mersenneforum.org  

Go Back   mersenneforum.org > Factoring Projects > Cunningham Tables

Reply
 
Thread Tools
Old 2006-08-27, 01:03   #1
Zeta-Flux
 
Zeta-Flux's Avatar
 
May 2003

7·13·17 Posts
Default Sieved?

I'm wondering if Cunningham numbers on the 3- and 3+ tables have been completely factored for small factors up to a specific size. In particular, I'm wondering if something like the following is true:

All numbers of the form 3^n-1 for 1000<n<100,000 must have a factor larger than 10^40.
Zeta-Flux is offline   Reply With Quote
Old 2006-08-27, 02:55   #2
philmoore
 
philmoore's Avatar
 
"Phil"
Sep 2002
Tracktown, U.S.A.

2×13×43 Posts
Default

Quote:
Originally Posted by Zeta-Flux View Post
I'm wondering if Cunningham numbers on the 3- and 3+ tables have been completely factored for small factors up to a specific size. In particular, I'm wondering if something like the following is true:

All numbers of the form 3^n-1 for 1000<n<100,000 must have a factor larger than 10^40.
Unfortunately, numbers of this size could be tested to this sort of limit only through ECM, which can only place a probability that factors of that size have been discovered. I suspect you need some sort of rigorous limit, which is beyond present-day computing possibilities.

I suspect that many numbers in this range may have not been tested beyond 25 digits, judging from my experience with the 2- and 2+ tables.
philmoore is offline   Reply With Quote
Old 2006-08-27, 03:00   #3
Zeta-Flux
 
Zeta-Flux's Avatar
 
May 2003

60B16 Posts
Default

Actually 25 digits would still be interesting (if it is true that they've all been tested up to this level).
Zeta-Flux is offline   Reply With Quote
Old 2006-08-27, 09:40   #4
xilman
Bamboozled!
 
xilman's Avatar
 
"π’‰Ίπ’ŒŒπ’‡·π’†·π’€­"
May 2003
Down not across

244158 Posts
Default

Quote:
Originally Posted by Zeta-Flux View Post
I'm wondering if Cunningham numbers on the 3- and 3+ tables have been completely factored for small factors up to a specific size. In particular, I'm wondering if something like the following is true:

All numbers of the form 3^n-1 for 1000<n<100,000 must have a factor larger than 10^40.
Around a year or so ago some of the Cunningham old-timers estimated how many factors under P40 were left in the tables. We all knew, of course, that we wouldn't know the answer for sure until all the numbers had been completely factored.

I certainly didn't win the competition. I forget the precise details but my guess was something like 2 remaining and 3 were duly found.

The consensus is that it is now very unlikely that there are any prime factors with fewer than 40 digits still to be discovered. None have been found this year. The smallest reported is P43 and there are 30 in my table for 2006 which arel under P50. There may be one or two mpre P4x to be added when I bring my table up to date.


Paul
xilman is offline   Reply With Quote
Old 2006-08-27, 09:46   #5
xilman
Bamboozled!
 
xilman's Avatar
 
"π’‰Ίπ’ŒŒπ’‡·π’†·π’€­"
May 2003
Down not across

3×31×113 Posts
Default

Quote:
Originally Posted by Zeta-Flux View Post
I'm wondering if Cunningham numbers on the 3- and 3+ tables have been completely factored for small factors up to a specific size. In particular, I'm wondering if something like the following is true:

All numbers of the form 3^n-1 for 1000<n<100,000 must have a factor larger than 10^40.
Er ... those aren't Cunningham numbers. The 3+ and 3- Cunningham tables only go as far as n=600 (1200 for the 3LM numbers).

I do not know of any tabulations of factorizations of the numbers in question. It would be easy enough to create such tables if they don't exist. If any are in existence, I doubt they would be complete much beyond p20 or so.



Paul
xilman is offline   Reply With Quote
Old 2006-08-28, 13:45   #6
Zeta-Flux
 
Zeta-Flux's Avatar
 
May 2003

7×13×17 Posts
Default

xilman,

If they are not techinically Cunningham numbers (yet), they are in the same spirit.

But, I would even be happy to know they have been checked up to 20 digits. The reason I ask is that, with the search for Mersenne primes, we do a lot of sieving for small factors. I was wondering if the same is done for the 3 tables (up to large exponents).
Zeta-Flux is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Backup of Manually Sieved SoB/PSP Ranges mazadillon Prime Sierpinski Project 0 2012-01-09 08:26
Sieved files/sieving coordination gd_barnes Conjectures 'R Us 32 2008-01-22 03:09
Offer your sieved files here kar_bon Riesel Prime Search 8 2008-01-08 04:52
Any Software for Sieved Trial Factoring in Other Bases? wblipp Operation Billion Digits 17 2006-09-24 02:09
It'd probably be best if I just sieved. jasong Sierpinski/Riesel Base 5 3 2005-03-14 03:40

All times are UTC. The time now is 14:22.

Sat Jan 23 14:22:08 UTC 2021 up 51 days, 10:33, 0 users, load averages: 2.68, 2.89, 2.87

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.