A188339 Primes p such that 2^p mod p^2 is prime.

5, 53, 61, 193, 227, 257, 307, 317, 383, 457, 577, 601, 607, 653, 727, 751, 947, 1019, 1031, 1039, 1049, 1093, 1123, 1193, 1259, 1283, 1409, 1471, 1483, 1607, 1613, 1667, 1987, 2011, 2029, 2203, 2357, 2371, 2377, 2909, 2939, 3011, 3049, 3089, 3163

Offset: 1

Author

Juri-Stepan Gerasimov, Mar 28 2011

Keywords

• nonn

Examples

			5 is a term because 5 is prime and (2^5 mod 5^2) = 32 mod 25 = 7 also prime.
		

Links

• Felix Fröhlich, Table of n, a(n) for n = 1..3119 (all terms up to 10^6)

Crossrefs

Cf. A066606.

Programs

Mathematica

Select[Prime[Range[500]], PrimeQ[PowerMod[2,#, #^2]] &] (* Alonso del Arte, Mar 28 2011 *)

PARI

forprime(p=2, 10^3, if(isprime(2^p%p^2), print1(p, ", "))) \\ Felix Fröhlich, Jun 28 2014