Re: Mersenne: M(M(127)) and other M(M(p))

[Will Edgington]

Chris Nash writes:

   I really hope that neither Will Edgington (with M(M(6972593))) nor Chip
   Kerchner (with M(M(1398269))) dedicated any computer time whatsoever to
   search for factors 2*k*M(p)+1 up to k=4.

I didn't, except perhaps to have mmtrial verify that the smaller k's
were sieved out.

   As Will's page

   http://www.garlic.com/~wedgingt/MMPstats.txt

   points out, since M(p)=1 mod 3, k cannot be 1 mod 3. Also, since M(p)=-1 mod
   8 for odd p>=3, k must be 0 or 1 mod 4 (otherwise 2 is not a quadratic
   residue of this supposed factor, the 8x+-1 condition).

Thanks; I'll add this to the next MMPstatus file and to mmtrial.c.
Should have thought of it myself, but quadratic residues are still new
to me.

                                                           Will
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