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-   -   New Fermat factors (https://www.mersenneforum.org/showthread.php?t=15449)

philmoore 2011-03-22 21:27

New Fermat factors
 
I see on Wilfrid Keller's site: [url]http://www.prothsearch.net/fermat.html[/url] that two new factors of Fermat numbers have been discovered recently including a 49-digit factor of F17 by David Bessel that appears to have been discovered using ECM with prime95/mprime. The other factor, the second known of F42 is credited to Roman Maznichenko, and Keller credits Durman for the software, but Luigi says over at [url]http://www.fermatsearch.org/news.html[/url] that it was discovered using Mark Rodenkirch's program GMP-Factor. Congratulations to everyone involved!

philmoore 2011-03-22 21:30

I see David's factor was already discussed in this thread:
[url]http://www.mersenneforum.org/showthread.php?t=15358[/url]
I don't know how I overlooked it, congrats again!

Moderators: feel free to append this to the other thread.

rogue 2011-03-22 21:59

[QUOTE=philmoore;256385]I see on Wilfrid Keller's site: [url]http://www.prothsearch.net/fermat.html[/url] that two new factors of Fermat numbers have been discovered recently including a 49-digit factor of F17 by David Bessel that appears to have been discovered using ECM with prime95/mprime. The other factor, the second known of F42 is credited to Roman Maznichenko, and Keller credits Durman for the software, but Luigi says over at [url]http://www.fermatsearch.org/news.html[/url] that it was discovered using Mark Rodenkirch's program GMP-Factor. Congratulations to everyone involved![/QUOTE]

Cool! AFAIK this is the first Fermat factor found with my software.

BTW Luigi, it is GMP-Fermat, not GMP-Factor. Would you mind fixing it?

Prime95 2011-03-23 01:18

In reviewing Keller's page, is there any reason why F25 and F26 (and maybe F27) cannot be moved to the "Factorizations known to be incomplete" section?

Who wants to volunteer to do the PRP tests?

ixfd64 2011-03-23 01:56

ATH tested those cofactors a while back and found them to be composite. However, I think that Wilfrid wants them to be independently verified first.

ATH 2011-03-23 02:17

[QUOTE=ixfd64;256417]ATH tested those cofactors a while back and found them to be composite. However, I think that Wilfrid wants them to be independently verified first.[/QUOTE]

Yeah I did them back following GIMPS first fermat factor. The discussion is in the same thread, post #35-#69: [URL="http://www.mersenneforum.org/showthread.php?t=12168"]http://www.mersenneforum.org/showthread.php?t=12168[/URL]

ET_ 2011-03-23 13:09

[QUOTE=rogue;256390]Cool! AFAIK this is the first Fermat factor found with my software.

BTW Luigi, it is GMP-Fermat, not GMP-Factor. Would you mind fixing it?[/QUOTE]

Sure I will! :blush:

Yesterday has been a tough day...

Luigi

philmoore 2011-03-23 19:29

[QUOTE=ATH;256419]Yeah I did them back following GIMPS first fermat factor. The discussion is in the same thread, post #35-#69: [URL="http://www.mersenneforum.org/showthread.php?t=12168"]http://www.mersenneforum.org/showthread.php?t=12168[/URL][/QUOTE]

The idea left hanging there was to do the Suyama test once using the GWNUM routines, and then to do it again using MLUCAS when Ernst got the 2^n+1 code added to it, then compare the residues and verify that they match. I could easily generate the residues with pfgw, but performing the GCD computation will take some thought. SCRIPT files in pfgw are not an efficient way to go on this, because SCRIPT is interpreted, and the overhead makes GCD computations way too slow for numbers the size of F25-F27. (Trust me, I've tried it!) But perhaps it could be done directly using George's GCD routine in the GWNUM library. GMP is another possibility, it would be interesting to compare with GWNUM on large numbers. Perhaps since Wilfrid Keller would like to see the computation done with two different sets of software, the GCD should be done both ways.

ATH 2011-03-24 01:36

I tried using the GMP function mpz_powm to calculate 3[sup]2[sup]2^(n-1)[/sup][/sup] mod F[sub]n[/sub]=2[sup]2[sup]n[/sup][/sup]+1 and timed it:

n=14: 1.945s
n=15: 12.143s
n=16: 73.373s
n=17: 415.121s

this suggest the time is roughly 2.6*10[sup]-11[/sup] * 5.98[sup]n[/sup] with R[sup]2[/sup] = 0.9999225.

