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 2009-02-05, 16:26 #1 Dougal     Jan 2009 Ireland 2×3×31 Posts Lucas-Lehmer Can someone please explain the test to me because i dont understand it properly.For example M3, works like this, (4^2)-2 mod 7, so thats 14/7=2,no remainder,so its prime But wikipedia shows this On the other hand, M11 = 2047 = 23 × 89 is not prime. To show this, we start with s set to 4 and update it 11−2 = 9 times, taking the results mod 2047:s ← ((4 × 4) − 2) mod 2047 = 14 What i dont understand is where the 14 comes from Thanks
2009-02-05, 16:32   #2
10metreh

Nov 2008

2×33×43 Posts

Quote:
 Originally Posted by Dougal Can someone please explain the test to me because i dont understand it properly.For example M3, works like this, (4^2)-2 mod 7, so thats 14/7=2,no remainder,so its prime But wikipedia shows this On the other hand, M11 = 2047 = 23 × 89 is not prime. To show this, we start with s set to 4 and update it 11−2 = 9 times, taking the results mod 2047:s ← ((4 × 4) − 2) mod 2047 = 14 What i dont understand is where the 14 comes from Thanks
((4 x 4) - 2) = 14
(14) mod 2047 = 14

Do you understand what "mod" means? (And it's not "moderator" in this case.)

 2009-02-05, 16:44 #3 Dougal     Jan 2009 Ireland 2×3×31 Posts i checked it on wikipedia and it said something about A mod N means the remainder of a/n.so what i thought it meant was 2047/14 and the remainder was 14,but that isnt possible,however i understand it now,its (4^2)-2=14,then you do this 11-2 times and when you get that far if,lets say x doesnt divide 2047 evenly then the number isnt prime.would that be right?(if you can make any sense out of my rambling).for mersenne numbers,you start with 4^2-2,how do you get the starting number for the llr test? Actually i looked further through it and it appears i still dont have a clue Thanks Last fiddled with by Dougal on 2009-02-05 at 16:49
2009-02-05, 17:14   #4
petrw1
1976 Toyota Corona years forever!

"Wayne"
Nov 2006

3·37·47 Posts

Quote:
 Originally Posted by Dougal Actually i looked further through it and it appears i still dont have a clue Thanks
Does George's example here help: http://www.mersenne.org/various/math.php

 2009-02-05, 17:25 #5 Dougal     Jan 2009 Ireland 2×3×31 Posts Sorry petrw1,doesnt seem to help much,maybe if i understood mod i'd understand it.Thanks anyway.i've done alot of messing about on a calculator and i now understand it.dont understand how you find out what number you start of with for llr. Last fiddled with by Dougal on 2009-02-05 at 18:13
2009-02-05, 18:19   #6
Mr. P-1

Jun 2003

7·167 Posts

Quote:
 Originally Posted by Dougal i thought it meant was 2047/14 and the remainder was 14
You have it backwards. 14 mod 2047 is the remainder of 14/2047.

Last fiddled with by Mr. P-1 on 2009-02-05 at 18:19

 2009-02-05, 19:05 #7 Dougal     Jan 2009 Ireland 2×3×31 Posts sorry,thats what i meant,i understand it now,just not the riesel version of it.
2009-02-05, 20:40   #8

"Richard B. Woods"
Aug 2002
Wisconsin USA

1E0C16 Posts

Quote:
 Originally Posted by Dougal sorry,thats what i meant,i understand it now,just not the riesel version of it.
I advise you, as a beginner, to just skip the parts about Riesel or LLR and not worry about it.

GIMPS is concerned with Mersenne (that's the "M" in "GIMPS"!) numbers. Riesel numbers are something else; some folks in GIMPS may also be interested in Riesel numbers, but there's no "R" in "GIMPS", so it's a side subject.

(There is a connection between Mersenne numbers and Riesel numbers ... but there are connections between all numbers!!)

Last fiddled with by cheesehead on 2009-02-05 at 20:44

 2009-02-06, 00:05 #9 Dougal     Jan 2009 Ireland 2728 Posts Thanks cheesehead(i think). Well if you think it would be a bit advanced for me then il leave it a while,But if anyones willing to try teach me id appreciate it.
 2009-02-06, 10:25 #10 ATH Einyen     Dec 2003 Denmark 64268 Posts M11: S0=4 S1=(42-2) mod 2047 = 14 mod 2047 = 14 S2=(142-2) mod 2047 = 194 mod 2047 = 194 S3=(1942-2) mod 2047 = 37634 mod 2047 = 788 S4=(7882-2) mod 2047 = 620942 mod 2047 = 701 S5=(7012-2) mod 2047 = 491399 mod 2047 = 119 S6=(1192-2) mod 2047 = 14159 mod 2047 = 1877 S7=(18772-2) mod 2047 = 3523127 mod 2047 = 240 S8=(2402-2) mod 2047 = 57598 mod 2047 = 282 S9=(2822-2) mod 2047 = 79522 mod 2047 = 1736 Since Sn-2=S9 != 0 then M11 is not prime.

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