Quartan prime

In mathematics, a quartan prime is a prime number of the form x⁴ + y⁴, where x > 0, y > 0. The odd quartan primes are of the form 16n + 1.

For example, 17 is the smallest odd quartan prime: 17 = 1⁴ + 2⁴.

Due to the rules behind even and odd numbers, only one of the two integers can be odd. If both are odd or even, the resulting integer will be even, and not prime (excluding the trivial solution of 1⁴ + 1⁴ = 2).

The first few quartan primes are