Fouvry-Iwaniec primes

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Fouvry-Iwaniec primes are prime numbers of the form $\scriptstyle k^{2}+p^{2}\,$ where $\scriptstyle p\,$ is a prime ($k$ may be composite). For example, 29 is a Fouvry-Iwaniec prime since $5^{2}+2^{2}=29$. Or 41, since $4^{2}+5^{2}=41$.

The Fouvry-Iwaniec primes below 200 are: 5, 13, 29, 41, 53, 61, 73, 89, 109, 113, 137, 149, 157, 173, 193. (See A185086).

These numbers are prime in $\scriptstyle \mathbb {Z} \,$ but composite in $\scriptstyle \mathbb {Z} [i]\,$. In the latter, they are the product of $\scriptstyle k+pi\,$ and $\scriptstyle k-pi\,$ (see Gaussian integers.)