A253624 Initial members of prime sextuples (p, p+2, p+12, p+14, p+24, p+26).

5, 17, 1277, 4217, 21587, 91127, 103967, 113147, 122027, 236867, 342047, 422087, 524957, 560477, 626597, 754967, 797567, 909317, 997097, 1322147, 1493717, 1698857, 1748027, 1762907, 2144477, 2158577, 2228507, 2398157, 2580647, 2615957

Offset: 1

Author

Karl V. Keller, Jr., Jan 06 2015

Keywords

• nonn

Comments

This sequence is primes p for which there exist three twin prime pairs (p, p+2), (p+12, p+14) and (p+24, p+26).

Excluding 5, this is a subsequence of each of the following: A128468 (a(n)=30n+17). A039949 (Primes of the form 30n-13), A181605 (twin primes ending in 7).

Note that not in all cases (p, p+2, p+12, p+14, p+24, p+26) are consecutive primes; the first p's for which (p, p+2, p+12, p+14, p+24, p+26) are consecutive primes are 4217, 21587, 91127, 103967, 236867, 342047, 422087, 560477, 797567, 909317, 1322147, 1493717, 1748027, 1762907, 2144477, 2158577, 2228507, 2615957 (not in OEIS). - Zak Seidov, May 16 2017

Examples

			For p = 17, the numbers 17, 19, 29, 31, 41, 43 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), A128468, A039949, A181605.

Programs

Maple

select(t -> andmap(isprime, [t,t+2,t+12,t+14,t+24,t+26]),
[5, seq(30*k+17,k=0..10^5)]); # Robert Israel, Jan 07 2015

Mathematica

Select[Prime@ Range[2*10^5], Times @@ Boole@ PrimeQ[# + {2, 12, 14, 24, 26}] == 1 &] (* Michael De Vlieger, May 16 2017 *)
Select[Prime[Range[200000]],AllTrue[#+{2,12,14,24,26},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 15 2021 *)

Python

from sympy import isprime
for n in range(1,10000001,2):
  if isprime(n) and isprime(n+2) and isprime(n+12) and isprime(n+14) and isprime(n+24) and isprime(n+26): print(n,end=', ')

Python

from sympy import isprime, primerange
def aupto(limit):
  alst = []
  for p in primerange(2, limit+1):
    if all(map(isprime, [p+2, p+12, p+14, p+24, p+26])): alst.append(p)
  return alst
print(aupto(3*10**6)) # Michael S. Branicky, May 17 2021