mersenneforum.org  

Go Back   mersenneforum.org > Great Internet Mersenne Prime Search > Math

Reply
 
Thread Tools
Old 2007-05-15, 00:34   #12
ewmayer
2ω=0
 
ewmayer's Avatar
 
Sep 2002
Rep├║blica de California

26·181 Posts
Default

Quote:
Originally Posted by maxal View Post
Thanks, ATH.
Please submit more terms to http://www.research.att.com/~njas/sequences/A123271
Max, since you apparently have edit privileges to the above page (I assume it was you who added the link to this thread), why don't you just add ATH's newly-reported terms yourself?
ewmayer is offline   Reply With Quote
Old 2007-05-15, 00:58   #13
m_f_h
 
m_f_h's Avatar
 
Feb 2007

24×33 Posts
Default

Quote:
Originally Posted by ATH View Post
I'm not sure how to submit terms, can you do it? The missing terms are:
-1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1
You have to open the link "Contribute new seq. or comment" (1st link on 2nd line at bottom), at best in a new window, and then fill in the form (in fact most of the work consists in emptying the form....)
(there are no "editing privileges" - submitting the form sends an email to N.Sloane who will incorporate the specially formatted data within some days, and mention the contributor & date for any new data, comment etc.).
Quote:
Btw it doesn't say that the sequence starts for n=2 or is that what "OFFSET 2,1" means?
Indeed.
m_f_h is offline   Reply With Quote
Old 2007-05-16, 00:23   #14
m_f_h
 
m_f_h's Avatar
 
Feb 2007

6608 Posts
Default

Can't we exploit the fact that D3=X(X^2-3)
successively gives all elements of the tree at given height,
and commutes with LL=X^2-2 ?
m_f_h is offline   Reply With Quote
Old 2008-10-04, 12:17   #15
ATH
Einyen
 
ATH's Avatar
 
Dec 2003
Denmark

BC116 Posts
Default

M37156667 interim Wd1 residue 833185DE0326B429 at iteration 37156663
M37156667 interim Wd1 residue 21F10ABD65A37DF4 at iteration 37156664
M37156667 interim Wd1 residue 36E916675C4F0334 at iteration 37156665
M37156667 interim Wd1 residue 0000000000000000 at iteration 37156666
M37156667 interim Wd1 residue 0000000000000000 at iteration 37156667
M37156667 is prime! Wd1: EA38283B,00000000

M43112609 interim Wd4 residue F042423AF370FBF0 at iteration 43112605
M43112609 interim Wd4 residue C395044781A6672D at iteration 43112606
M43112609 interim Wd4 residue 138F82F361A9E5B9 at iteration 43112607
M43112609 interim Wd4 residue 0000000000000000 at iteration 43112608
M43112609 interim Wd4 residue 0000000000000000 at iteration 43112609
M43112609 is prime! Wd4: 5B377150,00000000

So:
M45: p=37156667 s[p-3]== 2^((p+1)/2) (mod Mp).
M46: p=43112609 s[p-3]== 2^((p+1)/2) (mod Mp).

Now we have 24+ and 21-.

penultimate.txt

Last fiddled with by ATH on 2008-10-04 at 12:17
ATH is offline   Reply With Quote
Old 2008-10-05, 03:45   #16
jinydu
 
jinydu's Avatar
 
Dec 2003
Hopefully Near M48

175810 Posts
Default

Isn't the next-to-last residue of a Mersenne prime never supposed to be 0? Because then the final residue would be 0^2 -2 = -2. Or am I forgetting something?
jinydu is offline   Reply With Quote
Old 2008-10-05, 04:19   #17
jrk
 
jrk's Avatar
 
May 2008

3×5×73 Posts
Default

Quote:
Originally Posted by jinydu View Post
Isn't the next-to-last residue of a Mersenne prime never supposed to be 0? Because then the final residue would be 0^2 -2 = -2. Or am I forgetting something?
The next-to-last residue is not zero. It only looks that way in some of the results.

