A165816 Prime congruent numbers (A165815) that are not equal to 5 or 7 (mod 8).

41, 137, 257, 313, 353, 457, 761, 1201, 1217, 1249, 1321, 2113, 2273, 2777, 2833, 2953, 3001, 3433, 3593, 3761, 3881, 4441, 4481, 4649, 4793, 4889, 5273, 5449, 5569, 5657, 5849, 6073, 6529, 7001, 7321, 7417, 7561, 7793, 8521, 8609, 9049, 9257, 9281

Offset: 1

Author

T. D. Noe, Sep 28 2009

Keywords

• nonn

Comments

Heegner proved that every prime p with p = 5 or 7 (mod 8) is a congruent number. See A003628 for those primes. All primes in this sequence equal 1 (mod 8).

Monsky proved that no prime of the form 8k+3 is a congruent number. - Jonathan Sondow, Nov 15 2017

Links

• T. D. Noe, Primes less than 10^7
• Kurt Heegner, Diophantische Analysis und Modulfunktionen, Math. Zeitschrift 56 (1952), 227-253.
• P. Monsky, Mock Heegner points and congruent numbers, Math. Zeit., 204 (1990), 45-67.
• Kent E. Morrison, Congruent Numbers

Crossrefs

Cf. A003273 (congruent numbers), A165815 (prime congruent numbers).