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

37, 67, 79, 97, 127, 157, 163, 211, 223, 257, 277, 307, 317, 331, 337, 353, 367, 373, 379, 389, 397, 401, 409, 439, 449, 457, 487, 499, 541, 547, 557, 577, 607, 613, 631, 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

Offset: 1

Author

Ralf Steiner, Sep 25 2018

Keywords

• nonn

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001097, A005384, A005385.

Programs

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

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

Maple

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

Mathematica

Select[Prime@ Range@ PrimePi[10^3], NoneTrue[{# - 2, # + 2, 2 # + 1, (# - 1)/2}, PrimeQ] &] (* Michael De Vlieger, Sep 26 2018 *)

PARI

isok(p) = isprime(p) && !isprime(p-2) && !isprime(p+2) && !isprime(2*p+1) && !isprime((p-1)/2); \\ Michel Marcus, Sep 26 2018

Formula

A000040\(A001097 U A005384 U A005385).