A155488 Primes p with property that p^2 is of the form x^2 + 40y^2.

7, 11, 13, 19, 23, 37, 41, 47, 53, 59, 89, 103, 127, 131, 139, 157, 167, 173, 179, 197, 211, 223, 241, 251, 263, 277, 281, 293, 317, 331, 367, 373, 379, 383, 397, 401, 409, 419, 449, 463, 487, 491, 499, 503, 521, 557, 569, 571, 601, 607, 613, 619, 641, 647

Offset: 1

Author

Zak Seidov, Jan 23 2009

Keywords

• nonn

Comments

All p^2 are congruent to {1, 9} (mod 40), as in A107145.

Rational primes that decompose in the field Q(sqrt(-10)). - N. J. A. Sloane, Dec 26 2017

Links

• Robert Price, Table of n, a(n) for n = 1..1000
• Zak Seidov, First 1000 terms
• Index to sequences related to decomposition of primes in quadratic fields

Crossrefs

Cf. A107145 (Primes of the form x^2 + 40y^2).

Programs

Maple

Load the Maple program HH given in A296920. Then run HH(-10, 200); This produces A155488, A296925, A293859. - N. J. A. Sloane, Dec 26 2017

Mathematica

Sqrt[#]&/@Select[Union[Flatten[Table[x^2+40y^2,{x,800},{y,100}]]],PrimeQ[Sqrt[#]]&] (* Harvey P. Dale, Jul 12 2025 *)