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 Register FAQ Search Today's Posts Mark Forums Read 2016-11-24, 08:26 #1 xsx   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"? (4^2-2)mod 8191=14 (14^2-2)mod 8191=194 (194^2-2)mod 8191=4870 (4870^2-2)mod 8191=3953 (3953^2-2)mod 8191=5970 (5970^2-2)mod 8191=1857 (1857^2-2)mod 8191=36 (36^2-2)mod 8191=1294 (1294^2-2)mod 8191=3470 (3470^2-2)mod 8191=128 (128^2-2)mod 8191=0   2016-11-24, 11:52   #2
paulunderwood

Sep 2002
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23×5×107 Posts Quote:
 Originally Posted by xsx How check it formula (8191 + 1) / 4(or any other depending on 8191) , is an remainder of the division division "Lucas - lehtera primality test"? (4^2-2)mod 8191=14 (14^2-2)mod 8191=194 (194^2-2)mod 8191=4870 (4870^2-2)mod 8191=3953 (3953^2-2)mod 8191=5970 (5970^2-2)mod 8191=1857 (1857^2-2)mod 8191=36 (36^2-2)mod 8191=1294 (1294^2-2)mod 8191=3470 (3470^2-2)mod 8191=128 (128^2-2)mod 8191=0
It's called the "Lucas Lehmer" test.

It checks only numbers of the form 2^p-1. (We know p must be a prime too.)

What you described is the LL test for 2^13-1 which is 8191, and is prime Last fiddled with by paulunderwood on 2016-11-24 at 11:59   2016-11-25, 03:31 #3 LaurV Romulan Interpreter   "name field" Jun 2011 Thailand 100111011011102 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 2016-11-25 at 03:33  Thread Tools Show Printable Version Email this Page

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