A154418 Primes p such that (p^2 + 4)/5 is prime.

19, 31, 41, 71, 79, 109, 131, 149, 151, 181, 191, 241, 251, 379, 409, 421, 499, 509, 541, 599, 631, 659, 709, 719, 769, 919, 1009, 1019, 1021, 1031, 1109, 1129, 1151, 1201, 1231, 1291, 1399, 1409, 1451, 1549, 1601, 1621, 1721, 1871, 1931, 2069, 2131, 2179

Offset: 1

Author

Vincenzo Librandi, Jan 09 2009, Dec 13 2010

Keywords

• nonn
• easy

Comments

The primes (p^2 + 4)/5 are 73, 193, 337, 1009, 1249, etc.

All terms == 1 or 9 (mod 10). - Robert Israel, Sep 16 2016

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Programs

Magma

[p: p in PrimesInInterval(7, 2500) | IsPrime((p^2+4) div 5)]; // Vincenzo Librandi, Oct 15 2012

Maple

select(p -> isprime(p) and isprime((p^2+4)/5), [seq(seq(10*i+j,j=[1,9]),i=0..1000)]); # Robert Israel, Sep 16 2016

Mathematica

Select[Prime[Range[200]], PrimeQ[(#^2 + 4)/5] &] (* Vincenzo Librandi, Oct 15 2012 *)

Extensions

Corrected and extended by Zak Seidov, Jan 13 2009