login
Numbers k such that 239*2^k+1 is prime.
0

%I #29 Mar 18 2022 07:25:24

%S 1,3,5,7,17,29,31,89,135,229,257,305,493,781,811,1177,1315,1709,2267,

%T 5283,6109,7763,7923,16481,18457,29187,39487,53393,59905,76267,109325,

%U 278595,307745,547433,651413,1072433,1936025,2076663

%N Numbers k such that 239*2^k+1 is prime.

%H Ray Ballinger, <a href="http://www.prothsearch.com/index.html">Proth Search Page</a>

%H Ray Ballinger and Wilfrid Keller, <a href="http://www.prothsearch.com/riesel1.html">List of primes k.2^n + 1 for k < 300</a>

%H Wilfrid Keller, <a href="http://www.prothsearch.com/riesel2.html">List of primes k*2^n - 1 for k < 300</a>

%H <a href="/index/Pri#riesel">Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime</a>

%t Select[Range[1000], PrimeQ[239*2^# + 1] & ] (* _Robert Price_, Dec 20 2018 *)

%o (PARI) is(n)=ispseudoprime(239*2^n+1) \\ _Charles R Greathouse IV_, Jun 13 2017

%K nonn,hard,more

%O 1,2

%A _N. J. A. Sloane_.

%E a(30)-a(38) from the Ray Ballinger and Wilfrid Keller link by _Robert Price_, Dec 20 2018

%E a(39) from _Jeppe Stig Nielsen_, May 30 2020

%E Duplicate term a(29)=59905 removed by _Georg Fischer_, Mar 18 2022