20100207, 16:42  #1 
Jul 2006
Calgary
5^{2}×17 Posts 
big factor
a p1 run of mine just found a 165 bit factor of m(51675341)

20100207, 17:02  #2 
Dec 2007
Cleves, Germany
211_{16} Posts 
c165 = p75.p91 = [2 x (3 x 23 x 563 x 2591 x 1875959) x 51675341 + 1] x [2 x (4783 x 10937 x 54751 x 4189763) x 51675341 + 1]
Still a nice find. 
20100207, 17:14  #3 
Jul 2006
Calgary
110101001_{2} Posts 

20100207, 17:48  #4 
Dec 2007
Cleves, Germany
211_{16} Posts 
I do this manually, and I prefer to isolate the k value.

20100207, 18:42  #5 
Jul 2006
Calgary
5^{2}×17 Posts 
I find that rather amazing. I didn't even realize the 165 bit factor was composite when you posted the factorization. I have only the faintest glimmering of the techniques you may have used. I see the 2kp+1 patterns
now but that's about my limit. 
20100207, 20:51  #6  
"Nathan"
Jul 2008
Maryland, USA
5·223 Posts 
Quote:
If you are unsure how the whole GIMPS factorization process works, you should read the info on the GIMPS Web site, and ask questions. I have been GIMPSing for 8 years, but only within the last 18 months have fully understood trial factoring bit levels, P1 bounds, etc. But as the exponents that we test get bigger (and hence require a bigger time investment for an LL test), it is essential to try and knock them out by factoring as many as possible. Factoring has likely saved tens (hundreds?) of thousands of GHz days since GIMPS began. 

20100207, 22:17  #7  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17×251 Posts 
Quote:
http://www.mersenne.org/report_expon...xp_lo=51675341 gives two factors. It's pretty easy to guess that the 165bit factor splits as these two numbers. From there, factorization is trivial. I used FactorDB when I checked, before ckdo even posted. Here are the numbers one less than the factors: 75 bits and 91 bits, or if you prefer the whole 165bit factor. Normally, P1 finds one prime factor when k is smooth to the necessary limits. When two factors are smooth to those limits, it finds both at once, as their product. Their product minus one is not necessarily smooth to the necessary limits to be found alone (almost impossible for GIMPS' practical purposes). Here is the 165bit P1: http://factordb.com/search.php?id=127092845 Last fiddled with by MiniGeek on 20100207 at 22:20 

20100207, 23:04  #8  
"Nathan"
Jul 2008
Maryland, USA
5×223 Posts 
Quote:
I'm thinking that there are quite a few folks running GIMPS that don't understand how the factoring process works (they just see their computer reading "Trial factoring to XX%" or doing this 3daylong thing called P1) and would like to learn more about it. As I said, it's only been recently (since the new assignment types have been opened up in v5) that I've really understood how the GIMPS factoring process works, and why it's so important. 

20100207, 23:35  #9  
Dec 2007
Cleves, Germany
1021_{8} Posts 
Quote:


20100208, 07:13  #10 
Sep 2006
Brussels, Belgium
2·5^{2}·31 Posts 
When Prime 95 reported a 159 bit factor for M39122179 in 2007, I posted it on the forum Not quite a PrimeNet P1 record, it turned out to be composite. I was wiser when a 175 bits factor was reported for M50996371 half a year ago (I checked with Alperton's applet and sure enough it was composite : the product of 77 and 99 bit factors.)
The biggest factors for Mersenne numbers found by P1 factoring are : 426315489966437174530195419710289226952407399 a 149 bit factor of 17504141 (k is 124 bits) and 4212419019412230280238456118524128112421481 a 142 bit factor of 35045431 (k is 116 bits) There are still bigger smallest non trivial (überhaupt ;) factors for Mersenne numbers but they where found by ECM or SNFS like the 324 bit factor for M727. Jacob Last fiddled with by S485122 on 20100208 at 07:14 Reason: nimbers because of numb fingers 
20100208, 15:16  #11  
Jul 2006
Calgary
5^{2}·17 Posts 
yes, I did:
P1 found a factor in stage #2, B1=610000, B2=16622500. UID: xxx/antec2, M51675341 has a factor: 24202210871494586645564966315136082223034579556649, AID: xxx... ... PrimeNet success code with additional info: Composite factor 24202210871494586645564966315136082223034579556649 = 19514686905730497955927 * 1240204928134798557283433087 Quote:
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