mersenneforum.org Factorising Mersenne composites
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 2015-10-14, 22:32 #1 CuriousKit   "J. Gareth Moreton" Feb 2015 Nomadic 1328 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 2973,421 - 1 today (October 14th, 2015), even though it's been triple-checked with the Lucas-Lehmer 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?
2015-10-15, 03:00   #2
Prime95
P90 years forever!

Aug 2002
Yeehaw, FL

2·3·1,193 Posts

Quote:
 Originally Posted by CuriousKit 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 2973,421 - 1 today (October 14th, 2015), even though it's been triple-checked with the Lucas-Lehmer 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?
For the fun of it. Some people like to move Mersenne numbers from the double-checked to has-a-known-factor state. Others like the even tougher challenge of moving Mersenne numbers from the has-a-known-factor state to all-factors-known state.

 2015-10-15, 03:31 #3 retina Undefined     "The unspeakable one" Jun 2006 My evil lair 2·2,939 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.
 2015-10-15, 04:04 #4 CuriousKit   "J. Gareth Moreton" Feb 2015 Nomadic 2·32·5 Posts For fun... heh, I can buy that! Although I'd hope we can stop the wars at least.
 2015-10-15, 12:32 #5 science_man_88     "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.
 2015-10-15, 12:51 #6 alpertron     Aug 2002 Buenos Aires, Argentina 31·43 Posts 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.
2015-10-15, 13:00   #7
R.D. Silverman

Nov 2003

723210 Posts

Quote:
 Originally Posted by CuriousKit 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 2973,421 - 1 today (October 14th, 2015), even though it's been triple-checked with the Lucas-Lehmer 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?
Welcome to "Wagstaff's stamp collection"

 2015-10-15, 19:25 #8 xilman Bamboozled!     "𒉺𒌌𒇷𒆷𒀭" May 2003 Down not across 100111110011112 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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