Mersenne non-primes - Page 2

wblipp · 2004-01-04, 19:12

Quote:

Originally posted by dsouza123
Could Prime95 if it allowed composite exponents be used to find factors

Prime95 works fine with composite exponents. The ElevenSmooth Special Project uses Prime95 to search for factors of composite exponents. We've found over fifty factors with Prime95.

One small issue with using Prime95 is that automatically search the Algebraic Factors, too, so for each factor you must figure out which Mersenne Primitive the factor belongs too. Will Edgington collects Mersenne factors, so you should check with him about previously known factors and report to him any newly discovered factors. Reach him through his Mersenne Page.

William

dsouza123 · 2004-01-04, 20:18

So to use composite exponents it requires using ECM in Prime95 to find factors, is this correct ?

Is it (ECM) restricted to 2^p + 1 or can it test 2^p - 1 ( the mersenne numbers (prime exponent) that are tested by trial factoring, p-1 factoring and LL ) ?
============================

How/where do you find the status (factor(s), composite, prime) of a mersenne number ( with a prime exponent) ?
I checked a status.txt file from Dec 2003 and it starts with the 7 millions.

For the M971 ( 2^971 - 1) mentioned how/where would it's status be found ?

wblipp · 2004-01-05, 05:16

Prime95 will also do P-1 factoring of composite exponents.

I haven't tried it, but I think Prime95 will do trial factoring of composite exponents. I suspect that it would only find factors of the primitive part, not the algebraic factors.

I know Prime95 works with 2^m-1. I think it also works with 2^m+1 in all modes.

Will Edgington's lowM.txt file shows the following entries for M(971)

M( 971 )E: 413817700 50000000 0.56
M( 971 )H: 144115188077210231
M( 971 )c: 293
M( 971 )o: 4294000000 4294000000

The file mersfmt.txt explains these. The E line shows that Will knows that somebody has done ECM work with B1=50M, although no more than 8 curves have been tried at this level. The H line shows the highest trial factor attempted. The "o" line shows that somebody has tried P-1 factoring with those bounds, meaning no stage 2 was used. The c line shows the remaining unfactored composite is 293 digits. There are not "C" lines, so no factors are known for this primitive. 971 is prime, so there are no algebraic factors.

For small exponents it is often faster to use GMP-ECM than Prime95 - run some timing comparisons to find what works best for your machine and your exponent.

If you use Prime95 with composite exponents, you should look at Philmoore's information on factoring highly composite Mersenne Numbers.

William

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2004-01-04, 20:18	#13
dsouza123 Sep 2002 1010010110₂ Posts	So to use composite exponents it requires using ECM in Prime95 to find factors, is this correct ? Is it (ECM) restricted to 2^p + 1 or can it test 2^p - 1 ( the mersenne numbers (prime exponent) that are tested by trial factoring, p-1 factoring and LL ) ? ============================ How/where do you find the status (factor(s), composite, prime) of a mersenne number ( with a prime exponent) ? I checked a status.txt file from Dec 2003 and it starts with the 7 millions. For the M971 ( 2^971 - 1) mentioned how/where would it's status be found ?

2004-01-05, 05:16	#14
wblipp "William" May 2003 New Haven 2·7·13² Posts	Prime95 will also do P-1 factoring of composite exponents. I haven't tried it, but I think Prime95 will do trial factoring of composite exponents. I suspect that it would only find factors of the primitive part, not the algebraic factors. I know Prime95 works with 2^m-1. I think it also works with 2^m+1 in all modes. Will Edgington's lowM.txt file shows the following entries for M(971) M( 971 )E: 413817700 50000000 0.56 M( 971 )H: 144115188077210231 M( 971 )c: 293 M( 971 )o: 4294000000 4294000000 The file mersfmt.txt explains these. The E line shows that Will knows that somebody has done ECM work with B1=50M, although no more than 8 curves have been tried at this level. The H line shows the highest trial factor attempted. The "o" line shows that somebody has tried P-1 factoring with those bounds, meaning no stage 2 was used. The c line shows the remaining unfactored composite is 293 digits. There are not "C" lines, so no factors are known for this primitive. 971 is prime, so there are no algebraic factors. For small exponents it is often faster to use GMP-ECM than Prime95 - run some timing comparisons to find what works best for your machine and your exponent. If you use Prime95 with composite exponents, you should look at Philmoore's information on factoring highly composite Mersenne Numbers. William