mersenneforum.org  

Go Back   mersenneforum.org > Factoring Projects > FermatSearch

Reply
 
Thread Tools
Old 2020-01-23, 16:54   #287
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

100011101001102 Posts
Thumbs up

We would be amiss to not notice this new find that has just shown on radars...

13 · 25523860 + 1 divides Fermat F(5523858)

Congratulations to Scott and the numerous PrimeGrid miners!
Batalov is offline   Reply With Quote
Old 2020-01-23, 17:39   #288
paulunderwood
 
paulunderwood's Avatar
 
Sep 2002
Database er0rr

65148 Posts
Default

Quote:
Originally Posted by Batalov View Post
We would be amiss to not notice this new find that has just shown on radars...

13 · 25523860 + 1 divides Fermat F(5523858)

Congratulations to Scott and the numerous PrimeGrid miners!
There is now no need to run a PRP/N-1 prime check on F(5523858)

Last fiddled with by paulunderwood on 2020-01-23 at 17:43
paulunderwood is offline   Reply With Quote
Old 2020-01-24, 02:41   #289
LaurV
Romulan Interpreter
 
LaurV's Avatar
 
Jun 2011
Thailand

8,741 Posts
Default

Quote:
Originally Posted by paulunderwood View Post
There is now no need to run a PRP/N-1 prime check on F(5523858)
haha, that was a good one.

Congrats to the finder(s) !
LaurV is online now   Reply With Quote
Old 2020-01-24, 13:52   #290
JeppeSN
 
JeppeSN's Avatar
 
"Jeppe"
Jan 2016
Denmark

100110112 Posts
Wink

Good old F(5523858): I always thought it would be composite, but I did not expect such a tiny prime divisor! /JeppeSN
JeppeSN is offline   Reply With Quote
Old 2020-01-24, 15:07   #291
Dr Sardonicus
 
Dr Sardonicus's Avatar
 
Feb 2017
Nowhere

346410 Posts
Default

Once upon a time, long long ago, I noted that if n > 2 and k < 2n+2 + 2, the fact that N = k*2n+2 + 1 divides Fn in and of itself proves N is prime. In the case at hand (n = 5523858), k = 13 satisfies this condition.

Last fiddled with by Dr Sardonicus on 2020-01-24 at 15:08 Reason: Omit unnecessary words!
Dr Sardonicus is offline   Reply With Quote
Old 2020-01-24, 20:35   #292
ET_
Banned
 
ET_'s Avatar
 
"Luigi"
Aug 2002
Team Italia

112368 Posts
Default

Any more infos about the discovery? like the surname of Scott, or the setup he used for the search, or the time he devoted to it?

Luigi
---

P.S. Dr. James Scott Brown.

Last fiddled with by ET_ on 2020-01-24 at 20:47
ET_ is offline   Reply With Quote
Old 2020-01-24, 20:45   #293
mathwiz
 
Mar 2019

1328 Posts
Default

Quote:
Originally Posted by ET_ View Post
Any more infos about the discovery? like the surname of Scott, or the setup he used for the search, or the time he devoted to it?

Luigi
---
https://primes.utm.edu/bios/page.php?id=1298 may at least answer some of your questions.
mathwiz is online now   Reply With Quote
Old 2020-01-24, 22:40   #294
ATH
Einyen
 
ATH's Avatar
 
Dec 2003
Denmark

3×11×89 Posts
Default

Quote:
Originally Posted by ET_ View Post
Any more infos about the discovery? like the surname of Scott, or the setup he used for the search, or the time he devoted to it?
His name is Scott Brown it seems:

http://primegrid.com/forum_thread.php?id=8778

https://www.primegrid.com/workunit.php?wuid=638323572

https://www.primegrid.com/show_user.php?userid=1178
ATH is offline   Reply With Quote
Old 2020-01-24, 23:41   #295
JeppeSN
 
JeppeSN's Avatar
 
"Jeppe"
Jan 2016
Denmark

5·31 Posts
Post

It is the same Scott Brown who found another Fermat factor, 9*2^2543551+1, back in 2011, in a similar way.

In PrimeGrid, the participants detect the primality (two persons do it concurrently, the one finishing first is declared the finder). Whether the new Proth prime divides any Fermat number (and/or generalized Fermat numbers with bases at most 12) is detected by PrimeGrid's server, not the participant's computer.

The link posted by ATH shows the timing (primality was reported "22 Jan 2020 | 15:00:58 UTC") and some hardware ("Intel(R) Core(TM) i7-4790 CPU @ 3.60GHz [Family 6 Model 60 Stepping 3]").

The other participant was Stefan Larsson (returned "22 Jan 2020 | 15:11:39 UTC").

At some point PrimeGrid will publish an official announcement (PDF).

This was PrimeGrid's first Fermat divisor in five years. They recently introduced a new subproject that focuses on Proth primes with low "k" (the odd multiplier) because that gives higher probability of Fermat divisors. This approach was recommended by Ravi Fernando and others.

/JeppeSN
JeppeSN is offline   Reply With Quote
Old 2020-01-25, 14:28   #296
Dr Sardonicus
 
Dr Sardonicus's Avatar
 
Feb 2017
Nowhere

23·433 Posts
Default

Just for fun, I looked for small prime factors of the numbers k*2^5523860 + 1, k = 1 to 12. For all but three of them, the smallest factor can be found mentally. For two of the remaining three, the smallest factor is still quite small.

k = 1 p = 17
k = 2 p = 3
k = 3 p = 14270779
k = 4 p = 5
k = 5 p = 3
k = 7 p = 2625617
k = 8 p = 3
k = 9 p = 5
k = 10 p = 11
k = 11 p = 3
k = 12 p = 7

For the remaining value, 6*2^5523860 + 1, I didn't look far enough to find any factors, but I didn't look all that far. Has (as I suspect) someone already found a factor by trial division, or otherwise shown it to be composite?
Dr Sardonicus is offline   Reply With Quote
Old 2020-01-25, 17:04   #297
JeppeSN
 
JeppeSN's Avatar
 
"Jeppe"
Jan 2016
Denmark

15510 Posts
Default

PrimeGrid's official announcement is here and can be found in this thread of theirs. /JeppeSN
JeppeSN is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
New Generalized Fermat factors Batalov Factoring 149 2017-02-20 12:06
Best case Fermat Factors yourskadhir Miscellaneous Math 5 2012-12-12 04:18
Generalized Fermat factors - why? siegert81 Factoring 1 2011-09-05 23:00
Weighted Fermat factors Top 20 Merfighters Factoring 0 2010-04-13 14:16
Fermat 12 factors already found? UberNumberGeek Factoring 6 2009-06-17 17:22

All times are UTC. The time now is 05:06.

Thu Sep 24 05:06:55 UTC 2020 up 14 days, 2:17, 0 users, load averages: 1.04, 1.06, 1.20

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.