Conjecture

[Artur]

Dear Max,
Could you help me understand some strange for me rule.
Prime numbers of the form  24n+7 are that same as A107006 
<http://www.research.att.com/%7Enjas/sequences/A107006>
but composite numbers of the form 24n+7 A135657 
<http://www.research.att.com/%7Enjas/sequences/A135657> are different as 
A135658 <http://www.research.att.com/%7Enjas/sequences/A135658>
of course I see that that A135657 
<http://www.research.att.com/%7Enjas/sequences/A135657> is subset of 
A135658 <http://www.research.att.com/%7Enjas/sequences/A135658>
but I don't see why numbers of the form 4x^2-4xy+7y^2. (for nonnegative 
x,y) have to be prime iff are congruent to 7 mod 24
(but not only because some composite 4x^2-4xy+7y^2 giving also rest 7 
when divided by 24 e.g 55,175, 247
ARTUR


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