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Sophie Germain primes p such that (2^(p+7)*5^(p+5)-204979)/9 is also prime.
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%I #19 Sep 08 2022 08:46:15

%S 5,11,239,4073

%N Sophie Germain primes p such that (2^(p+7)*5^(p+5)-204979)/9 is also prime.

%C Intersection of A005384 and A266421.

%C a(n) mod 19, a(n) mod 29, a(n) mod 37, and a(n) mod 59 are also primes.

%C a(5) > 70000 (if it exists).

%t Select[ Prime[ Range[600]], PrimeQ[2# + 1] && PrimeQ[(2^(#+7) * 5^(#+5) - 204979) / 9] &]

%o (Magma) [p: p in PrimesUpTo(500) | IsPrime(2*p+1) and IsPrime((2^(p+7)*5^(p+5)-204979) div 9)]; // _Vincenzo Librandi_, Jan 07 2016

%Y Cf. A005384, A266421

%K nonn,hard,more

%O 1,1

%A _Mikk Heidemaa_, Dec 30 2015