mersenneforum.org  

Go Back   mersenneforum.org > Great Internet Mersenne Prime Search > Data > mersenne.ca

Reply
 
Thread Tools
Old 2021-07-01, 22:56   #23
James Heinrich
 
James Heinrich's Avatar
 
"James Heinrich"
May 2004
ex-Northern Ontario

350410 Posts
Default

Quote:
Originally Posted by kriesel View Post
That's more computer cycles (and James cycles) than I anticipated but would do the job.
The James cycles were not that many, and the computer cycles were considerably fewer than I expected.
I first ran it through GIMPS range (<1000M):
Quote:
Examined 43,381,507 square factors in 5.4 minutes
Found 0 cases where any known factors is a square factor.
Since it ran quickly I then ran it in the rest of the 1G-10G range:
Quote:
Examined 242,435,609 square factors in 28.1 minutes
Still no examples found.
James Heinrich is offline   Reply With Quote
Old 2021-07-02, 14:02   #24
Uncwilly
6809 > 6502
 
Uncwilly's Avatar
 
"""""""""""""""""""
Aug 2003
101×103 Posts

272016 Posts
Default

For a factor to be square of another factor it would still have to be a factor in its own right.
So for q to be a factor it would have to both be (2kp+1)(2kp+1) and 2Жp+1

(2kp+1)(2kp+1) = 2Жp+1
4k2p2 + 4kp + 1 = 2Жp + 1
4k2p2 + 4kp = 2Жp
2k2p + 2k = Ж
2k(kp +1) = Ж

As there any to prove that this can't be?
Uncwilly is online now   Reply With Quote
Old 2021-07-02, 14:38   #25
slandrum
 
Jan 2021
California

2×3×37 Posts
Default

Quote:
Originally Posted by Uncwilly View Post
For a factor to be square of another factor it would still have to be a factor in its own right.
So for q to be a factor it would have to both be (2kp+1)(2kp+1) and 2Жp+1
...
As there any to prove that this can't be?
No obvious way, the same argument applies to any composite factor of a Mersenne number, and the composite factors are all of the form 2kp+1 (as are the factors 1 and the Mersenne number M(p) itself).

That's why it's still open as to whether a Mersenne number can have a square (>1) as a factor.
slandrum is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Factor found that should have been found by P-1 tha Data 65 2020-08-05 21:11
F12 factor found? johnadam74 FermatSearch 16 2016-11-03 12:10
Irritated Mersenne factor found philmoore Operazione Doppi Mersennes 30 2013-08-28 17:16
found this factor tha Factoring 4 2007-06-18 19:56
After a factor is found it keeps on going jocelynl Software 6 2004-08-07 01:31

All times are UTC. The time now is 05:38.


Mon Oct 25 05:38:35 UTC 2021 up 94 days, 7 mins, 0 users, load averages: 1.25, 1.02, 1.02

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.