mersenneforum.org > Data New mersenne factor found, what to do with it?
 User Name Remember Me? Password
 Register FAQ Search Today's Posts Mark Forums Read

2021-07-01, 22:56   #23
James Heinrich

"James Heinrich"
May 2004
ex-Northern Ontario

23·32·72 Posts

Quote:
 Originally Posted by kriesel 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.

 2021-07-02, 14:02 #24 Uncwilly 6809 > 6502     """"""""""""""""""" Aug 2003 101×103 Posts 24×631 Posts 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?
2021-07-02, 14:38   #25
slandrum

Jan 2021
California

3618 Posts

Quote:
 Originally Posted by Uncwilly 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.

 Similar Threads Thread Thread Starter Forum Replies Last Post tha Data 65 2020-08-05 21:11 johnadam74 FermatSearch 16 2016-11-03 12:10 philmoore Operazione Doppi Mersennes 30 2013-08-28 17:16 tha Factoring 4 2007-06-18 19:56 jocelynl Software 6 2004-08-07 01:31

All times are UTC. The time now is 12:02.

Sat Nov 27 12:02:19 UTC 2021 up 127 days, 6:31, 0 users, load averages: 0.92, 1.27, 1.24