A248523 Initial members of prime quadruples (n, n+2, n+144, n+146).

5, 137, 1787, 1997, 2237, 2657, 3527, 4127, 4337, 4787, 8087, 12107, 13757, 14447, 17987, 19697, 21377, 23057, 23687, 31247, 32297, 34157, 34367, 35447, 37547, 38567, 39227, 43397, 48677, 51197, 51827, 53087, 58907, 65027, 65837

Offset: 1

Author

Karl V. Keller, Jr., Jan 11 2015

Keywords

• nonn

Comments

This sequence is prime n, where there exist two twin prime pairs of (n,n+2), (n+144,n+146).

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

Examples

			For n=137, the numbers 137, 139, 281, 283, are primes.
		

Links

• Karl V. Keller, Jr., Table of n, a(n) for n = 1..100000
• Eric Weisstein's World of Mathematics, Prime Quadruplet.
• Eric Weisstein's World of Mathematics, Twin Primes
• Wikipedia, Twin prime

Crossrefs

Cf. A077800 (twin primes), A128468, A039949, A181605.

Programs

Python

from sympy import isprime
for n in range(1,10000001,2):
    if isprime(n) and isprime(n+2) and isprime(n+144) and isprime(n+146): print(n,end=', ')