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Primes of the form p^2 + 12*q^2, p, q primes.
1

%I #10 Oct 08 2024 09:28:55

%S 73,97,157,229,277,337,349,397,409,421,577,613,661,709,757,829,877,

%T 1009,1069,1117,1429,1549,1621,1669,1741,1789,2053,2269,2293,2389,

%U 2437,2557,2797,2857,2917,3109,3301,3517,3529,3637

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

%C A variant of the cuban primes.

%C Green & Sawhney prove that this sequence is infinite. - _Charles R Greathouse IV_, Oct 08 2024

%H Zak Seidov, <a href="/A268426/a268426.txt">Table of a(n), p, q for n=1..116.</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=5^2+12*2^2, 97= 7^2+12* 2^2, 157= 7^2+12*3^2.

%o (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

%Y Cf. A002407.

%K nonn

%O 1,1

%A _Zak Seidov_, Feb 04 2016