A152295 Primes of the form : (p-n)/(n+1)=prime and (n+1)*p+n=prime. n=5.

17, 71, 83, 107, 191, 227, 251, 263, 431, 443, 479, 503, 587, 827, 839, 911, 983, 1091, 1151, 1163, 1187, 1619, 1667, 1847, 1907, 2087, 2243, 2459, 2591, 3023, 3467, 4463, 4871, 4943, 5471, 5519, 5651, 5807, 5903, 6131, 6203, 6299, 6311, 6563, 6983, 7127

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Dec 02 2008

Keywords

• nonn

Comments

This is the general form : (p-n)/(n+1)=primeand(n+1)*p+n=prime; 'Safe' primes and'Sophie Germain' primes just one part of this general form; If n=1 then we got'Safe' primes and'Sophie Germain' primes.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..3000

Crossrefs

Cf. A059455, A152292, A152293, A152294

Programs

Mathematica

lst={};n=5;Do[p=Prime[k];If[PrimeQ[(p-n)/(n+1)]&&PrimeQ[(n+1)*p+n],AppendTo[lst,p]],{k,7!}];lst
Select[Prime[Range[1000]],AllTrue[{(#-5)/6,6#+5},PrimeQ]&] (* This program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 29 2014 *)