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A352170 Primes p such that p+4, 3*p+4 and 3*p+8 are also prime.

%I A352170 #13 Mar 09 2022 09:08:17
%S A352170 3,13,103,223,823,2953,7873,11113,11863,13033,13963,16063,22153,23743,
%T A352170 24763,27733,30133,31513,34213,35593,39883,41893,43063,50383,51043,
%U A352170 54493,62983,65323,66343,68473,71593,72643,87793,88423,98893,101203,106363,110563,127873,134593,136603,158563,164623,165703
%N A352170 Primes p such that p+4, 3*p+4 and 3*p+8 are also prime.
%C A352170 Members p of A023200 such that 3*p+4 is also in A023200.
%C A352170 Except for 3, all terms == 13 (mod 30).
%H A352170 Martin Ehrenstein, <a href="/A352170/b352170.txt">Table of n, a(n) for n = 1..10000</a>
%e A352170 a(4) = 223 is a term because 223, 223+4 = 227, 3*223+4 = 673 and 3*223+8 = 677 are all prime.
%p A352170 select(p -> isprime(p) and isprime(p+4) and isprime(3*p+4) and isprime(3*p+8), [3,seq(i,i=13..10^6,30)]);
%t A352170 Select[Range[200000], AllTrue[{#, # + 4, 3*# + 4, 3*# + 8}, PrimeQ] &] (* _Amiram Eldar_, Mar 07 2022 *)
%o A352170 (Python)
%o A352170 from sympy import sieve, isprime
%o A352170 for p in sieve.primerange(0, 10**6):
%o A352170     if(all(isprime(q) for q in [p+4, 3*p+4, 3*p+8])):
%o A352170         print (p, end=", ") # _Martin Ehrenstein_, Mar 09 2022
%Y A352170 Intersection of A023200, A023209 and A023210.
%K A352170 nonn
%O A352170 1,1
%A A352170 _J. M. Bergot_ and _Robert Israel_, Mar 07 2022