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A319673 Primes that are neither a twin prime nor a Sophie Germain or safe prime.

%I A319673 #38 Aug 02 2025 08:29:02
%S A319673 37,67,79,97,127,157,163,211,223,257,277,307,317,331,337,353,367,373,
%T A319673 379,389,397,401,409,439,449,457,487,499,541,547,557,577,607,613,631,
%U A319673 647,673,677,691,701,709,727,733,739,751,757,769,773,787,797,853,877,907,919,929,937,941,947,967,971,977,991,997
%N A319673 Primes that are neither a twin prime nor a Sophie Germain or safe prime.
%H A319673 Amiram Eldar, <a href="/A319673/b319673.txt">Table of n, a(n) for n = 1..10000</a>
%F A319673 A000040\(A001097 U A005384 U A005385).
%e A319673 37 is prime, but it is not a twin prime (neither 35 nor 39 are prime), it is not a Sophie Germain prime (2*37 + 1 = 75 is not prime), and it is not a safe prime ((37 - 1)/2 = 18 is not prime).  So 37 is in the sequence.
%p A319673 select(p->isprime(p) and not isprime(p-2) and not isprime(p+2) and not isprime(2*p+1) and not isprime((p-1)/2),[$1..1000]); # _Muniru A Asiru_, Sep 27 2018
%t A319673 Select[Prime@ Range@ PrimePi[10^3], NoneTrue[{# - 2, # + 2, 2 # + 1, (# - 1)/2}, PrimeQ] &] (* _Michael De Vlieger_, Sep 26 2018 *)
%o A319673 (PARI) isok(p) = isprime(p) && !isprime(p-2) && !isprime(p+2) && !isprime(2*p+1) && !isprime((p-1)/2); \\ _Michel Marcus_, Sep 26 2018
%o A319673 (GAP) Filtered([1..1000],p->IsPrime(p) and not IsPrime(p-2) and not IsPrime(p+2) and not IsPrime(2*p+1) and not IsPrime((p-1)/2)); # _Muniru A Asiru_, Sep 27 2018
%o A319673 (Magma) [p: p in PrimesUpTo(1000) | not IsPrime(p-2) and not IsPrime(p+2)and not IsPrime(2*p+1)and not IsPrime((p-1) div 2)]; // _Vincenzo Librandi_, Oct 25 2018
%Y A319673 Cf. A000040, A001097, A005384, A005385.
%K A319673 nonn
%O A319673 1,1
%A A319673 _Ralf Steiner_, Sep 25 2018