A260554 Primes p such that p = q^2 + 4*r^2 where q and r are also primes.
41, 61, 109, 137, 149, 157, 269, 317, 389, 397, 461, 509, 557, 653, 701, 773, 797, 857, 877, 941, 977, 997, 1013, 1061, 1181, 1277, 1453, 1493, 1613, 1637, 1697, 1733, 1877, 1949, 1973, 1997, 2141, 2237, 2309, 2333, 2357, 2477, 2693, 2837, 2909, 2957, 3373
Offset: 1
Keywords
Examples
149 is in the sequence because 149 = 7^2 + 4*5^2 and 149, 7 and 5 are all primes.
Links
- Colin Barker, Table of n, a(n) for n = 1..1400
- John Friedlander and Henryk Iwaniec, Coordinate distribution of Gaussian primes, J. Eur. Math. Soc. (JEMS) 24 (2022), pp. 737-772. arXiv:1811.05507 [math.NT]
- Ben Green and Mehtaab Sawhney, Primes of the form p^2 + nq^2, arXiv preprint (2024). arXiv:2410.04189 [math.NT]
Programs
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Mathematica
Select[#1^2 + 4 #2^2 & @@ # & /@ Tuples[Prime@ Range@ 60, 2], PrimeQ] // Sort (* Michael De Vlieger, Jul 29 2015 *)
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PARI
list(lim)=my(v=List()); lim\=1; forprime(q=2,sqrtint((lim-9)\4), my(t=4*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
Comments