A121616 - OEIS (original) (raw)

31, 211, 4651, 61051, 371281, 723901, 1803001, 2861461, 4329151, 4925281, 7086451, 7944301, 14835031, 19611901, 23382031, 44119351, 54664711, 86548801, 97792531, 162478501, 189882031, 267217051, 293109961, 306740281, 490099501

COMMENTS

Might be called "Pentan primes" (in analogy with Cuban primes, of the form (n+1)^3-n^3), or "Nexus primes of order 5" (cf. link below).

Indices k such that Nexus number of order 5 (or A022521(k-1) = k^5 - (k-1)^5) is prime are listed in A121617 = {2, 3, 6, 11, 17, 20, 25, 28, 31, 32, 35, 36, 42, 45, 47, 55, 58, 65, 67, 76, 79, 86, 88, 89, 100,...}.

The last digit is always 1 because 5 is the Pythagorean prime A002144(1). a(1) = 31 is the Mersenne prime A000668(3).

MATHEMATICA

Select[Table[n^5 - (n-1)^5, {n, 1, 200}], PrimeQ]

Select[Differences[Range[100]^5], PrimeQ] (* Harvey P. Dale, Nov 03 2021 *)

PROG

(Magma) [a: n in [0..110] | IsPrime(a) where a is (n+1)^5-n^5]; // Vincenzo Librandi, Jan 20 2020