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A152388
Primes p such that (p-n)/(n+1) and (n+1)*p+n are both prime, with n=127.
1
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
1,1
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.
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Definition clarified by Harvey P. Dale, Apr 30 2023
STATUS
approved