This means n=25 would take roughly 7*10[sup]8[/sup] sec ~ 22 years.

jasonp 2011-03-24 01:47

[QUOTE=philmoore;256452]GMP is another possibility, it would be interesting to compare with GWNUM on large numbers. Perhaps since Wilfrid Keller would like to see the computation done with two different sets of software, the GCD should be done both ways.[/QUOTE]
GMP has had a sub-quadratic GCD for several years now, and even F31-size GCDs take only a few hours and < 5GB of memory.

R. Gerbicz 2011-03-24 02:32

[QUOTE=ATH;256471]I tried using the GMP function mpz_powm to calculate 3[sup]2[sup]2^(n-1)[/sup][/sup] mod F[sub]n[/sub]=2[sup]2[sup]n[/sup][/sup]+1 and timed it:

n=14: 1.945s
n=15: 12.143s
n=16: 73.373s
n=17: 415.121s

this suggest the time is roughly 2.6*10[sup]-11[/sup] * 5.98[sup]n[/sup] with R[sup]2[/sup] = 0.9999225.

This means n=25 would take roughly 7*10[sup]8[/sup] sec ~ 22 years.[/QUOTE]

By FFT that should be O(4^n*n*log(n)).

akruppa 2011-03-24 12:24

If you want multiplications modulo Fermat numbers, you should call the Schönhage-Strassen code in GMP directly (mul_fft) since it has an implicit modulus 2^n+1. That should give you a factor 2 speedup and asymptotically O(n log(n) log(log(n))) run-time.

rogue 2011-06-23 10:31

9*2^2543551+1 Divides F2543548, found by PrimeGrid.

rogue 2011-06-23 21:44

7333*2^138560+1 Divides F(138557), also by PrimeGrid

rogue 2011-07-02 23:58

3771*2^221676+1 Divides F(221670), by PrimeGrid.

ET_ 2011-07-06 13:53

43714055 · 2^3337 + 1 divides F(3335), by Nikolay Kamenyuk (FermatSearch).

Luigi :smile:

rogue 2011-07-09 00:38

4479*2^226618+1 divides F226614, again by PrimeGrid.

ixfd64 2011-07-09 02:08

Dayam, PrimeGrid is sure on a roll...

JohnFullspeed 2011-07-09 06:27

Please
 
Could you confirm me that I have well understand

F14= 116928085873074369829035993834596371340386703423373313
the only factor find is 319546020820551643220672513
and all primes less than 700000000000000 have been tested

[URL]http://www.prothsearch.net/fermat.html#Prime[/URL]

John

Ralf Recker 2011-07-09 06:47

[QUOTE=JohnFullspeed;265912]Could you confirm me that I have well understand

F14= 116928085873074369829035993834596371340386703423373313
the only factor find is 319546020820551643220672513
and all primes less than 700000000000000 have been tested

[URL]http://www.prothsearch.net/fermat.html#Prime[/URL]

John[/QUOTE]

F[SUB]14[/SUB] is a little bigger than that:

F[SUB]14[/SUB] = 2[SUP]2[SUP]14[/SUP][/SUP]+1 = 2[SUP]16384[/SUP]+1 = 116928085873074369829035993834596371340386703423373313 · C4880

Tests were conducted up to 7*10[SUP]14[/SUP]*2[SUP]16[/SUP]+1

Another way to write the known factor is: 1784180997819127957596374417642156545110881094717 * 2[SUP]16[/SUP]+1

[CODE]Sat Jul 9 09:28:17 2011 : --------------------------------------------------
Sat Jul 9 09:28:17 2011 : Found a factor for F14: 1784180997819127957596374417642156545110881094717*2^16+1
Sat Jul 9 09:28:17 2011 :
Sat Jul 9 09:28:17 2011 : Current k : 1784180997819127957596374417642156545110881094717
Sat Jul 9 09:28:17 2011 : Tested ks : 94718
Sat Jul 9 09:28:17 2011 :
Sat Jul 9 09:28:17 2011 : Sieving to : 1742539 [131073. Prime]
Sat Jul 9 09:28:17 2011 :
Sat Jul 9 09:28:17 2011 : Step : F14-1 mod (k*2^16+1).
Sat Jul 9 09:28:17 2011 :
Sat Jul 9 09:28:17 2011 : Work time : 0:00:00:00
[/CODE]A quick look at the coefficient is enough to see that this factor most likely wasn't found by trial division :smile:
[CODE]Sat Jul 9 09:35:21 2011 : Speed :
Sat Jul 9 09:35:21 2011 :
Sat Jul 9 09:35:21 2011 : 22409390 k / second
[/CODE]

ET_ 2011-07-09 10:54

[QUOTE=rogue;265899]4479*2^226618+1 divides F226614, again by PrimeGrid.[/QUOTE]

Any official announcement link?