If the next-to-last residue is positive, it is of the form:

2^((p+1)/2)

In binary, a power of two has only a single '1' bit and the rest are zeroes.

When p is bigger than or equal to 127, then the '1' bit in the p-1 residue will be outside the 64-bit residue, making the 64-bit residue have all-zeroes, but the full residue is not zero.

Look at the p-1 residue of M61: 0000000080000000 or 2^31.
jrk is offline   Reply With Quote
Old 2008-10-06, 02:06   #18
ATH
Einyen
 
ATH's Avatar
 
Dec 2003
Denmark

300910 Posts
Default

Quote:
Originally Posted by jinydu View Post
Isn't the next-to-last residue of a Mersenne prime never supposed to be 0? Because then the final residue would be 0^2 -2 = -2. Or am I forgetting something?
Yeah its either -2(p+1)/2 or +2(p+1)/2. If its + in binary it will be 10000...millions of zeros..00000 and the 64bit residue will be 0x0000000000000000. If its - the residue will be 2^p-1 - 2(p+1)/2, which in binary is 1111...millions of 1's...111101111...millions of 1's...11111, so the 64 bit residue will in hex be 0xFFFFFFFFFFFFFFFF.

Last fiddled with by ATH on 2008-10-06 at 02:08
ATH is offline   Reply With Quote
Old 2009-06-22, 12:38   #19
ATH
Einyen
 
ATH's Avatar
 
Dec 2003
Denmark

3×17×59 Posts
Default

M42643801 interim Wd4 residue 56D4857CEECAE826 at iteration 42643797
M42643801 interim Wd4 residue 1FE903F0A3186A6F at iteration 42643798
M42643801 interim Wd4 residue DAACA15663F030C8 at iteration 42643799
M42643801 interim Wd4 residue FFFFFFFFFFFFFFFF at iteration 42643800
M42643801 interim Wd4 residue 0000000000000000 at iteration 42643801
M42643801 is prime! Wd4: B7E878A9,00000000

M46: p=42643801 s[p-3]== - 2^((p+1)/2) (mod Mp).

Now there is 24+ and 22- :

penultimate.txt
resultspenultimate.txt

Last fiddled with by ATH on 2009-06-22 at 12:38
ATH is offline   Reply With Quote
Old 2009-06-22, 15:57   #20
ewmayer
2ω=0
 
ewmayer's Avatar
 
Sep 2002
Rep├║blica de California

26×181 Posts
Default

Thanks for the table addition, ATH.

Now, anyone want to trot out a curious-though-likely-spurious statistical correlation, perhaps with the phase of the moon or one of the major stock market indices at time of discovery?
ewmayer is offline   Reply With Quote
Old 2009-06-22, 16:07   #21
henryzz
Just call me Henry
 
henryzz's Avatar
 
"David"
Sep 2007
Cambridge (GMT/BST)

579410 Posts
Default

Quote:
Originally Posted by ATH View Post
Now there is 24+ and 22- :
hopefully that means that we have missed two with - below the highest prime
henryzz is offline   Reply With Quote
Old 2009-06-25, 10:07   #22
plandon
 
May 2009
Loughborough, UK

22·11 Posts
Default

Quote:
Originally Posted by henryzz View Post
hopefully that means that we have missed two with - below the highest prime
The sequence above is for the discovered primes.

Maybe it is best just to submit the entries up to the completely checked range and add the rest as a comment to Sloanes. Otherwise A123271 will have to be corrected if another prime is discovered out of sequence.
plandon is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
lucas-lehmer theorem Robot2357 Math 6 2013-06-15 03:10
Can zero be an "intermediate step" value in Lucas-Lehmer? That Don Guy Math 10 2012-02-03 18:02
lucas lehmer outstretch science_man_88 Miscellaneous Math 7 2010-07-14 12:35
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 03:02.

Thu Jan 21 03:02:34 UTC 2021 up 48 days, 23:13, 0 users, load averages: 1.01, 1.32, 1.41

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.