

A329551


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


1



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
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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)]);


PROG

(MAGMA) [p:p in PrimesUpTo(50000)forall{m: m in [2*p2, 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



