Hi folks
> Wait, that might just be the reason to search! Will only searched up to
> k=4 for M(M(6972593)), but if 2*k*M(p)+1 divides M(M(p)), then you've just
> beaten the world record! Non-Mersenne's might once again grace the top
> 10 list!
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.
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).
It follows then the first possible factor of M(M(p)) has k=5.
Chris Nash
Lexington KY
UNITED STATES
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