A237017 Primes which start a Cunningham chain of length 4 where every entity of the chain is smallest of the prime number pair (p, p+8).

359, 1069199, 1392269, 2614169, 10528649, 16981379, 18287309, 19463519, 21071489, 21171509, 22121579, 24857639, 40887569, 41809259, 76130129, 88362479, 118136279, 128893049, 131612609, 153318449, 289743689, 315495539

Offset: 1

Author

Abhiram R Devesh, Feb 02 2014

Keywords

• nonn

Comments

a(n) generates a Cunningham chain of length 4 and a_n(i) + 8 is also prime for i = 1,2,3 and 4.

This sequence is infinite under Dickson's conjecture.

Examples

			a(1)=359, with associated Cunningham chain 359, 719, 1439, 2879; all of which are the lower member of a pair (p, p+8): (359,367), (719,727), (1439,1447), (2879,2887).
		

Links

• Chris K. Caldwell, Cunningham chain

Crossrefs

Cf. A236443, A178421, A005602, A059763.

Programs

Python

from sympy import isprime, primerange
is_a237017 = lambda p: all(isprime(q) for q in (p+8, 2*p+1, 2*p+9, 4*p+3, 4*p+11, 8*p+7, 8*p+15))
print(*[p for p in primerange(10**7) if is_a237017(p)], sep=', ')
# David Radcliffe, May 11 2025