mersenneforum.org  

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

Reply
 
Thread Tools
Old 2007-03-28, 02:45   #1
jasong
 
jasong's Avatar
 
"Jason Goatcher"
Mar 2005

3×7×167 Posts
Default Could a Distributed Computing approach help find the smallest Brier number?

I ask this question in total ignorance of the math involved. I throw this out there just to see if people think DCing could help this problem.

For those of you who don't know what a Brier number is, I'll explain. When you're searching for large prime numbers, there's a basic formula, k*b^n+c. For the most part, most people concentrate where b equals 2, and c is plus or minus 1. For k*2^n-1, there are k's where all n from 1 to infinity will give the equation a composite number, and it's the same thing for k*2^n+1, but usually with different numbers. The smallest number for k*2^n-1 is believed to be 509203, for +1, I think it's 78557(not sure). A Brier number is a number, k, where both k*2^n-1 and k*2^n+1 will yield composite numbers for all n from 1 to infinity.

My question is,"Is it possible to use distributed computing to help solve the lowest Brier number problem in a timely fashion?" For the record, I know searching for primes below the smallest known Brier number is kind of idiotic since it's so unbelievably huge. I'm wondering if there is a possibility to do some sort of covering set research, in an attempt to find a smaller number.

Last fiddled with by jasong on 2007-03-28 at 02:51
jasong is offline   Reply With Quote
Old 2007-03-28, 03:30   #2
drake2
 
Aug 2005

24 Posts
Question

The mathworld.com description for Brier Number currently says

"The first few are 878503122374924101526292469, 3872639446526560168555701047, 623506356601958507977841221247, ... "

The comment field of Sequence A076335 in the The On-Line Encyclopedia of Integer Sequences states

"These are just the smallest examples known - there may be smaller ones."

Don't one of these two statements need to be corrected or is there no rigor in the field of mathematics?
drake2 is offline   Reply With Quote
Old 2007-03-28, 07:41   #3
Orgasmic Troll
Cranksta Rap Ayatollah
 
Orgasmic Troll's Avatar
 
Jul 2003

64110 Posts
Default

Quote:
Originally Posted by drake2 View Post
The mathworld.com description for Brier Number currently says

"The first few are 878503122374924101526292469, 3872639446526560168555701047, 623506356601958507977841221247, ... "

The comment field of Sequence A076335 in the The On-Line Encyclopedia of Integer Sequences states

"These are just the smallest examples known - there may be smaller ones."

Don't one of these two statements need to be corrected or is there no rigor in the field of mathematics?
None at all. Try psychology, I hear those guys are sticklers.
Orgasmic Troll is offline   Reply With Quote
Old 2007-03-28, 16:22   #4
R.D. Silverman
 
R.D. Silverman's Avatar
 
Nov 2003

11101001001002 Posts
Default

Quote:
Originally Posted by drake2 View Post
The mathworld.com description for Brier Number currently says

"The first few are 878503122374924101526292469, 3872639446526560168555701047, 623506356601958507977841221247, ... "

The comment field of Sequence A076335 in the The On-Line Encyclopedia of Integer Sequences states

"These are just the smallest examples known - there may be smaller ones."

Don't one of these two statements need to be corrected or is there no rigor in the field of mathematics?
What needs correcting? I see nothing wrong with the statements.
R.D. Silverman is offline   Reply With Quote
Old 2007-03-28, 17:05   #5
jasonp
Tribal Bullet
 
jasonp's Avatar
 
Oct 2004

3×1,181 Posts
Default

Quote:
Originally Posted by drake2 View Post
"The first few are 878503122374924101526292469, 3872639446526560168555701047, 623506356601958507977841221247, ... "

The comment field of Sequence A076335 in the The On-Line Encyclopedia of Integer Sequences states

"These are just the smallest examples known - there may be smaller ones."

Don't one of these two statements need to be corrected or is there no rigor in the field of mathematics?
Read 'the first few' above as 'the first few we have found'.

jasonp
jasonp is offline   Reply With Quote
Old 2007-05-29, 13:30   #6
robert44444uk
 
robert44444uk's Avatar
 
Jun 2003
Oxford, UK

1,979 Posts
Default

Quote:
Originally Posted by jasong View Post

I'm wondering if there is a possibility to do some sort of covering set research, in an attempt to find a smaller number.
You might want to check the Carlos Rivera site that talks about Briers and which also provides some useful correspondence by persons who have looked at strategies for smaller Briers in some depth.

http://www.primepuzzles.net/problems/prob_029.htm

I have been corresponding with Prof. Caldwell on techniques for Sierpinski/Riesel any base and he suggests there are alternatives to the traditional covering set approach (using primes modulo a certain base) which, in particular, look at known algebraic factoring methods to allow for a pseudo-cover to replace one or more of the primes in the cover, or will allow for a smaller covering set.

For example x^3 - a^3 = (x - a)(x^2 + ax + a^2)

When you set a=1, then this becomes x^3-1, which gives you a form of k*2^3-1, k*2^6-1, k^2^9-1...(pseudo order 3 base 2) as k*2^(3*integer) is still a cube if k is a cube.

Other useful factoring tools might be used to give pseudo cover, for both + and - cases. Aurifeuillian for example.

This type of strategy has not been investigated as far as I am aware for the Brier case.

But it would take a lot of brain power, which I am in limited supply, to investigate all the possibilities. But if it produced a smaller Brier, then it would be a breakthrough.

Last fiddled with by robert44444uk on 2007-05-29 at 13:45
robert44444uk is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Etiquettes of Distributed Computing a1call Miscellaneous Math 8 2018-05-21 16:25
Given sigma(n)-n, find the smallest possible n mart_r Aliquot Sequences 6 2013-07-23 20:50
GNFS distributed computing andi314 Factoring 50 2005-05-11 00:56
The difference between P2P and distributed computing and grid computing GP2 Lounge 2 2003-12-03 14:13
Can you find the smallest number? Fusion_power Puzzles 8 2003-11-18 19:36

All times are UTC. The time now is 15:11.


Mon Nov 29 15:11:39 UTC 2021 up 129 days, 9:40, 0 users, load averages: 1.61, 1.52, 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.