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Old 2003-09-07, 03:12   #4
GP2
 
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Sep 2003

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Another question for those worried about missing Mersenne primes might be: have any exponents fallen through the cracks? That is, untested, un-trial-factored, and unassigned.

This can be verified by combining all unique exponents from:
- BAD (probably redundant, all exps in BAD should already be in LUCAS_V.TXT too)
- LUCAS_V.TXT
- HRF3.TXT
- factors (the file produced by decomp -f 1 100000000 on FACTORS.CMP)
- nofactor (the file produced by decomp -n 1 100000000 on NOFACTOR.CMP)
- status.txt (the up-to-the-hour file of all current assignments of Primenet)
- cleared.txt (the up-to-the-hour file of all current cleared exponents, probably entirely redundant unless you insist on catching any exponents cleared in the few days since the last database update of BAD, LUCAS_V.TXT etc. which occurs more or less weekly)
- a 39-line file of known Mersenne prime exponents

and comparing this combined list of exponents to a file of all prime numbers less than 100,000,000. It is very easy to generate the latter file by the way... a program like sieve2310.c by John Moyer does this in a few seconds on a 2.8 GHz P4.

The comparison can be done with standard Linux utilities like cut, sort, uniq, comm, sed.

It turns out that there are no "missing" exponents less than 79.3 M.


If we omit "nofactors" from the set of files above, we can discover if there are any exponents which have been trial-factored, but not LL tested or currently assigned by Primenet. It turns out there are indeed some, but this is easily explained as manual tests or people using non-Primenet programs like Glucas or Mlucas on ranges that George has reserved for them.

Here is the complete list of "trial-factored but not-LL-tested or currently assigned by Primenet" exponents less than M39. Nothing alarming here. On the other hand, if there was a "missing" exponent somewhere well behind the current leading edge of double-checks, it would be time for conspiracy theories.
:)


12495941
12808997
12809701
12809717
12822037
12822581
12822619
12822713
12823441
12824093
12827161
12827189
12827329
12827539
12827561
12827743
12827897
12827989
12828031
12829651
13110371

There are 20 "trial-factored but not-LL-tested or currently assigned by Primenet" exponents in the 12M range, 14 in the 13M range, 85 in the 14M range, etc.
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