A180474 Primes p such that p^5 + p^3 + 1 is a prime.

2, 3, 5, 17, 23, 41, 47, 113, 131, 137, 149, 251, 263, 281, 293, 311, 317, 449, 503, 659, 677, 827, 881, 887, 1409, 1787, 1889, 1913, 2003, 2069, 2081, 2267, 2393, 2531, 2591, 2657, 2729, 3083, 3221, 3329, 3347, 3767, 4001, 4211, 4229, 4583, 4931, 4967, 5333

Offset

1,1

Comments

If n is the index of the sequence member, then there is the following asymptotic behavior of the sequence: n is approximately equal to sqrt(3*k) where k is the prime index so that the number of a(n)'s is the square root of 3 times the number of primes.

Links

Table of n, a(n) for n=1..49.

Example

a(5)=23 since 23^5 + 23^3 + 1 = 6448511 is a prime.

Mathematica

Select[Prime[Range[750]], PrimeQ[#^5+#^3+1]&] (* Harvey P. Dale, Sep 12 2016 *)

Prog

(Magma) [p: p in PrimesUpTo(6000)|IsPrime(p^5+p^3+1)] // Vincenzo Librandi, Jan 29 2011

Crossrefs

Cf. A000040.

Sequence in context: A353153 A121558 A240679 * A155978 A235925 A106859

Adjacent sequences: A180471 A180472 A180473 * A180475 A180476 A180477

Keyword

less,nonn

Author

Carmine Suriano, Sep 07 2010

Status

approved