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A319673 Primes that are neither a twin prime nor a Sophie Germain or safe prime. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 14 19:53 EDT 2021. Contains 343903 sequences. (Running on oeis4.)