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
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