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[分享] 分享一个大整数的分解2^727-1

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发表于 2020-7-27 14:08:45 | 显示全部楼层 |阅读模式

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2^727-1=7060034896770543742372772105511569658378384779628943811708504827156734\
5759029962497646848024880749924272446637457099914453082421646959773690\
6638272121736526607699022870679030143158018123175881930939339869708632\
591433727
一共219位的整数

其中一个素数因子:

17606291711815434037934881872331611670777491166445300472749449436575622328171096762265466521858927
是98位的整数
另外一个素数因子
40099499726183758517891939428601665707063794593443940689888526556802581529262728143398959743444150539520890742947533452401
是122位的素数

经过mathematica判定都是素数!

梅森数
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 2020-7-27 14:10:23 | 显示全部楼层
Lattice Siever, Mersenne Number (2^727)-1
Dear Lattice Siever,

This is a project that breaks a 219-digit number, using the Special Number Field Sieve (SNFS). This specific Mersenne number, M727, is the smallest Mersenne number (with prime exponent) for which there is no known prime factor. We know that M727 is composite by the Lucas-Lehmer test, used to find Mersenne primes (in the Great Internet Mersenne Prime Search, www.mersenne.org, for example). But a very extensive effort to find small factors, estimated to be sufficient to find an average prime factor with 50-digits, was unsuccessful. The program collects data used to build a large matrix, precisely the same method used to break RSA-keys. Building and solving the matrix problem for M727 provides a test of the methods used to break RSA-keys, and is roughly as hard as breaking an RSA-key with 460-bits (140-digits, such as RSA-140).

This calculation was not distributed.
https://www.lehigh.edu/~bad0/mer727.html
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
发表于 2020-7-29 23:02:12 | 显示全部楼层
mathematica 发表于 2020-7-27 14:10
Lattice Siever, Mersenne Number (2^727)-1
Dear Lattice Siever,

https://www.mersenne.org/report_ ... e=1&exp_hi=2000

忘记最小的未分解的梅森数该怎么搜索了
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
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