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Pythagorean primes

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The Pythagorean primes are primes which are the sum of two squares, implying that among the Gaussian integers, these numbers are Gaussian composites

The even prime and the odd primes of form are Pythagorean (sum of two squares), while the odd primes of form are not Pythagorean (not the sum of two squares).

A002144 Pythagorean odd primes: primes of form .

{5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 137, 149, 157, 173, 181, 193, 197, 229, 233, 241, 257, 269, 277, 281, 293, 313, 317, 337, 349, 353, 373, 389, 397, 401, 409, 421, 433, 449, ...}

Non-Pythagorean primes

The non-Pythagorean primes are primes which are NOT the sum of two squares, implying that among the Gaussian integers, these numbers are Gaussian primes.

A002145 Non-Pythagorean primes: primes of form .

{3, 7, 11, 19, 23, 31, 43, 47, 59, 67, 71, 79, 83, 103, 107, 127, 131, 139, 151, 163, 167, 179, 191, 199, 211, 223, 227, 239, 251, 263, 271, 283, 307, 311, 331, 347, 359, 367, 379, 383, 419, 431, ...}