A252862 Initial members of prime sextuples (n, n+2, n+6, n+8, n+18, n+20).

11, 18041, 97841, 165701, 392261, 663581, 1002341, 1068701, 1155611, 1329701, 1592861, 1678751, 1718861, 1748471, 2159231, 2168651, 2177501, 2458661, 2596661, 3215741, 3295541, 3416051, 3919241, 4353311, 5168921, 5201291, 5205461, 6404771

Offset: 1

Author

Karl V. Keller, Jr., Dec 23 2014

Keywords

• nonn

Comments

This sequence is prime n, where there exist three twin prime pairs of (n,n+2), (n+6,n+8) and (n+18,n+20).

This is a subsequence of A132232 (Primes congruent to 11 mod 30 ).

Also, this is a subsequence of A128467 (30k+11).

Examples

			For n = 18041, the numbers, 18041, 18043, 18047, 18049, 18059, 18061, are primes.
		

Links

• Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Twin Primes
• Wikipedia, Twin prime

Crossrefs

Cf. A077800 (twin primes), A030430 (primes,10*n+1), A132232, A128467, A172456.

Programs

Mathematica

Select[Prime[Range[2500]], Union[PrimeQ[{#, # + 2, # + 6, # + 8, # + 18, # + 20}]] = {True} &] (* Alonso del Arte, Dec 23 2014 *)
Select[Prime[Range[450000]],AllTrue[#+{2,6,8,18,20},PrimeQ]&] (* Harvey P. Dale, Jun 11 2023 *)

PARI

forprime(p=1,10^7,if(isprime(p+2) && isprime(p+6) && isprime(p+8) && isprime(p+18) && isprime(p+20), print1(p,", "))) \\ Derek Orr, Dec 31 2014

Python

from sympy import isprime
for n in range(1,10000001,2):
  if isprime(n) and isprime(n+2) and isprime(n+6) and isprime(n+8) and isprime(n+18) and isprime(n+20): print(n,end=', ')