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Old 2011-09-30, 23:29   #1
philmoore
 
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Default 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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Old 2011-10-01, 01:13   #2
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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
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Old 2011-10-01, 14:21   #3
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PrimeNet still doesn't have it.
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Old 2011-10-01, 15:50   #4
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Quote:
Originally Posted by philmoore View Post
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
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Old 2011-10-03, 20:36   #5
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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.
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Old 2011-10-03, 20:46   #6
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Quote:
Originally Posted by philmoore View Post
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?
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Old 2011-10-03, 21:47   #7
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Quote:
Originally Posted by R.D. Silverman View Post
Have you tested the cofactor?
Yes, see the last sentence of the first post.
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Old 2011-10-04, 01:34   #8
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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?
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Old 2012-05-30, 19:20   #9
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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?
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Old 2012-05-30, 19:47   #10
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Quote:
Originally Posted by siegert81 View Post
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
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Old 2012-05-30, 21:38   #11
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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.
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