A233540 Primes p such that p+2, p+8, and p+12 are all prime.

5, 11, 29, 59, 71, 101, 269, 431, 1289, 1481, 2129, 2339, 2381, 2789, 4721, 5519, 5639, 5849, 6569, 6959, 8999, 10091, 13679, 14549, 16061, 16649, 16691, 18119, 19379, 19421, 19751, 21011, 21491, 22271, 25931, 27689, 27791, 28619, 31181, 32369, 32561, 32831

Offset: 1

Author

K. D. Bajpai, Dec 12 2013

Keywords

• nonn

Comments

The primes produced (p, p+2, p+8, p+12) are not always consecutive primes.

Examples

			29 is in the sequence because 29, 29 + 2 = 31, 29 + 8 = 37, and 29 + 12 = 41 are all prime.
		

Links

• Michael B. Porter, Table of n, a(n) for n = 1..2300

Crossrefs

Cf. A007530 (prime quadruples).

Cf. A078848 (same prime differences, but with consecutive primes).

Programs

Maple

KD := proc() local a,b,c,p; p:=ithprime(n);a:=p+2;b:=p+8;c:=p+12;if isprime(a)and isprime(b) and isprime(c) then RETURN (p); fi; end: seq(KD(), n=1..10000);
# K. D. Bajpai, Dec 27 2013

Mathematica

Select[Prime[Range[4000]],AllTrue[#+{2,8,12},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 04 2016 *)

PARI

is_a233540(p) = isprime(p) && isprime(p+2) && isprime(p+8) && isprime(p+12) \\ Michael B. Porter, Dec 27 2013

Formula

A046141 INTERSECT A046134. - R. J. Mathar, Aug 20 2019