login
Numbers k such that 100^k - 99^k is prime.
89

%I #24 Oct 22 2024 03:19:29

%S 2,5,19,59,1013,2371,13967,44683

%N Numbers k such that 100^k - 99^k is prime.

%C Terms > 10000 correspond to probable primes.

%C a(9) > 10^5. - _Robert Price_, Jul 10 2013

%t lst={}; k=100; Do[If[PrimeQ[k^n-(k-1)^n], Print[n]; AppendTo[lst, n]], {n, 10^5}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Aug 26 2008 *)

%o (PARI) forprime(p=2,1e5,if(ispseudoprime(100^p-99^p),print1(p", "))) \\ _Charles R Greathouse IV_, Jun 10 2011

%Y Cf. A000043, A057468, A059801, A059802, A062572-A062665.

%K nonn,hard

%O 1,1

%A _Mike Oakes_, May 18 2001, May 19 2001

%E Edited by _T. D. Noe_, Oct 30 2008

%E a(7)-a(8) from _Robert Price_, Jul 10 2013