Re: Mersenne: M727 has a factor?!?!?

[David A. Miller]

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]

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Re: Mersenne: M727 has a factor?!?!?

[Eric Hahn]

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


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