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
Keywords
Examples
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.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Programs
-
Magma
[p: p in PrimesUpTo(5000) | IsPrime(p^3*q^3 + p + q) where q is NextPrime(p)];
-
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]] &]
-
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