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

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

Offset: 1

Author

Robert G. Wilson v, Dec 05 2001

Keywords

• nonn
• more

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

• Eric Weisstein's World of Mathematics, Primality Test

Crossrefs

Cf. A058911 (k^k+k+1), A182383 (corresponding primes, including 2 for k=0).

Programs

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}]

PARI

is(n)=ispseudoprime(n^n-n+1) \\ Charles R Greathouse IV, Jun 13 2017

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

Extensions

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