mersenneforum.org  

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

Reply
 
Thread Tools
Old 2006-04-02, 18:15   #12
wblipp
 
wblipp's Avatar
 
"William"
May 2003
New Haven

3×787 Posts
Default

Quote:
Originally Posted by wblipp
This thread pulls together discussions that have been buried on several different threads.
There has recently been renewed discussion about Silverman and Wagstaff's paper A Practical Analysis of Elliptical Curve Factoring.

In this message we have agreement that Brent's version of the 2-parameter Dickman function is correct, along with an assurance that the error is cosmetic:

http://www.mersenneforum.org/showpos...0&postcount=68


In this message we have a summary of the idea as using Baye's Theorem to update the Dickman function:

http://www.mersenneforum.org/showpos...7&postcount=15


At first glance it appears that changing the Dickman function should change Equation 4.6, but I haven't yet taken the time to look into that issue.
wblipp is offline   Reply With Quote
Old 2006-04-02, 18:40   #13
R.D. Silverman
 
R.D. Silverman's Avatar
 
Nov 2003

164448 Posts
Default

Quote:
Originally Posted by wblipp

In this message we have a summary of the idea as using Baye's Theorem to update the Dickman function:
Actually, the Bayes' Thm. computations in the paper use the following theorem for the prior, rather than Dickman's function:

The probability that a large integer X has a factor between y and y^(1+e)
is e/(e+1). So, for example, the probability that an integer (say) near
200 digits has a factor between 50 and 60 digits gives e = .2 and a
probability of 1/6. This allows use to compute a density function for
the probability that a factor exists in the range of interest. We then apply
Bayes' Thm. using the ECM failures as a sample.
R.D. Silverman is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Distribution of Mersenne Factors tapion64 Miscellaneous Math 21 2014-04-18 21:02
Known factors distribution graphs James Heinrich Data 21 2013-09-26 19:54
The ultimate prime test ? Carl Fischbach Miscellaneous Math 33 2009-09-11 20:49
strange factors distribution?? pegaso56 Information & Answers 19 2009-06-29 15:04
Distribution of Mersenne prime factors mod 6 alpertron Math 0 2006-06-23 20:07

All times are UTC. The time now is 06:55.

Sun Apr 18 06:55:34 UTC 2021 up 10 days, 1:36, 0 users, load averages: 1.69, 1.57, 1.60

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.