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

1,1

Links

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

Formula

A000040\(A001097 U A005384 U A005385).

Example

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.

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 *)

Prog

(PARI) isok(p) = isprime(p) && !isprime(p-2) && !isprime(p+2) && !isprime(2*p+1) && !isprime((p-1)/2); \\ Michel Marcus, Sep 26 2018
(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, Ocy 25 2018

Crossrefs

Cf. A000040, A001097, A005384, A005385.

Sequence in context: A226697 A117475 A145486 * A121764 A131499 A217659

Adjacent sequences: A319670 A319671 A319672 * A319674 A319675 A319676

Keyword

nonn

Author

Ralf Steiner, Sep 25 2018

Status

approved