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Dear All, I wonder what the numbers(primes) of the form of 2^n + x^2 (where n is even) are called? What are their properties? Any references to look at? Thank you.

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Could you please provide some motivation for considering this particular property; to me it is not self-explanantory this is interesting. Thanks in advance. –  quid Feb 25 '13 at 13:29
    
Voted to close as not a real question, in view of lack of motivation. –  quid Feb 25 '13 at 20:05

1 Answer 1

Primes of the form $2^n+k$ have been considered, see the talk of Carl Pomerance. Among the square numbers $k=y^2$ the case $k=1$ is the most famous one, e.g., primes of the from $2^n+1$. Then necessarily $n$ is a power of $2$, so that these primes are just the Fermat primes $F_k=2^{2^k}+1$. Another special case are the primes of the form $2^n+n^2$, see sequence A064539 at integer sequences. Then necessarily $n\equiv 0 \mod 3$.

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