20151014, 22:32  #1 
"J. Gareth Moreton"
Feb 2015
Nomadic
2×3^{2}×5 Posts 
Factorising Mersenne composites
I have to ask... beyond a simple curiosity, is there any reason behind attempting to factorise a Mersenne number that has already been proven to be composite? I noticed that the user "westicles" successfully found a factor in 2^{973,421}  1 today (October 14^{th}, 2015), even though it's been triplechecked with the LucasLehmer primality test. Of course, the factor found in this case is 88 bits long, so is definitely an impressive find, but is there a good reason for looking for the factors in such composites?

20151015, 03:00  #2  
P90 years forever!
Aug 2002
Yeehaw, FL
2·3·1,193 Posts 
Quote:


20151015, 03:31  #3 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
5,879 Posts 
To add to Prime95's post. The entire project is also for the fun of it. So it doesn't matter if someone wants to factor, or run an LL, or neither; the world will still turn as usual and wars will still be fought as usual.

20151015, 04:04  #4 
"J. Gareth Moreton"
Feb 2015
Nomadic
1011010_{2} Posts 
For fun... heh, I can buy that! Although I'd hope we can stop the wars at least.

20151015, 12:32  #5 
"Forget I exist"
Jul 2009
Dumbassville
8,369 Posts 
the main use I could find for it is in trying to eliminate factors for later exponents as they can't share factors unless the exponent itself is composite). Of course this probably would never work.

20151015, 12:51  #6 
Aug 2002
Buenos Aires, Argentina
10100111000_{2} Posts 
Well, in July I found the prime factor 782521855299947974696932851410613860657 of M1864739. I've been running the P1 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:
(2^17907431)/(146840927*158358984977*3835546416767873*20752172271489035681) = PRP539014 (2^7501511)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263) = PRP225744 (2^6759771)/(1686378749257*7171117283326998925471) = PRP203456 (2^5765511)/4612409/64758208321/242584327930759 = PRP173528 (2^4884411)/(61543567*30051203516986199) = PRP147012 (2^4403991)/(16210820281161978209*31518475633*880799) = PRP132538 (2^2700591)/540119/6481417/7124976157756725967 = PRP81265 
20151015, 13:00  #7  
Nov 2003
16100_{8} Posts 
Quote:


20151015, 19:25  #8 
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
27D5_{16} Posts 
SSW isn't the only person with a stamp collection. I have one and so do you though, to be fair, I'm the one looking after your stamp albums for the moment.
Nothing wrong with stamp collection as long as it's clear at least to the collector that that is the activity being undertaken. For the avoidance of doubt, I'm pretty sure that you agree. 
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