%I #10 Oct 08 2024 09:27:05
%S 73,79,103,193,199,223,271,313,439,463,751,823,991,1039,1063,1087,
%T 1303,1423,1543,1567,1663,1759,1783,1831,1873,1999,2143,2287,2383,
%U 2503,2833,3343,3463,3583,3631,3823,3847,3943,4447,4513,4639,4783,5023,5167,5407
%N Primes p such that p = q^2 + 6*r^2 where q and r are also primes.
%C Green & Sawhney prove that this sequence is infinite. - _Charles R Greathouse IV_, Oct 08 2024
%H Colin Barker, <a href="/A260555/b260555.txt">Table of n, a(n) for n = 1..1500</a>
%H Ben Green and Mehtaab Sawhney, <a href="https://arxiv.org/abs/2410.04189">Primes of the form p^2 + nq^2</a>, arXiv preprint (2024). arXiv:2410.04189 [math.NT]
%e 73 is in the sequence because 73 = 7^2 + 6*2^2 and 73, 7 and 2 are all primes.
%t Select[#1^2 + 6 #2^2 & @@ # & /@ Tuples[Prime@ Range@ 60, 2], PrimeQ] // Sort (* _Michael De Vlieger_, Jul 29 2015 *)
%o (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
%Y Cf. A260553, A260554, A260556, A260557.
%K nonn
%O 1,1
%A _Colin Barker_, Jul 29 2015