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

%I A329551 #24 Sep 08 2022 08:46:24
%S A329551 2,59,107,227,389,587,839,977,1217,1259,1319,2957,3947,4889,5189,5519,
%T A329551 6449,7949,8039,8297,8609,9467,11279,11399,12119,13397,14627,14969,
%U A329551 15497,15647,19709,22229,22907,25847,27437,28619,29759,30389,32609,34877,36497,37277,39857,40289,42569,45779,46889
%N A329551 Primes p such that 4*p+3, 6*p+5 and 8*p+7 are all primes.
%C A329551 All terms but the first == 17 or 29 (mod 30).
%C A329551 Thus the least possible difference between successive terms is 12.
%C A329551 The first terms p such that p+12 is also a term are 3518687, 5412257, 9447017, 10454177, 45093887, 58628777, 94327967.
%H A329551 Robert Israel, <a href="/A329551/b329551.txt">Table of n, a(n) for n = 1..10000</a>
%e A329551 a(4)=227 is a member because 227, 4 * 227 + 3 = 911, 6 * 227 + 5 = 1367, and 8 * 227 + 7 = 1823 are all primes.
%p A329551 filter:= p -> isprime(p) and isprime(4*p+3) and isprime(6*p+5) and isprime(8*p+7):
%p A329551 select(filter, [2, seq(i,i=5..100000, 6)]);
%t A329551 Select[Prime[Range[5000]],AllTrue[{4#+3,6#+5,8#+7},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jun 08 2021 *)
%o A329551 (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
%Y A329551 Contains A107021.
%K A329551 nonn
%O A329551 1,1
%A A329551 _J. M. Bergot_ and _Robert Israel_, Nov 16 2019