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

11, 17, 41, 43, 47, 137, 313, 359, 389, 401, 491, 557, 577, 709, 757, 829, 863, 929, 937, 953, 1129, 1163, 1249, 1301, 1307, 1439, 1597, 1627, 1693, 1847, 2087, 2311, 2351, 2437, 2663, 2731, 2741, 3109, 3119, 3217, 3253, 4027, 4219, 4271, 4547, 4637, 5189, 5237

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

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.
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.

Maple

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

Mathematica

Prime@Select[Range[1000], PrimeQ[Prime[#]^3* Prime[# + 1]^3 + Prime[#] + Prime[# + 1]] &]

Prog

(PARI) forprime(p=1, 5000, q=nextprime(p+1); if(ispseudoprime(p^3*q^3 + p + q), print1(p, ", ")));
(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
(Magma) [p: p in PrimesUpTo(5000) | IsPrime(p^3*q^3 + p + q) where q is NextPrime(p)];

Crossrefs

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

Sequence in context: A317678 A098649 A078872 * A181421 A290530 A163387

Adjacent sequences: A291371 A291372 A291373 * A291375 A291376 A291377

Keyword

nonn

Author

K. D. Bajpai, Aug 23 2017

Status

approved