mersenneforum.org  

Go Back   mersenneforum.org > Extra Stuff > Miscellaneous Math

Reply
 
Thread Tools
Old 2016-08-01, 22:56   #12
paulunderwood
 
paulunderwood's Avatar
 
Sep 2002
Database er0rr

65028 Posts
Default

I have extended the nub of this thread a little further, but it still seems to be computationally useless.

For example b = 3 and p = 61 so that mp = 2^61 - 1, I ran this:

Code:
? p=61;mp=2^p-1;D=mp-1;V=factor(D,1000000);forbigdiv(D,d -> r=lift(Mod(3,mp)^(D/d));if(2^logint(r,2)==r,print(">>>"d))) 
>>>1
>>>61
>>>3
>>>183
>>>9
>>>549
Where "forbigdiv" is given here

This means 3^((mp-1)/549) == 2^n for some n OR 3^4200078341008550 == 2^n for some n, thus implying M61 is prime.

I will experiment with other bases b, for example p ...

Last fiddled with by paulunderwood on 2016-08-01 at 23:21
paulunderwood is offline   Reply With Quote
Old 2016-08-01, 23:38   #13
science_man_88
 
science_man_88's Avatar
 
"Forget I exist"
Jul 2009
Dumbassville

100000110000002 Posts
Default

Quote:
Originally Posted by paulunderwood View Post

Code:
? p=61;mp=2^p-1;D=mp-1;V=factor(D,1000000);forbigdiv(D,d -> r=lift(Mod(3,mp)^(D/d));if(2^logint(r,2)==r,print(">>>"d))) 
>>>1
>>>61
>>>3
>>>183
>>>9
>>>549
is your intent for D/d to get the largest one's out of the way first as D/2 will be the biggest exponent and will also be a divisor of D.

Last fiddled with by science_man_88 on 2016-08-01 at 23:46
science_man_88 is offline   Reply With Quote
Old 2016-08-02, 00:05   #14
paulunderwood
 
paulunderwood's Avatar
 
Sep 2002
Database er0rr

2×1,697 Posts
Default

Quote:
Originally Posted by science_man_88 View Post
is your intent for D/d to get the largest one's out of the way first as D/2 will be the biggest exponent and will also be a divisor of D.
Some order is possible, I guess.
paulunderwood is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Is it faster to run 1 worker or many? arbiter21 Information & Answers 17 2016-02-05 05:04
My CPU is getting faster and faster ;-) lidocorc Software 2 2008-11-08 09:26
3-PRP faster than LL for GIMPS? bearnol Math 35 2005-10-12 14:33
Faster way to do LLT? 1260 Miscellaneous Math 23 2005-09-04 07:12
Faster than LL? clowns789 Miscellaneous Math 3 2004-05-27 23:39

All times are UTC. The time now is 20:00.

Sat Sep 19 20:00:51 UTC 2020 up 9 days, 17:11, 1 user, load averages: 1.37, 1.45, 1.56

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, 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.