寻找大素数简单了，1亿位大素数找到难度不大

太阳

太阳

太阳

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太阳

太阳

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wlc1

yangchuanju

100000000±1000中间共有106个素数
99999043 is prime
99999073 is prime
99999077 is prime
99999079 is prime
99999089 is prime
99999103 is prime
99999113 is prime
99999131 is prime
99999157 is prime
99999167 is prime
99999187 is prime
99999217 is prime
99999247 is prime
99999257 is prime
99999259 is prime
99999307 is prime
99999323 is prime
99999329 is prime
99999343 is prime
99999353 is prime
99999373 is prime
99999401 is prime
99999437 is prime
99999439 is prime
99999481 is prime
99999509 is prime
99999517 is prime
99999539 is prime
99999541 is prime
99999547 is prime
99999551 is prime
99999563 is prime
99999587 is prime
99999589 is prime
99999611 is prime
99999617 is prime
99999623 is prime
99999643 is prime
99999677 is prime
99999703 is prime
99999721 is prime
99999773 is prime
99999787 is prime
99999821 is prime
99999827 is prime
99999839 is prime
99999847 is prime
99999931 is prime
99999941 is prime
99999959 is prime
99999971 is prime
99999989 is prime
100000007 is prime
100000037 is prime
100000039 is prime
100000049 is prime
100000073 is prime
100000081 is prime
100000123 is prime
100000127 is prime
100000193 is prime
100000213 is prime
100000217 is prime
100000223 is prime
100000231 is prime
100000237 is prime
100000259 is prime
100000267 is prime
100000279 is prime
100000357 is prime
100000379 is prime
100000393 is prime
100000399 is prime
100000421 is prime
100000429 is prime
100000463 is prime
100000469 is prime
100000471 is prime
100000493 is prime
100000541 is prime
100000543 is prime
100000561 is prime
100000567 is prime
100000577 is prime
100000609 is prime
100000627 is prime
100000643 is prime
100000651 is prime
100000661 is prime
100000669 is prime
100000673 is prime
100000687 is prime
100000717 is prime
100000721 is prime
100000793 is prime
100000799 is prime
100000801 is prime
100000837 is prime
100000841 is prime
100000853 is prime
100000891 is prime
100000921 is prime
100000937 is prime
100000939 is prime
100000963 is prime
100000969 is prime

yangchuanju

指数是亿附近素数时，梅森数为3千万为数值；一亿位梅森数的指数约为3.3亿。
太阳先生先别找一亿位的梅森素数啦，只有找到指数稍大于一亿的梅森素数就能得到梅森素数大奖，第51号梅森素数的指数8200多万。
指数在一亿以内或许还有1-2个梅森素数，或许已经没有啦，请在稍大于一亿的素数中寻找。

yangchuanju

太阳 发表于 2022-1-16 11:13

761838257201=7*19*23*249048139，2^761838257201-1不是梅森数，位数等于229336167262位。
它肯定是合数，至少含有4个素因子，最小的多大，最大的多大无法估计。

28719782237是素数，2^28719782237-1是梅森数，位数等于8645515923位。
如果它不是梅森素数，必将分解成几个素因子的乘积，各个素因子多大，无法估计；素因子个数也无法估计。

当p、q、r都是素数时，
2^pqr-1=(2^pq)^r-1=(2^pq-1)*(…)=[(2^p)^q-1]*(…)*(…)=[2^p-1]*(…)*(…)*(…)
同理可得2^pqr-1=[2^q-1]*(…)*(…)*(…)
2^pqr-1=[2^r-1]*(…)*(…)*(…)
故有2^pqr-1=[2^r-1]* [2^q-1]* [2^p-1]*(…)
例2^105-1=2^(3*5*7)-1=(2^3-1)*(2^5-1)*(2^7-1)=7*31*127*…
实际2^105-1=40564819207303340847894502572031<32>
=7^2*31*71*127*151*337*29191*106681*122921*152041