mersenneforum.org  

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

Reply
 
Thread Tools
Old 2004-11-12, 16:29   #1
Bob Underwood
 
Nov 2004

416 Posts
Default Generalized Repunit primes

Has anyone tried to create a distributed computing project for Generalized Repunit Primes? Andy Steward had a webpage on this subject that seems to be discontinued. I miss it. It seem like a project that would be easy to understand and share:

So ill state it again here:
Repunits are 'repetitions of the unit', a series of ones. Eleven is a prime and written R2. One hundred eleven is 3X37, a composite written R3. 1111 is R4 and is composite. The prime repunits are quite rare: R2 ,R19, R23, R317, R1031 have been discovered so far--and that's it! Two other Rs are pending, suspected but not yet shown to be prime. It is necessary but NOT sufficient for the R number to be prime for the Repunit to be prime .What a suprise to think the simple number ONE holds any mysteries.
In bases other than 10 the Reps are also rare. In base two...well, you know about that!

Would there be any point in limiting the search to prime bases?

Bob
Bob Underwood is offline   Reply With Quote
Old 2004-11-12, 18:15   #2
rogue
 
rogue's Avatar
 
"Mark"
Apr 2003
Between here and the

23·751 Posts
Default

Check out http://www.worldofnumbers.com/
rogue is online now   Reply With Quote
Old 2004-11-13, 03:27   #3
Bob Underwood
 
Nov 2004

22 Posts
Default Thanks

Thanks to Rogue for the reference to repunits in base 10. The list of repunit PRIMES is quite small. Only five have been discovered so far. In base 2 we have found 40 (?). At this very moment an elite world wide network of computers is almost continuously crunching numbers just to find the next Repunit in base two. In all probability yours is among them, dedicated to this task between your keystrokes.

The repunit primes in other bases were investigated by Stewart but i find no mirror site and his compilations may be stored deep in the computers of secretive mathematicians who delight in clandestine arcane manipulations far from the prying eyes of the internet and thus lost to civilization. Alas! Can we really trust Them to share??

Think how many centuries passed between the 13 polyhedra first described by Archimedes and their rediscovery by Kepler! Think how the value of Pi was calculated accurately to 15 decimals and then..and then... Lost..never to recover such accuracy again until the late 19th century .Need we revisit the Dark Ages when we, of all people, are keenly aware of the power of distributed computing at our disposal? Do we not owe it to ourselves and to the generations that follow to hold back the twilight of Mathematical indifference?


I Implore you,fellow searchers, to GENERALIZE. YOur noble efforts are indeed appreciated but there are so many of us focused exclusively on Base two repunits--it is as if All the other numbers do not exist! --surely in your generosity a few of you could dedicate a token of your time and talent to establish a DISTRIBUTED search for Repunits in other bases.
Bob Underwood is offline   Reply With Quote
Old 2004-11-13, 14:00   #4
wpolly
 
wpolly's Avatar
 
Sep 2002
Vienna, Austria

3×73 Posts
Default

In base two the GRU can be tested using the n+1 test easily, but in general the main obstacle of GRU primality proving is to FACTOR the cyclotomic numbers involved in the factors of n-1.
wpolly is offline   Reply With Quote
Old 2004-11-13, 14:24   #5
Bob Underwood
 
Nov 2004

1002 Posts
Default GENERALIZED REPUNIT PRIMES

And so, wpolly, is there now any tabulation of those factors anywhere on the net?
Bob Underwood is offline   Reply With Quote
Old 2004-11-13, 15:37   #6
ET_
Banned
 
ET_'s Avatar
 
"Luigi"
Aug 2002
Team Italia

112438 Posts
Default

Quote:
Originally Posted by Bob Underwood
And so, wpolly, is there now any tabulation of those factors anywhere on the net?
Try here:

http://mathworld.wolfram.com/Repunit.html

In general, a repunit in base b is a number of the form

Mbn = (bn-1)/(b-1)

It's easy to create a list of those numbers, but not trivial, according to their size, to check for their primality.


Luigi

Last fiddled with by ET_ on 2004-11-13 at 15:44
ET_ is offline   Reply With Quote
Old 2004-11-14, 08:02   #7
Maybeso
 
Maybeso's Avatar
 
Aug 2002
Portland, OR USA

1000100102 Posts
Default

I followed ET's link, and then to Cunningham Number, at the bottom of the page it says
Quote:
Updated factorizations were published in Brillhart et al. (1988). The tables have been extended by Brent and te Riele (1992) to
b = 13, ..., 100 with n < 255 for b < 30, and n < 100 for b >= 30.
All numbers with exponent 58 and smaller, and all composites with <= 90 digits have now been factored.
So any coordinated effort should start somewhere beyond this.
To find any current efforts, I suggest you search for the Cunningham project, or for factors of Cunningham Numbers.

