20090205, 16:26  #1 
Jan 2009
Ireland
2×3×31 Posts 
LucasLehmer
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:
Thanks 
20090205, 16:32  #2  
Nov 2008
2×3^{3}×43 Posts 
Quote:
(14) mod 2047 = 14 Do you understand what "mod" means? (And it's not "moderator" in this case.) 

20090205, 16:44  #3 
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 112 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 4^22,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 20090205 at 16:49 
20090205, 17:14  #4  
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
3·37·47 Posts 
Quote:


20090205, 17:25  #5 
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 20090205 at 18:13 
20090205, 18:19  #6 
Jun 2003
7·167 Posts 
You have it backwards. 14 mod 2047 is the remainder of 14/2047.
Last fiddled with by Mr. P1 on 20090205 at 18:19 
20090205, 19:05  #7 
Jan 2009
Ireland
2×3×31 Posts 
sorry,thats what i meant,i understand it now,just not the riesel version of it.

20090205, 20:40  #8  
"Richard B. Woods"
Aug 2002
Wisconsin USA
1E0C_{16} Posts 
Quote:
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 20090205 at 20:44 

20090206, 00:05  #9 
Jan 2009
Ireland
272_{8} 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. 
20090206, 10:25  #10 
Einyen
Dec 2003
Denmark
6426_{8} Posts 
M11:
S_{0}=4 S_{1}=(4^{2}2) mod 2047 = 14 mod 2047 = 14 S_{2}=(14^{2}2) mod 2047 = 194 mod 2047 = 194 S_{3}=(194^{2}2) mod 2047 = 37634 mod 2047 = 788 S_{4}=(788^{2}2) mod 2047 = 620942 mod 2047 = 701 S_{5}=(701^{2}2) mod 2047 = 491399 mod 2047 = 119 S_{6}=(119^{2}2) mod 2047 = 14159 mod 2047 = 1877 S_{7}=(1877^{2}2) mod 2047 = 3523127 mod 2047 = 240 S_{8}=(240^{2}2) mod 2047 = 57598 mod 2047 = 282 S_{9}=(282^{2}2) mod 2047 = 79522 mod 2047 = 1736 Since S_{n2}=S_{9} != 0 then M11 is not prime. 
Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
LucasLehmer Primes  henryzz  And now for something completely different  42  20190603 14:09 
LucasLehmer test  Mathsgirl  Information & Answers  23  20141210 16:25 
lucaslehmer theorem  Robot2357  Math  6  20130615 03:10 
lucas lehmer outstretch  science_man_88  Miscellaneous Math  7  20100714 12:35 
LucasLehmer Test  storm5510  Math  22  20090924 22:32 