A260555 Primes p such that p = q^2 + 6*r^2 where q and r are also primes.

73, 79, 103, 193, 199, 223, 271, 313, 439, 463, 751, 823, 991, 1039, 1063, 1087, 1303, 1423, 1543, 1567, 1663, 1759, 1783, 1831, 1873, 1999, 2143, 2287, 2383, 2503, 2833, 3343, 3463, 3583, 3631, 3823, 3847, 3943, 4447, 4513, 4639, 4783, 5023, 5167, 5407

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..1500

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

Example

73 is in the sequence because 73 = 7^2 + 6*2^2 and 73, 7 and 2 are all primes.

Mathematica

Select[#1^2 + 6 #2^2 & @@ # & /@ Tuples[Prime@ Range@ 60, 2], PrimeQ] // Sort (* Michael De Vlieger, Jul 29 2015 *)

Prog

(PARI) list(lim)=my(v=List()); lim\=1; forprime(q=2, sqrtint((lim-9)\6), my(t=6*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, A260556, A260557.

Sequence in context: A153646 A179516 A180558 * A345550 A345804 A064667

Adjacent sequences: A260552 A260553 A260554 * A260556 A260557 A260558

Keyword

nonn

Author

Colin Barker, Jul 29 2015

Status

approved