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

2,2

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

Links

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

Formula

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

Example

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

Prog

(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

Crossrefs

Cf. A075468.

Sequence in context: A218101 A241228 A306290 * A028032 A348055 A025986

Adjacent sequences: A075466 A075467 A075468 * A075470 A075471 A075472

Keyword

nonn

Author

Lior Manor, Sep 18 2002

Status

approved