A065797 Numbers k such that k^k - k + 1 is prime.

2, 5, 13, 155, 1551, 1841, 2167, 2560

Offset

1,1

Comments

The Mathematica program tests for probable primality. It is unclear which of the numbers k^k - k + 1 have been proved prime. - Dean Hickerson, Apr 26 2003

The first four terms result from deterministic primality tests, while terms >= 156 currently correspond to probable primes. - Giuseppe Coppoletta, Dec 26 2014

If it exists, a(9) > 32000. - Dmitry Petukhov, Sep 12 2021

Links

Table of n, a(n) for n=1..8.

Eric Weisstein's World of Mathematics, Primality Test

Maple

select(n -> isprime(n^n-n+1), [$1..3000]); # Robert Israel, Dec 29 2014

Mathematica

Do[If[PrimeQ[n^n-n+1], Print[n]], {n, 1, 3000}]

Prog

(Sage) [n for n in (1..155) if (n^n-n+1).is_prime(proof=True)]
# deterministic test
(Sage) [n for n in (1..5000) if (n^n-n+1).is_prime(proof=False)]
# probabilistic test Giuseppe Coppoletta, Dec 26 2014
(PARI) is(n)=ispseudoprime(n^n-n+1) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

Cf. A058911 (n^n+n+1).

Sequence in context: A241248 A275698 A186450 * A196273 A128772 A272106

Adjacent sequences: A065794 A065795 A065796 * A065798 A065799 A065800

Keyword

nonn,more

Author

Robert G. Wilson v, Dec 05 2001

Extensions

More terms from John Sillcox (JMS21187(AT)aol.com), Apr 23 2003

Status

approved