A329551 Primes p such that 4*p+3, 6*p+5 and 8*p+7 are all primes.

2, 59, 107, 227, 389, 587, 839, 977, 1217, 1259, 1319, 2957, 3947, 4889, 5189, 5519, 6449, 7949, 8039, 8297, 8609, 9467, 11279, 11399, 12119, 13397, 14627, 14969, 15497, 15647, 19709, 22229, 22907, 25847, 27437, 28619, 29759, 30389, 32609, 34877, 36497, 37277, 39857, 40289, 42569, 45779, 46889

Offset

1,1

Comments

All terms but the first == 17 or 29 (mod 30).

Thus the least possible difference between successive terms is 12.

The first terms p such that p+12 is also a term are 3518687, 5412257, 9447017, 10454177, 45093887, 58628777, 94327967.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(4)=227 is a member because 227, 4 * 227 + 3 = 911, 6 * 227 + 5 = 1367, and 8 * 227 + 7 = 1823 are all primes.

Maple

filter:= p -> isprime(p) and isprime(4*p+3) and isprime(6*p+5) and isprime(8*p+7):
select(filter, [2, seq(i, i=5..100000, 6)]);

Mathematica

Select[Prime[Range[5000]], AllTrue[{4#+3, 6#+5, 8#+7}, PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 08 2021 *)

Prog

(Magma) [p:p in PrimesUpTo(50000)|forall{m: m in [-2*p-2, 0, 2*p+2]| IsPrime(6*p+5+m)}]; // Marius A. Burtea, Nov 17 2019

Crossrefs

Contains A107021.

Sequence in context: A232848 A215393 A141869 * A153925 A100273 A138982

Adjacent sequences: A329548 A329549 A329550 * A329552 A329553 A329554

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Nov 16 2019

Status

approved