mersenneforum.org  

Go Back   mersenneforum.org > Extra Stuff > Blogorrhea > jasong

Reply
 
Thread Tools
Old 2008-12-26, 08:30   #1
jasong
 
jasong's Avatar
 
"Jason Goatcher"
Mar 2005

5×701 Posts
Default Assuming the goal is mega-primes, is base-3 better

I'm running the base-3 challenge at the moment, just for the heck of it, and it's amazing how dense it is with primes.

I know that for a given k and n, base-2 is the fastest to run. But if a person's goal is simply to "find big-ass primes," would it not be better to concentrate on base-3? I mean, think about it. ALL primes, except 2 and 3, are of the form 6k+/-1. And when k is even and b is 3, those are the ONLY numbers you get.(yes, I realize 6k+/-1 is a necessary but not sufficent condition)

I think this is something that needs to be seriously considered.
jasong is offline   Reply With Quote
Old 2008-12-26, 10:19   #2
axn
 
axn's Avatar
 
Jun 2003

12F216 Posts
Default

Quote:
Originally Posted by jasong View Post
I know that for a given k and n, base-2 is the fastest to run. But if a person's goal is simply to "find big-ass primes," would it not be better to concentrate on base-3?
A small correction. It is not just "for a given k and n" -- it is "for a given number of approximately same size". That is to say, if N=k*2^n and M=k*3^m are approximately same number of digits, then the base-2 number will be much faster than the base-3 number because of the current state-of-the-art in FFT (i.e IBDWT which is only implemented for base-2).

In addition, the base 3 series grows faster than the base-2 series.

Quote:
Originally Posted by jasong View Post
I mean, think about it. ALL primes, except 2 and 3, are of the form 6k+/-1. And when k is even and b is 3, those are the ONLY numbers you get.
This works equally well for base-2, all it needs is k be a multiple of 3. In fact, that is the key principle behind the heavy weight k's being used by 15K and RPS projects. So this is not an important consideration.
axn is online now   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
S/R Base 5 Primes reported in 2016 Joe O Sierpinski/Riesel Base 5 5 2016-08-21 17:47
S/R Base 5 Primes reported in 2014 Joe O Sierpinski/Riesel Base 5 1 2016-03-14 04:30
S/R Base 5 Primes reported in 2012 odicin Sierpinski/Riesel Base 5 16 2013-01-09 20:18
S/R Base 5 Primes in 2010 Joe O Sierpinski/Riesel Base 5 36 2010-12-31 04:05
List of all base 5 primes? gd_barnes Sierpinski/Riesel Base 5 2 2008-07-01 04:09

All times are UTC. The time now is 09:47.

Thu Jan 28 09:47:08 UTC 2021 up 56 days, 5:58, 0 users, load averages: 3.55, 3.12, 2.67

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.