mersenneforum.org  

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

Reply
 
Thread Tools
Old 2020-08-05, 05:31   #23
Citrix
 
Citrix's Avatar
 
Jun 2003

157010 Posts
Default

Quote:
Originally Posted by Citrix View Post
1) Why do we have to use all the primes in B1. A smaller subset set of primes in B1 might have an lower hammer weight N. We then take this smaller subset and the remaining B1 primes (or move them to the B2 stage). Have you tried this?
Thinking about this further... all primes in B1 are not necessary and it does not need to be an absolute multiple of powersmooth(1000000). Some primes can be twice, some three times etc.

Turning the problem around - instead of fixing a number powersmooth (x) and then searching we leave both input and output variable.

If we are flexible with above --- then we could generate a 2^n+c that has a lot of factors (smooth) and c is relatively small and we can control number of bits in n. This should have a low hammer weight.

OR generate a number with low hammer weight that has a lot of factors.
Citrix is offline   Reply With Quote
Old 2020-08-29, 02:57   #24
LaurV
Romulan Interpreter
 
LaurV's Avatar
 
Jun 2011
Thailand

2×11×397 Posts
Default

Mihai, there is a way to reduce that number of bits, but the multiple becomes such big, that would be impossible to use, as you will need soooOOO many more squarings, you gain nothing. For example, instead of computing b^e (with odd e), you can compute b^(2^ord(2,e))/b. What's in parenthesis is a power of 2, so it has no additional "pops", and the resulted power (after division) is a multiple of e (by definition of ord). But what you get there is HUUGE, way beyond b^(2^p-2) that you compute for PRP, haha.
LaurV is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Primorial offsets robert44444uk Prime Gap Searches 7 2018-11-29 08:40
Primorial calculation FreakyPotato Programming 7 2015-02-06 10:33
Primorial puzzle Citrix Puzzles 3 2006-03-07 15:07
Primorial question Dougy Math 2 2005-07-28 13:13
Multiple systems/multiple CPUs. Best configuration? BillW Software 1 2003-01-21 20:11

All times are UTC. The time now is 08:27.

Fri Sep 18 08:27:36 UTC 2020 up 8 days, 5:38, 0 users, load averages: 1.64, 1.81, 1.74

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.