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A291374 Primes p such that p^3*q^3 + p + q is prime, where q is next prime after p.

%I A291374 #10 Sep 08 2022 08:46:19
%S A291374 11,17,41,43,47,137,313,359,389,401,491,557,577,709,757,829,863,929,
%T A291374 937,953,1129,1163,1249,1301,1307,1439,1597,1627,1693,1847,2087,2311,
%U A291374 2351,2437,2663,2731,2741,3109,3119,3217,3253,4027,4219,4271,4547,4637,5189,5237
%N A291374 Primes p such that p^3*q^3 + p + q is prime, where q is next prime after p.
%H A291374 Charles R Greathouse IV, <a href="/A291374/b291374.txt">Table of n, a(n) for n = 1..10000</a>
%e A291374 a(1) = 11 is prime; 13 is the next prime: 11^3*13^3 + 11 + 13 = 1331*2197 + 11 + 13 = 2924231 that is a prime.
%e A291374 a(2) = 17 is prime; 19 is the next prime: 17^3*19^3 + 17 + 19 = 4913*6859 + 17 + 19 = 33698303 that is a prime.
%p A291374 select(p -> andmap(isprime, [p,(p^3*nextprime(p)^3+p+nextprime(p))]), [seq(p,p=1..10^4)]);
%t A291374 Prime@Select[Range[1000], PrimeQ[Prime[#]^3* Prime[# + 1]^3 + Prime[#] + Prime[# + 1]] &]
%o A291374 (PARI) forprime(p=1,5000, q=nextprime(p+1); if(ispseudoprime(p^3*q^3 + p + q), print1(p, ", ")));
%o A291374 (PARI) list(lim)=my(v=List(),p=2,p3=8,q3); forprime(q=3,nextprime(lim\1+1), q3=q^3; if(isprime(p3*q3+p+q), listput(v,p)); p=q; p3=q3); Vec(v) \\ _Charles R Greathouse IV_, Aug 23 2017
%o A291374 (Magma) [p: p in PrimesUpTo(5000) | IsPrime(p^3*q^3 + p + q) where q is NextPrime(p)];
%Y A291374 Cf. A000040, A001043, A006094, A030078, A096342, A120398, A126148, A152241, A291339.
%K A291374 nonn
%O A291374 1,1
%A A291374 _K. D. Bajpai_, Aug 23 2017