A236443 Primes which start a Cunningham chain of length 4 where every entity of the chain is smallest of twin prime.

253679, 1138829, 58680929, 90895769, 124253009, 269877299, 392071679, 613813199, 1014342209, 1277981669, 1413015029, 1453978679, 1753585679, 2919331379, 3424037189, 3538972709, 4025789039, 4175762009, 4362439199, 4843208789, 5708418869, 5795508599

Offset: 1

Author

Abhiram R Devesh, Jan 26 2014

Keywords

• nonn

Comments

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

This sequence is infinite under Dickson's conjecture. - Charles R Greathouse IV, Jan 29 2014

Terms are congruent to -1 mod 210. - David Radcliffe, Aug 06 2025

Examples

			a(1)=253679, with associated Cunningham chain 253679, 507359, 1014719, 2029439, all of which are the lower member of a pair of twin primes.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Chris Caldwell, Cunningham chain

Crossrefs

Cf. A178421, A005602, A059763.

Programs

PARI

is(n)=n%210==209 && isprime(n) && isprime(n+2) && isprime(2*n+1) && isprime(2*n+3) && isprime(4*n+3) && isprime(4*n+5) && isprime(8*n+7) && isprime(8*n+9)
forstep(n=419,1e9,[1470, 420, 420],if(is(n),print(n))) \\ Charles R Greathouse IV, Jan 29 2014

Python

from sympy import isprime
def is_A236443(n):
    return (isprime(n) and isprime(n+2) and isprime(2*n+1) and isprime(2*n+3) and
            isprime(4*n+3) and isprime(4*n+5) and isprime(8*n+7) and isprime(8*n+9))
print([n for n in range(209, 10**9, 210) if is_A236443(n)]) # David Radcliffe, Aug 06 2025

Extensions

More terms from T. D. Noe, Jan 29 2014