Well, in July I found the prime factor 782521855299947974696932851410613860657 of

M1864739. I've been running the P-1 algorithm on Mersenne numbers with

**known** factors for numbers less than M2000000. The idea is to try to find a "probably completely factored" Mersenne number, where that term means a product of primes and a probable prime.

I had several successes so far:

Code:

(2^1790743-1)/(146840927*158358984977*3835546416767873*20752172271489035681) = PRP539014
(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263) = PRP225744
(2^675977-1)/(1686378749257*7171117283326998925471) = PRP203456
(2^576551-1)/4612409/64758208321/242584327930759 = PRP173528
(2^488441-1)/(61543567*30051203516986199) = PRP147012
(2^440399-1)/(16210820281161978209*31518475633*880799) = PRP132538
(2^270059-1)/540119/6481417/7124976157756725967 = PRP81265

The number at the right of "PRP" is the number of digits of that probable prime.