A115349 Numbers k such that (4*k^5 + 1) is prime.

1, 12, 15, 19, 27, 40, 49, 57, 60, 90, 93, 102, 132, 133, 147, 148, 153, 177, 190, 219, 240, 249, 258, 265, 274, 277, 280, 294, 313, 324, 337, 342, 363, 382, 394, 435, 448, 453, 462, 483, 489, 502, 522, 534, 538, 550, 580, 588, 609, 613, 634, 643, 648, 649

Offset: 1

Author

Parthasarathy Nambi, Mar 07 2006

Keywords

• nonn
• easy

Examples

			If k=90 then (4*90^5 + 1) = 23619600001, which is prime.
If k=133 then (4*133^5 + 1) = 166463183573, which is prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A115104, A001912.

Programs

Magma

[n: n in [0..1500] | IsPrime(4*n^5 + 1)]; // Vincenzo Librandi, Jan 31 2011

Maple

select(t -> isprime(4*t^5+1), [$1..1000]); # Robert Israel, Jun 19 2018

Mathematica

Do[If[PrimeQ[4*n^5 + 1], Print[n]], {n, 0, 1000}]
Select[Range[700],PrimeQ[4#^5+1]&] (* Harvey P. Dale, Aug 25 2023 *)

PARI

is(n)=isprime((4*n^5+1)) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

More terms from Craig Baribault (csb166(AT)psu.edu), Mar 14 2006 and Jessica M. Cornwall (jmc510(AT)psu.edu), Mar 22 2006