A120480 Primes of the form k^5 + k^2 + 1.

3, 37, 32833, 3200401, 14349637, 52523101, 130692997, 254806273, 459167941, 2706790087, 3486790963, 3939047533, 10510110703, 12762826651, 14025528757, 14693292433, 16850593873, 23863550761, 34359754753, 38579506813

Offset: 1

Author

Jonathan Vos Post, Jul 21 2006

Keywords

• easy
• nonn

Comments

The values of k such that k^5 + k^2 + 1 is prime are 1, 2, 8, 20, 27, 35, 42, 48, 54, 77, 81, 83, 101, 105, 107, 108, 111, 119, 128, 131. Little is known about primality in quintic forms.

Examples

			a(1) = 3 = 1^5 + 1^2 + 1.
a(2) = 37 = 2^5 + 2^2 + 1.
a(3) = 132833 = 8^5 + 8^2 + 1.
a(4) = 3200401 = 20^5 + 20^2 + 1.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A000040.

Programs

Magma

[a: n in [0..160] | IsPrime(a) where a is n^5+n^2+1 ]; // Vincenzo Librandi, Dec 22 2010

Mathematica

Select[Table[k^5+k^2+1,{k,150}],PrimeQ] (* Harvey P. Dale, Oct 29 2020 *)