A052291 Primes p such that 4p^2 + 1 is also prime.

2, 3, 5, 7, 13, 37, 47, 67, 73, 103, 157, 163, 193, 233, 317, 337, 547, 587, 647, 653, 677, 683, 773, 827, 883, 887, 947, 983, 1013, 1063, 1087, 1163, 1297, 1327, 1373, 1487, 1493, 1523, 1553, 1567, 1607, 1627, 1637, 1657, 1663, 1667, 1723, 1867, 1873

Offset: 1

Author

Labos Elemer, Feb 08 2000

Keywords

• nonn
• easy

Examples

			The 5th term is 13 and 4*169+1 = 677 is also a prime.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000
• Marek Wolf, Search for primes of the form m^2+1, arXiv:0803.1456 [math.NT], 2008-2010.

Crossrefs

Cf. A052292.

Programs

Magma

[p: p in PrimesUpTo(2000) | IsPrime(4*p^2+1)]; // Vincenzo Librandi, Apr 11 2013

Mathematica

Select[Prime[Range[300]],PrimeQ[4 #^2 + 1]&] (* Vincenzo Librandi, Apr 11 2013 *)