A164623 Primes p such that p*(p-1)/2-5 and p*(p-1)/2+5 are also prime numbers.

13, 157, 673, 1069, 1117, 1153, 1213, 1597, 2029, 2089, 2437, 2713, 2833, 3613, 4057, 4909, 5653, 6337, 6529, 7549, 7993, 8053, 9613, 10789, 11497, 11689, 12073, 12373, 13309, 13669, 13789, 14173, 15289, 15937, 16249, 18097, 18637, 19249, 19993

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Aug 17 2009

Keywords

• nonn
• easy

Comments

Primes A000040(k) such that A008837(k)+-5 are also prime numbers.

Examples

			13 is in the sequence because 13*6-5=73 and 13*6+5=83 are both prime.
		

Links

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

Crossrefs

Cf. A008846, A020882, A068228, A068229, A082539, A086519, A107159, A158708, A139494, A164620, A164621, A164622, A023203.

Programs

Mathematica

Select[Prime[Range[2300]], PrimeQ[# (# - 1)/2 - 5] && PrimeQ[# (# - 1)/2 + 5] &]

PARI

forprime(p=2,10^6,my(b=binomial(p,2));if(isprime(b-5)&isprime(b+5),print1(p,", "))); /* Joerg Arndt, Apr 10 2013 */

Extensions

Edited by R. J. Mathar, Aug 20 2009

Mathematica code adapted to the definition by Bruno Berselli, Apr 10 2013