20161124, 08:26  #1 
Nov 2016
1 Posts 
Are it possible?
How check it formula (8191 + 1) / 4(or any other depending on 8191) , is an remainder of the division division "Lucas  lehtera primality test"?
(4^22)mod 8191=14 (14^22)mod 8191=194 (194^22)mod 8191=4870 (4870^22)mod 8191=3953 (3953^22)mod 8191=5970 (5970^22)mod 8191=1857 (1857^22)mod 8191=36 (36^22)mod 8191=1294 (1294^22)mod 8191=3470 (3470^22)mod 8191=128 (128^22)mod 8191=0 
20161124, 11:52  #2  
Sep 2002
Database er0rr
2^{3}×5×107 Posts 
Quote:
It checks only numbers of the form 2^p1. (We know p must be a prime too.) What you described is the LL test for 2^131 which is 8191, and is prime Last fiddled with by paulunderwood on 20161124 at 11:59 

20161125, 03:31  #3 
Romulan Interpreter
"name field"
Jun 2011
Thailand
10011101101110_{2} Posts 
I think his/her question is "how to check if some number (example: (8191+1)/4=8192/4=2048 given by OP) appears as a residue in the set of some LL test residues" (example LL test for M13 given by OP).
Answer: you can not, unless you do all the LL test "da capo al fine" (from the beginning to the end). If that would be possible, then you would have a "shortcut" to do the LL test in only two iterations, by checking if either (Mp+1)/2 or its negative appears in the residue list. This can only happen if Mp is prime. Last fiddled with by LaurV on 20161125 at 03:33 