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Numbers k such that k^k+2 is prime.
6

%I #18 Dec 15 2023 13:53:25

%S 1,3,737,1349

%N Numbers k such that k^k+2 is prime.

%C All terms are odd. Next term is greater than 3500. 1349^1349+2 is a probable prime with length 4223.

%C The next term, if it exists, is greater than 50000. - _Hugo Pfoertner_, Jun 28 2019

%C The next term, if it exists, is greater than 430000. - _Ryan Propper_, Dec 15 2023

%e 737 is in the sequence because 737^737+2 is prime.

%t Do[If[PrimeQ[n^n+2], Print[n]], {n, 3500}]

%o (PARI) is(n)=ispseudoprime(n^n+2) \\ _Charles R Greathouse IV_, May 22 2017

%Y Cf. A100408.

%K more,nonn,hard

%O 1,2

%A _Farideh Firoozbakht_, Nov 19 2004