Mersenne: M727 has a factor?!?!?
Hi!! Tell me I'm wrong... and if not, what happened?? I just made a slight error in adding a P-1 factor assignment to the WORKTODO.INI file for M727 and came up with the following result (on screen): P-1 on P727 with B1=30, B2=1 P727 stage 1 complete. 116 transforms. Time: 0.018 sec. (4659194 clocks) Stage 1 GCD complete. Time: 0.001 sec. (164887 clocks) P727 has a factor: 11633 and in the RESULTS.TXT file: [Sat Apr 08 10:43:37 2000] P-1 found a factor in stage #1, B1=30, B2=1. UID: Net_Force/V20, P727 has a factor: 11633 This meets all the criteria too 1) 11633 is PRIME. 2) 2kp+1 = 2*(8)*727+1 = 11633 3) 8n+1 = 8*(1454)+1 = 11633 4) 2^p (mod n) = 2^727 (mod 11633) = 1 Eric P.S. the error in question was: Pminus1=727,1E16,0,0,0 _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: M727 has a factor?!?!?
P-1 on P727 with B1=30, B2=1 P727 stage 1 complete. 116 transforms. Time: 0.018 sec. (4659194 clocks) Stage 1 GCD complete. Time: 0.001 sec. (164887 clocks) P727 has a factor: 11633 This meets all the criteria too 1) 11633 is PRIME. 2) 2kp+1 = 2*(8)*727+1 = 11633 3) 8n+1 = 8*(1454)+1 = 11633 4) 2^p (mod n) = 2^727 (mod 11633) = 1 11633 divides M1454 where 1454 = 2*727, but 11633 does not divide M727. Your #4 calculation has a bug, probably a rounding error; the correct result is 11631. In fact: M( 1454 )C: 11633 M( 1454 )C: 52068472442119144511578580563 M( 1454 )C: 59803996769241650545074361210286131 M( 1454 )D That is, M1454 is considered to be completely factored even though it is a multiple of M727, which is known to be composite but has no known prime factors. There are other cases like this in the data. From my "reverse method" program, I should now have all factors less than about 1.6 billion for _any_ Mersenne number with an exponent less than 2^30 (just over a billion). Will http://www.garlic.com/~wedgingt/mersenne.html _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: M727 has a factor?!?!?
Hi!! Tell me I'm wrong... and if not, what happened?? P727 has a factor: 11633 Look carefully: that's P727, which denotes 2^727+1. You must have accidentally specified "factor 2^n+1" when you started the work. This small factor was reported because there is no entry in LOWP.TXT for P727; it was removed after P727 was finished last year--by me, incidentally. Alas, P727's evil twin M727 remains unfactored. David A. Miller [EMAIL PROTECTED] _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: M727 has a factor?!?!?
Will Edgington wrote: P-1 on P727 with B1=30, B2=1 P727 stage 1 complete. 116 transforms. Time: 0.018 sec. (4659194 clocks) Stage 1 GCD complete. Time: 0.001 sec. (164887 clocks) P727 has a factor: 11633 This meets all the criteria too 1) 11633 is PRIME. 2) 2kp+1 = 2*(8)*727+1 = 11633 3) 8n+1 = 8*(1454)+1 = 11633 4) 2^p (mod n) = 2^727 (mod 11633) = 1 11633 divides M1454 where 1454 = 2*727, but 11633 does not divide M727. Your #4 calculation has a bug, probably a rounding error; the correct result is 11631. Well, I went back and did it by hand!! You're right about #4... BTW, George wrote that what I got was a result of a parsing error on the part of Prime95 (it did 2^727+1, not 2^727-1). R = 1 727 = 1011010111 E=727D=1R=2A=4 E=363D=1R=8A= 16 E=181D=1R= 128A= 256 E= 90D=0R= 128A= 7371 E= 45D=1R= 1215A= 5531 E= 22D=0R= 1215A= 8804 E= 11D=1R= 6133A=11370 E= 5D=1R= 4008A=11004 E= 2D=0R= 4008A= 119 E= 1D=1R=11632A= 2528 E= 0*11632* Eric _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
