Proof

[Graeme McRae]

D'oh!  Sorry, I didn't read the later messages in this thread -- I see now 
the converse is what really needs proving.  So...
Never mind!

----- Original Message ----- 
From: "Graeme McRae" <g_m at mcraefamily.com>
To: <grafix at csl.pl>; "N. J. A. Sloane" <njas at research.att.com>
Cc: "seqfan" <seqfan at ext.jussieu.fr>
Sent: Sunday, April 27, 2008 1:39 PM
Subject: Re: Proof


>A simpler proof...  I considered the 576 possible combinations of x,y (mod 
>24), and found that possible values of 4x^2-4xy+7y^2 are 0, 4, 7, 12, 15, 
>and 16.  Of these, only 7 (mod 24) can be prime.
>




Replying to a comment from "Eric", Apr 18 2008:

You said:

inside
A001348  Mersenne numbers: 2^p - 1, where p is prime.
there is no crossref to
A100105 2^prime(n)-prime(n).

but

A072752             1, 2, 4, 6, 10, 12, 16, 19, 22, 28, 32, 36, 44, 49, 52,
58
Maximum gap in one-stage prime-sieves.
approach
(A001348 - A100105)=1, 2, 4, 6, 10, 12, 16, 18, 22, 28, 30, 36, 40, 42, 46,
60, 0, 0


is the sequence of primes-1. 

NJAS