A152293 Primes of the form : (p-n)/(n+1)=prime and (n+1)*p+n=prime. n=3.

11, 31, 47, 151, 271, 359, 439, 599, 719, 1031, 1759, 1871, 2287, 2711, 2767, 2879, 3719, 3911, 4079, 5119, 5527, 5791, 6199, 6271, 6991, 7151, 7607, 7727, 8447, 8647, 8831, 9151, 9391, 9511, 9839, 10159, 10687, 10847, 11279, 12479, 12919, 13487

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Dec 02 2008

Keywords

• nonn
• changed

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.

Crossrefs

Cf. A059455, A152292

Programs

Mathematica

lst={};n=3;Do[p=Prime[k];If[PrimeQ[(p-n)/(n+1)]&&PrimeQ[(n+1)*p+n],AppendTo[lst,p]],{k,7!}];lst
Select[Prime[Range[1600]],AllTrue[{(#-3)/4,4#+3},PrimeQ]&] (* Harvey P. Dale, Aug 24 2025 *)