# near-square prime

A is a prime number $p$ of the form $n^{2}+k$, with $n$ being any integer and $0<|k|<|n|$ also an integer. Since for any nonzero real number $x$ it is always the case that $x^{2}\geq 0$, it doesn’t matter if $n$ is negative.

 5 149 4 29 53 3 67 103 2 11 83 1 5 17 37 101 0 1 4 9 16 25 36 49 64 81 100 121 144 $-1$ 3 $-2$ 7 23 47 79 $-3$ 97 $-4$ $-5$ 31 59 139

Fermat primes are near-square primes for $k=1$ with the additional requirement that $n=2^{2^{m}-1}$, while Carol primes are near-square primes for $k=-2$ with the additional requirement that $n=2^{m}-1$.

For $k=-1$, only $n=2$ gives a prime, namely 3.

Title near-square prime NearsquarePrime 2013-03-22 18:57:37 2013-03-22 18:57:37 PrimeFan (13766) PrimeFan (13766) 6 PrimeFan (13766) Definition msc 11A41