You could also check if Brent and te Riele published their tables.

I would really like to know what different algorithms were used for each of the searches.

Last fiddled with by Maybeso on 2004-11-14 at 08:03
Maybeso is offline   Reply With Quote
Old 2004-11-14, 16:36   #8
wblipp
 
wblipp's Avatar
 
"William"
May 2003
New Haven

92416 Posts
Default

Quote:
Originally Posted by Maybeso
You could also check if Brent and te Riele published their tables.
Brent regularly updates a list of known factors of an Β± 1 for a and n less than 10,000. It's pretty sparse for the larger values of both a and n, but gives a place to accumulate and share found factors. He doesn't appear to have any way to tell primes from unfactored composites, though.

http://web.comlab.ox.ac.uk/oucl/work...t/factors.html

William
wblipp is offline   Reply With Quote
Old 2004-11-14, 19:38   #9
xilman
Bamboozled!
 
xilman's Avatar
 
"π’‰Ίπ’ŒŒπ’‡·π’†·π’€­"
May 2003
Down not across

1019410 Posts
Default

Quote:
Originally Posted by Bob Underwood
The repunit primes in other bases were investigated by Stewart but i find no mirror site and his compilations may be stored deep in the computers of secretive mathematicians who delight in clandestine arcane manipulations far from the prying eyes of the internet and thus lost to civilization. Alas! Can we really trust Them to share??
In my experience, people who search for these things are only too willing to share. Other than the bragging rights for having found them, there are very, very few rewards for spending the time and effort involved in the search.

Note that all repunits are of the form (b^n-1)/(b-1) and so if you want to find examples in other people's results you should concentrate on such as the Cunningham project and Richard Brent's compendium of such things.

Paul
xilman is offline   Reply With Quote
Old 2004-11-16, 10:42   #10
wpolly
 
wpolly's Avatar
 
Sep 2002
Vienna, Austria

3·73 Posts
Default

Quote:
Originally Posted by Bob Underwood
And so, wpolly, is there now any tabulation of those factors anywhere on the net?
www.asahi-net.or.jp/~KC2H-MSM/cn/
wpolly is offline   Reply With Quote
Old 2004-11-19, 15:13   #11
Bob Underwood
 
Nov 2004

22 Posts
Default

Quote:
Originally Posted by xilman
In my experience, people who search for these things are only too willing to share. Other than the bragging rights for having found them, there are very, very few rewards for spending the time and effort involved in the search.

Note that all repunits are of the form (b^n-1)/(b-1) and so if you want to find examples in other people's results you should concentrate on such as the Cunningham project and Richard Brent's compendium of such things.

Paul

All said tongue firmly embeded in cheek! Of course we share , Gauss being a notable exception. This was written in the faint hope that hyped eloquence might be considered mildly amusing and also in the hope that the distributed network could be applied to this search. I am not a mathematician but somehow find this problem reasonably enchanting. Elsewhere in these forums it has been said that "we" do not need another factoring project". ((whoever "WE" is )). Am i alone in thinking that a few non mathematicians would be willing to lend their computers to such a project? What could possibly be more fascinating than the number ONE? ( oops!, tongue in cheek -- Again!)

The beauty of GIMPS is that you professionals have finally allowed your cheering fans to touch the ball. Its a shame to see only a FEW powerful univerity computers crunching away at these calculations when entire networks of computing power remain idle. I work for the US Postal Service. Every supervisor has a computer and these computers are only used to retrieve files. If the Postal Service were to lend its vast network to your effort you can bet they would soon issue a commemorative stamp congratulating themselves as the proud discoverers of the 42nd .Of course ive suggested this to the powers that be...and have yet to recieve a reply.
Bob
Bob Underwood is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
generalized minimal (probable) primes sweety439 sweety439 68 2020-11-26 16:20
Searching for generalized repunit PRP sweety439 sweety439 231 2020-11-06 12:30
generalized repunit PRP sweety439 And now for something completely different 1 2016-12-07 15:58
Generalized Mersenne Primes Unregistered Homework Help 6 2012-10-31 14:16
Generalized Mersenne Primes Cyclamen Persicum Math 1 2004-01-30 15:11

All times are UTC. The time now is 03:39.

Fri Nov 27 03:39:23 UTC 2020 up 78 days, 50 mins, 4 users, load averages: 2.57, 1.80, 1.58

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.