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Numbers k such that 321*2^k+1 is prime.
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%I #10 Dec 20 2024 10:48:52

%S 1,5,32,68,109,128,133,212,241,653,776,1339,1787,2659,6388,6547,8365,

%T 16699,62861,64795,83227,195376,278875,442480,542876,730321,1168576,

%U 1257859,1629307,4715725

%N Numbers k such that 321*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/riesel1a.html">List of primes k.2^n + 1 for 300 < k < 600</a>

%H Y. Gallot, <a href="http://www.utm.edu/research/primes/programs/gallot/index.html">Proth.exe: Windows Program for Finding Large Primes</a>

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ProthPrime.html">Proth Prime</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>

%p select(n->isprime(321*2^n+1),[$1..1000]); # _Muniru A Asiru_, Dec 31 2018

%t Select[Range[1000], PrimeQ[321*2^# + 1] &] (* _Robert Price_, Dec 31 2018 *)

%Y Cf. A002255, A050527.

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Dec 31 2018

%E a(30) from _Jeppe Stig Nielsen_, Dec 20 2024