A075469 Maximal m such that n^n-m and n^n+m are both primes, or -1 if there is no such m.

1, 20, 253, 3122, 46651, 823540, 16777155, 387420478, 9999999939, 285311670528, 8916100448227, 302875106592216, 11112006825558003, 437893890380859368, 18446744073709551537, 827240261886336764070, 39346408075296537575383

Offset: 2

Author

Lior Manor, Sep 18 2002

Keywords

• nonn

Comments

Are there any negative terms?

Of course the Goldbach conjecture implies that the answer is "no"; further, the first thousand terms are positive. - Charles R Greathouse IV, Mar 16 2016

Examples

			a(4) = 253 since 4^4-253 = 3 and 4^4+253 = 509 are both prime.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 2..386

Crossrefs

Cf. A075468.

Cf. A000312, A047949.

Programs

PARI

a(n)=my(N=n^n); forprime(p=2,N, if(isprime(2*N-p), return(N-p))); -1 \\ Charles R Greathouse IV, Mar 16 2016

Formula

a(n) = A047949(n^n). - Michel Marcus, Jun 09 2013