A152388 Primes p such that (p-n)/(n+1) and (n+1)*p+n are both prime, with n=127.

6143, 11519, 23039, 205823, 253439, 345599, 417023, 463103, 752639, 1071359, 1474559, 1511423, 1753343, 1766399, 1903103, 2188799, 2271743, 2711039, 2741759, 2747903, 2813183, 2997503, 3032063, 3258623, 3371519, 3463679

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.

Crossrefs

Cf. A152292, A152293, A152294, A152295

Programs

Mathematica

lst={};n=127;Do[p=Prime[k];If[PrimeQ[(p-n)/(n+1)]&&PrimeQ[(n+1)*p+n],AppendTo[lst,p]],{k,2*9!}];lst
Select[Prime[Range[250000]],AllTrue[{(#-127)/128,128#+127},PrimeQ]&] (* Harvey P. Dale, Apr 30 2023 *)

Extensions

Definition clarified by Harvey P. Dale, Apr 30 2023