login
Numbers k such that 1 + 8*10^k + 100^k is prime.
4

%I #27 Jun 30 2024 11:21:33

%S 1,3,6,9,13,17,29,63,90,531,14286,30617,37815

%N Numbers k such that 1 + 8*10^k + 100^k is prime.

%C No more terms up to k = 7500.

%C 14286, 30617, and 37815, found by Daniel Heuer in 2001-2002, are also terms; see Caldwell link. - _Jeppe Stig Nielsen_, Jan 30 2022

%H Chris K. Caldwell, <a href="https://primes.utm.edu/primes/search.php?Description=%5E10%5E%25%2B8*10%5E%25%2B1&amp;OnList=all&amp;Number=20&amp;Style=HTML">Prime Pages, Database Search Output</a>

%t Select[Range[1000], PrimeQ[1 + 8 10^# + 100^# ] &] (* _Vincenzo Librandi_, Apr 26 2014 *)

%o (PARI) is(n)=ispseudoprime(1+8*10^n+100^n) \\ _Charles R Greathouse IV_, Jun 13 2017

%Y Cf. A171376, A171411, A171459, A171554.

%K more,hard,nonn

%O 1,2

%A _Jason Earls_, Dec 10 2009

%E a(11)-a(13) from _Lucas A. Brown_, Mar 04 2024