mersenneforum.org  

Go Back   mersenneforum.org > Extra Stuff > Miscellaneous Math

Reply
 
Thread Tools
Old 2010-07-11, 13:29   #1
science_man_88
 
science_man_88's Avatar
 
"Forget I exist"
Jul 2009
Dumbassville

26·131 Posts
Default lucas lehmer outstretch

I was told to post on the forum instead of annoying CRGreathouse. so here I am
basically i wan't to find a way to easily connect certain p values with s in a new way.

s2-2 =k*2p-1
(s2-2)/k + 1 = 2p


p=log2((s2-2)/k + 1)

this works for s(n-1) can we figure out a generalisation for any amount of n change ? if so can we apply it easily and can anyone get the log2() part reduced more ?
science_man_88 is offline   Reply With Quote
Old 2010-07-11, 13:34   #2
retina
Undefined
 
retina's Avatar
 
"The unspeakable one"
Jun 2006
My evil lair

22×1,531 Posts
Default

Quote:
Originally Posted by science_man_88 View Post
s2-2 =k*2p-1
(s2-2)/k + 1 = 2p
Where did you learn your algebra? I'd ask for my money back if I was you.
retina is online now   Reply With Quote
Old 2010-07-11, 14:03   #3
CRGreathouse
 
CRGreathouse's Avatar
 
Aug 2006

32·5·7·19 Posts
Default

There's an arithmetic error in your post.

Quote:
Originally Posted by science_man_88 View Post
this works for s(n-1) can we figure out a generalisation for any amount of n change ? if so can we apply it easily and can anyone get the log2() part reduced more ?
I don't understand your goal here. What does "for any amount of n change" mean? What does "get the log2() part reduced more" mean?
CRGreathouse is offline   Reply With Quote
Old 2010-07-11, 16:08   #4
science_man_88
 
science_man_88's Avatar
 
"Forget I exist"
Jul 2009
Dumbassville

26·131 Posts
Default

Quote:
Originally Posted by CRGreathouse View Post
There's an arithmetic error in your post.



I don't understand your goal here. What does "for any amount of n change" mean? What does "get the log2() part reduced more" mean?
I can't find the error you talk of, and if it's truly incorrect then why care for either answer.

sorry log2(2^p)

Last fiddled with by science_man_88 on 2010-07-11 at 16:09
science_man_88 is offline   Reply With Quote
Old 2010-07-11, 16:14   #5
science_man_88
 
science_man_88's Avatar
 
"Forget I exist"
Jul 2009
Dumbassville

838410 Posts
Default

s2-2 =k*(2p-1) =correction
(s2-2)/k =2p-1
((s2-2)/k)+1 =2p
log2(((s2-2)/k)+1) =p

Last fiddled with by science_man_88 on 2010-07-11 at 16:15
science_man_88 is offline   Reply With Quote
Old 2010-07-11, 16:20   #6
science_man_88
 
science_man_88's Avatar
 
"Forget I exist"
Jul 2009
Dumbassville

100000110000002 Posts
Default

Quote:
Originally Posted by CRGreathouse View Post
There's an arithmetic error in your post.



I don't understand your goal here. What does "for any amount of n change" mean? What does "get the log2() part reduced more" mean?
the n change part means for any s within the sequence (so for 2^5-1 instead of using the 5th one in the sequence; n=4 as n=0 for the first; I could try and use a lower number.) the reason a wanted the log2(((s2-2)/k)+1) reduced is to get a lower comparison of s and p. like p*k isn't that big compared with k*2^p-1 same idea in reducing the log.
science_man_88 is offline   Reply With Quote
Old 2010-07-13, 00:16   #7
science_man_88
 
science_man_88's Avatar
 
"Forget I exist"
Jul 2009
Dumbassville

26·131 Posts
Default

Quote:
Originally Posted by science_man_88 View Post
the n change part means for any s within the sequence (so for 2^5-1 instead of using the 5th one in the sequence; n=4 as n=0 for the first; I could try and use a lower number.) the reason a wanted the log2(((s2-2)/k)+1) reduced is to get a lower comparison of s and p. like p*k isn't that big compared with k*2^p-1 same idea in reducing the log.
s=4;*
science_man_88 is offline   Reply With Quote
Old 2010-07-14, 12:35   #8
science_man_88
 
science_man_88's Avatar
 
"Forget I exist"
Jul 2009
Dumbassville

26·131 Posts
Default

log2(((s^4 - 4*s^2 + 2)/k)+1) = p is the next one up. I can continue this but the equations get longer and without getting a lower fraction to go with it works out to log(Mersenne number(p) +1) which isn't very helpful.
science_man_88 is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Lucas-Lehmer Primes henryzz And now for something completely different 42 2019-06-03 14:09
Lucas-Lehmer test Mathsgirl Information & Answers 23 2014-12-10 16:25
lucas-lehmer theorem Robot2357 Math 6 2013-06-15 03:10
Lucas-Lehmer Test storm5510 Math 22 2009-09-24 22:32
Lucas-Lehmer Dougal Information & Answers 9 2009-02-06 10:25

All times are UTC. The time now is 11:38.

Tue Apr 20 11:38:24 UTC 2021 up 12 days, 6:19, 0 users, load averages: 2.28, 2.04, 1.97

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.