20110930, 23:29  #1 
"Phil"
Sep 2002
Tracktown, U.S.A.
2136_{8} Posts 
Irritated Mersenne factor found
This just turned up today:
[Fri Sep 30 03:16:31 2011] ECM found a factor in curve #97, stage #2 Sigma=7408035135864132, B1=3000000, B2=300000000. M524287 has a factor: 65997004087015989956123720407169 M524287 is the iterated Mersenne number M(M(19)). Will Edgington keeps the status of these numbers at: http://www.garlic.com/~wedgingt/MMPstats.txt I also verified that the cofactor by the five known prime factors is composite, and also not a prime power, using a script file and pfgw. Last fiddled with by philmoore on 20110930 at 23:30 
20111001, 01:13  #2 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
10AB_{16} Posts 
The group order shows that this was a close find near the B1. The B1 was 3,000,000, and the penultimate factor was 2,927,861. Congratulations!
Last fiddled with by MiniGeek on 20111001 at 01:13 
20111001, 14:21  #3 
Jun 2003
7·167 Posts 
PrimeNet still doesn't have it.

20111001, 15:50  #4  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2^{3}×13×101 Posts 
Quote:
You're a better man than I, Gunga Din. I'd never seriously consider running ECM on a number of that size. How long did each curve take? Paul 

20111003, 20:36  #5 
"Phil"
Sep 2002
Tracktown, U.S.A.
2×13×43 Posts 
I was doing about 1.7 curves per day on each core of an old Pentium D. Slow progress, of course, but not so slow compared to the ECM work currently being done on Fermat numbers.

20111003, 20:46  #6 
Nov 2003
1D24_{16} Posts 

20111003, 21:47  #7 
"Phil"
Sep 2002
Tracktown, U.S.A.
2×13×43 Posts 

20111004, 01:34  #8 
∂^{2}ω=0
Sep 2002
Repรบblica de California
2^{6}·181 Posts 
Very nice. I expect it won't be too long before you're running ECM on M(M(31))  what do you estimate the stage 1 and 2 memory needs for such a computation would be?

20120530, 19:20  #9 
Dec 2010
2×37 Posts 
Very nice find! I just noticed today when I looked at the MMPStats.txt page.
Two questions: 1. Have any of the double Mersenne numbers been completed factored? 2. What's the best software to use in order to search for factors of double Mersenne numbers? 
20120530, 19:47  #10  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
24410_{8} Posts 
Quote:
MM3 = 2^(2^31)1 = 2^71 = 127 MM5 = 2^(2^51)1 = 2^311 = 2147483647 MM7 = 2^(2^71)1 = 2^1271 = 170141183460469231731687303715884105727 All of the above are fully factored into primes, so I can safely answer the first question in the affirmative. 2. It depends. Finding factors of MM13 might still be possible with ECM and/or P1. Factoring larger ones is likely to be the province of trial division at the moment. Paul 

20120530, 21:38  #11 
Dec 2010
1001010_{2} Posts 
Sorry, I meant to ask this question:
Have any of the double Mersenne *composites* been completely factored? (The first one seems to be 2^81911, MM13) Also, how can I use Prime95 to trial factor Mersenne numbers beyond the default stopping point? I can't seem to get Prime95 to do trial factoring of a specific Mersenne number. 
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