A291464 - OEIS

%I #14 Sep 11 2023 13:13:53

%S 2,11,13,41,97,277,389,1093,1229,1409,1429,1627,1823,1931,1979,2437,

%T 2521,2549,2657,2689,2719,2729,2731,2969,3019,3413,3539,3593,3613,

%U 3623,3697,4003,4027,4289,4327,4583,4751,5051,5323,5503,5657,5783,6143,6221,6299,6329

%N Primes p such that p^3*q^3 + p^2 + q^2 is prime, where q is next prime after p.

%H Robert Israel, <a href="/A291464/b291464.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1) = 2 is prime; 3 is the next prime: 2^3*3^3 + 2^2 + 3^2 = 8*27 + 4 + 9 = 229 that is a prime.

%e a(2) = 11 is prime; 13 is the next prime: 11^3*13^3 + 11^2 + 13^2 = 1331*2197 + 121 + 169 = 2924497 that is a prime.

%p select(p -> andmap(isprime,[p,(p^3*nextprime(p)^3+p^2+nextprime(p)^2)]), [seq(p, p=1..10^4)]);

%t Select[Prime[Range[5000]], PrimeQ[#^3*NextPrime[#]^3 + #^2 + NextPrime[#]^2] &]

%t Select[Partition[Prime[Range[1000]],2,1],PrimeQ[#[[1]]^3 #[[2]]^3+#[[1]]^2+#[[2]]^2]&][[;;,1]] (* _Harvey P. Dale_, Sep 11 2023 *)

%o (PARI) forprime(p=1, 5000, q=nextprime(p+1); p3=p^3; p2=p^2; q3=q^3; q2=q^2; if(ispseudoprime(p3*q3 + p2 + q2), print1(p, ", ")));

%o (Magma) [p: p in PrimesUpTo(5000) | IsPrime(p^3*q^3 + p^2 + q^2) where q is NextPrime(p)];

%Y Cf. A000040, A001043, A006094, A030078, A096342, A120398, A126148, A152241, A291339, A291374.

%K nonn

%O 1,1

%A _K. D. Bajpai_, Aug 24 2017