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A243583 Primes p for which p + 4 and p^3 + 4 are primes.

%I A243583 #34 May 22 2025 10:21:38
%S A243583 3,7,19,79,103,109,277,379,487,967,1489,1663,1867,2857,3019,3253,3613,
%T A243583 3697,4003,4783,4969,5413,5437,5503,5569,5647,5923,7477,7669,7687,
%U A243583 7699,7789,7933,8233,8779,9007,9319,9547,9739,10597,11257,11467,11593,11827,12037
%N A243583 Primes p for which p + 4 and p^3 + 4 are primes.
%C A243583 This is a subsequence of:
%C A243583 A023200: Primes p such that p + 4 is also prime.
%C A243583 A073573: Numbers n such that n^3 + 4 is prime.
%H A243583 Abhiram R Devesh, <a href="/A243583/b243583.txt">Table of n, a(n) for n = 1..1000</a>
%e A243583 p = 3 is in this sequence because p + 4 = 7  (prime) and p^3 + 4 = 31 (prime).
%e A243583 p = 7 is in this sequence because p + 4 = 11  (prime) and p^3 + 4 = 347 (prime).
%o A243583 (Python)
%o A243583 import sympy.ntheory as snt
%o A243583 n=2
%o A243583 while n>1:
%o A243583     n1=n+4
%o A243583     n2=((n**3)+4)
%o A243583     ##Check if n1 and n2 are also primes.
%o A243583     if snt.isprime(n1)== True and snt.isprime(n2)== True:
%o A243583         print(n, " , " , n1, " , ", n2)
%o A243583     n=snt.nextprime(n)
%o A243583 (PARI) s=[]; forprime(p=2, 20000, if(isprime(p+4) && isprime(p^3+4), s=concat(s, p))); s \\ _Colin Barker_, Jun 11 2014
%Y A243583 Cf. A023200, A073573.
%K A243583 nonn,easy
%O A243583 1,1
%A A243583 _Abhiram R Devesh_, Jun 09 2014