A293859 -id:A293859 - cp's OEIS frontend

A296925 Inert rational primes in the field Q(sqrt(-10)).

3, 17, 29, 31, 43, 61, 67, 71, 73, 79, 83, 97, 101, 107, 109, 113, 137, 149, 151, 163, 181, 191, 193, 199, 227, 229, 233, 239, 257, 269, 271, 283, 307, 311, 313, 337, 347, 349, 353, 359, 389, 421, 431, 433, 439, 443, 457, 461, 467, 479, 509, 523, 541, 547, 563, 577, 587, 593, 599, 617, 631, 643, 661, 673, 683, 701, 709

Offset: 1

N. J. A. Sloane, Dec 26 2017

Primes that are congruent to 3, 17, 21, 27, 29, 31, 33, or 39 mod 40. - Amiram Eldar, Nov 17 2023

Primes p such that the Legendre symbol (-10/p) = -1, i.e., -10 is not a square modulo p. - Jianing Song, Oct 23 2024

Cf. A155488, A293859, A296920.

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

Select[Prime[Range[127]], KroneckerSymbol[-10, #] == -1 &] (* Amiram Eldar, Nov 17 2023 *)

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

Original entry on oeis.org

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

Zak Seidov, Jan 23 2009

nonn

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

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

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

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

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

cp's OEIS Frontend

A296925 Inert rational primes in the field Q(sqrt(-10)).

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