547,689,811,211,693,677,147,548,478,866,962,501,384,438,260,291,732,348,885,311,160,828,538,416,585,028,255,604,666,224,831,890,918,801,847,068,222,203,140,521,026,698,435,488,732,958,028,878,050,869,736,186,900,714,720,710,555,703,168,729,087
第 16 到第 38 个梅森素数的指数是:
2,203、2,281、3,217、4,253、4,423、9,689、9,941、11,213、19,937、21,701、23,209、44,497、86,243、110,503、132,049、216,091、756,839、859,433、1,257,787、1,398,269、2,976,221、3,021,377、6,972,593
后面的指数是: 13,466,917、20,996,011、24,036,583
但不知道这之间还有没有其它梅森素数,这也就是说,不能肯定上面三个数是否就是第 39、40、41 个梅森素数的指数。
[ Last edited by ben on 2005-1-13 at 08:13 PM ] |