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%I #6 Apr 30 2023 17:05:42
%S 6143,11519,23039,205823,253439,345599,417023,463103,752639,1071359,
%T 1474559,1511423,1753343,1766399,1903103,2188799,2271743,2711039,
%U 2741759,2747903,2813183,2997503,3032063,3258623,3371519,3463679
%N Primes p such that (p-n)/(n+1) and (n+1)*p+n are both prime, with n=127.
%C 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.
%t 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
%t Select[Prime[Range[250000]],AllTrue[{(#-127)/128,128#+127},PrimeQ]&] (* _Harvey P. Dale_, Apr 30 2023 *)
%Y Cf. A152292, A152293, A152294, A152295
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Dec 02 2008
%E Definition clarified by _Harvey P. Dale_, Apr 30 2023
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