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Primes p of the form k^(2*k) + 1.
0

%I #18 Sep 13 2024 15:57:54

%S 2,17,65537

%N Primes p of the form k^(2*k) + 1.

%C Prime terms from A167436.

%C Also primes p of the form (k^2)^k + 1.

%C Corresponding values of k: 1, 2, 4, ...; if a(4) exists, k must be larger than 1024.

%e 65537 = 4^8 + 1 = 16^4 + 1.

%t Select[Table[n^(2n)+1,{n,20}],PrimeQ] (* _Harvey P. Dale_, Apr 01 2021 *)

%o (Magma) [n^(2*n) + 1: n in [1..700] | IsPrime(n^(2*n) + 1)];

%Y Cf. A121270 (primes of the form k^k + 1), A167436 (n^(2*n) + 1).

%K nonn,bref,hard

%O 1,1

%A _Jaroslav Krizek_, Mar 06 2016