A172256 Primes p such that 2*p+-3 are both nonprimes.

59, 61, 79, 103, 109, 131, 149, 151, 163, 179, 239, 257, 271, 281, 293, 313, 359, 367, 389, 401, 419, 449, 479, 491, 499, 541, 569, 571, 593, 601, 619, 673, 677, 683, 691, 709, 719, 733, 761, 769, 821, 823, 829, 839, 857, 877, 883, 911, 919, 947, 953, 971, 983, 1009

Offset: 1

Author

Juri-Stepan Gerasimov, Jan 30 2010

Keywords

• nonn

Comments

In the first 10000 primes there are 5698 terms (~57% of the primes). In the 10000 primes from prime(1,000,000,000) to prime(1,000,010,000) there are 8432 primes in this sequence or ~84%. It seems likely the density of these terms within the primes slowly approaches 100%. This indicates the density of "Prime Septets", as defined in A268593 (which rely upon primes in the complement of this sequence), declines steadily at larger n. - Richard R. Forberg, Feb 12 2016

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A131426, A141468.

Programs

Magma

[p: p in PrimesUpTo(1100)| not IsPrime(2*p+3)and not IsPrime(2*p-3)] // Vincenzo Librandi, Dec 08 2010

Mathematica

npQ[n_]:=Module[{c=2n},!PrimeQ[c+3]&&!PrimeQ[c-3]]; Select[Prime[ Range[ 200]],npQ] (* Harvey P. Dale, Jan 21 2013 *)
Select[Prime[Range[200]],NoneTrue[2#+{3,-3},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 25 2019 *)

PARI

isok(p) = isprime(p) && !isprime(2*p+3) && !isprime(2*p-3); \\ Michel Marcus, Feb 12 2016

Extensions

Corrected and extended by Vincenzo Librandi, Apr 01 2010