Irritated Mersenne factor found

philmoore · 2011-09-30, 23:29

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.

Mini-Geek · 2011-10-01, 01:13

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!

Mr. P-1 · 2011-10-01, 14:21

PrimeNet still doesn't have it.

xilman · 2011-10-01, 15:50

Quote:

Originally Posted by philmoore

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.

Nice one!

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

philmoore · 2011-10-03, 20:36

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.

R.D. Silverman · 2011-10-03, 20:46

Quote:

Originally Posted by philmoore

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.

Have you tested the cofactor?

philmoore · 2011-10-03, 21:47

Quote:

Originally Posted by R.D. Silverman

Have you tested the cofactor?

Yes, see the last sentence of the first post.

ewmayer · 2011-10-04, 01:34

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?

siegert81 · 2012-05-30, 19:20

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?

xilman · 2012-05-30, 19:47

Quote:

Originally Posted by siegert81

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?

1. MM2 = 2^(2^2-1)-1 = 2^3-1 = 7
MM3 = 2^(2^3-1)-1 = 2^7-1 = 127
MM5 = 2^(2^5-1)-1 = 2^31-1 = 2147483647
MM7 = 2^(2^7-1)-1 = 2^127-1 = 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 P-1. Factoring larger ones is likely to be the province of trial division at the moment.

Paul

siegert81 · 2012-05-30, 21:38

Sorry, I meant to ask this question:

Have any of the double Mersenne *composites* been completely factored? (The first one seems to be 2^8191-1, 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.

2011-09-30, 23:29	#1
philmoore "Phil" Sep 2002 Tracktown, U.S.A. 2·13·43 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 2011-09-30 at 23:30

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2011-10-01, 01:13	#2
Mini-Geek Account Deleted "Tim Sorbera" Aug 2006 San Antonio, TX USA 17·251 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 Mini-Geek on 2011-10-01 at 01:13

2011-10-01, 14:21	#3
Mr. P-1 Jun 2003 1169₁₀ Posts	PrimeNet still doesn't have it.

2011-10-03, 20:36	#5
philmoore "Phil" Sep 2002 Tracktown, U.S.A. 2136₈ 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.

2011-10-04, 01:34	#8
ewmayer ∂²ω=0 Sep 2002 República de California 2×3×1,931 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?

2012-05-30, 19:20	#9
siegert81 Dec 2010 1001010₂ 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?

2012-05-30, 21:38	#11
siegert81 Dec 2010 2×37 Posts	Sorry, I meant to ask this question: Have any of the double Mersenne composites been completely factored? (The first one seems to be 2^8191-1, 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.