A268426 Primes of the form p^2 + 12*q^2, p, q primes.

73, 97, 157, 229, 277, 337, 349, 397, 409, 421, 577, 613, 661, 709, 757, 829, 877, 1009, 1069, 1117, 1429, 1549, 1621, 1669, 1741, 1789, 2053, 2269, 2293, 2389, 2437, 2557, 2797, 2857, 2917, 3109, 3301, 3517, 3529, 3637

Offset: 1

Author

Zak Seidov, Feb 04 2016

Keywords

• nonn

Comments

A variant of the cuban primes.

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

Examples

			73=5^2+12*2^2, 97= 7^2+12* 2^2, 157= 7^2+12*3^2.
		

Links

• Zak Seidov, Table of a(n), p, q for n=1..116.
• Ben Green and Mehtaab Sawhney, Primes of the form p^2 + nq^2, arXiv preprint (2024). arXiv:2410.04189 [math.NT]

Crossrefs

Cf. A002407.

Programs

PARI

list(lim)=my(v=List()); lim\=1; forprime(q=2, sqrtint((lim-25)\12), my(t=12*q^2); forprime(p=5, sqrtint(lim-t), my(r=t+p^2); if(isprime(r), listput(v, r)))); Set(v) \\ Charles R Greathouse IV, Oct 08 2024