A260557 Primes p such that p = q^2 + 10*r^2 where q and r are also primes.

89, 139, 211, 379, 401, 419, 499, 569, 619, 659, 881, 1019, 1051, 1091, 1259, 1409, 1451, 1459, 1499, 1571, 1619, 1699, 1721, 1811, 1889, 1931, 1979, 2099, 2339, 2459, 2531, 2579, 2699, 2939, 3011, 3251, 3299, 3371, 3539, 3571, 3659, 3761, 3779, 3851, 4019

Offset

1,1

Comments

Green & Sawhney prove that this sequence is infinite. - Charles R Greathouse IV, Oct 08 2024

Links

Colin Barker, Table of n, a(n) for n = 1..1750

Ben Green and Mehtaab Sawhney, Primes of the form p^2 + nq^2, arXiv preprint (2024). arXiv:2410.04189 [math.NT]

Example

419 is in the sequence because 419 = 13^2 + 10*5^2 and 419, 13 and 5 are all primes.

Mathematica

Select[#1^2 + 10 #2^2 & @@ # & /@ Tuples[Prime@ Range@ 36, 2], PrimeQ] // Sort (* Michael De Vlieger, Jul 29 2015 *)

Prog

(PARI) list(lim)=my(v=List()); lim\=1; forprime(q=2, sqrtint((lim-9)\10), my(t=10*q^2); forprime(p=3, sqrtint(lim-t), my(r=t+p^2); if(isprime(r), listput(v, r)))); Set(v) \\ Charles R Greathouse IV, Oct 08 2024

Crossrefs

Cf. A260553, A260554, A260555, A260556.

Sequence in context: A377012 A360422 A109560 * A141938 A267819 A031416

Adjacent sequences: A260554 A260555 A260556 * A260558 A260559 A260560

Keyword

nonn

Author

Colin Barker, Jul 29 2015

Status

approved