Luigi

Ralf Recker 2011-07-09 12:16

[QUOTE=ET_;265937]Any official announcement link?

Luigi[/QUOTE]
Not yet.

philmoore 2011-07-09 18:32

[QUOTE=JohnFullspeed;265912]
The only factor find is 319546020820551643220672513
John[/QUOTE]

This is a factor of F13, not F14.

rogue 2011-09-12 16:15

25*2^2141884+1 Divides F2141872, by PrimeGrid

axn 2011-09-12 18:00

[QUOTE=rogue;271545]25*2^2141884+1 Divides F2141872, by PrimeGrid[/QUOTE]

The comment is not proper. It is not archived under "Divides Fermat" category. Would come at number 5 there.

EDIT:- Also, Divides GF comments are missing.

bdodson 2011-09-13 02:45

[QUOTE=axn;271554]The comment is not proper. It is not archived under "Divides Fermat" category. Would come at number 5 there.

EDIT:- Also, Divides GF comments are missing.[/QUOTE]
I'm not clear about your objection here. The Prime pages gives
the complete Primegrid report as
[code]
25*2^2141884+1 Divides F2141872
25*2^2141884+1 Divides GF(2141871,5)
25*2^2141884+1 Divides xGF(2141872,5,2)
25*2^2141884+1 Divides xGF(2141867,5,4)
25*2^2141884+1 Divides xGF(2141872,8,5)
25*2^2141884+1 Divides GF(2141872,10) [/code]
So that, while this newly found prime divides several GF's and xGF's,
the first line asserts that this prime also divides the given Fermat
number. Further, while this is listed as a "user comment", we also
have
[code]
Official Comment: Divides F2141872!!!!, generalized Fermat [/code]
The front page on Primegrid also notes
[code]
... [this is] PrimeGrid's 8th Prime Fermat Divisor in the Proth Prime
Search project: 25*2^2141884+1 Divides F(2141872). This is the
292nd known divisor and the 9th found in 2011. [/code]
I don't see a "number 5" there. :question:

-Bruce*

axn 2011-09-13 03:23

The archival tags section ([url]http://primes.utm.edu/primes/page.php?id=101943#tags[/url]) only shows Generalized Fermat.

It should also be filed under "Divides Fermat", "Divides GF(*,5)", and "Divides GF(*,10)" ([url]http://primes.utm.edu/top20/sizes.php[/url]). i.e. these entries should be properly mentioned in the "official comments" section, not just the "unofficial comments" section. Perhaps someone can email Prof Caldwell?

bdodson 2011-09-13 13:39

[QUOTE=axn;271588]The archival tags section ([url]http://primes.utm.edu/primes/page.php?id=101943#tags[/url]) only shows Generalized Fermat.

It should also be filed under "Divides Fermat", "Divides GF(*,5)", and "Divides GF(*,10)" ([url]http://primes.utm.edu/top20/sizes.php[/url]). i.e. these entries should be properly mentioned in the "official comments" section, not just the "unofficial comments" section. Perhaps someone can email Prof Caldwell?[/QUOTE]
Ah, you're objecting to the Prime Pages report; not disputing that this
is a new Fermat divisor. Thanks. I crunched a bunch of these n = 2M+
primality tests myself, before that range completed; but haven't gotten
above n = 1.738M yet. Just finding the prime is such an unlikely occurance,
being a Fermat divisor with k = 25 a great bonus (cf. 1/k chance).

The divisor itself is relatively unusual; many of the recent Primegrid finds
have primes with exponent n+3 or n+4 dividing F_n, while this one has
n+12. -bdodson*

rogue 2012-01-06 23:10

329*2^1246017+1 Divides F(1246013), discovered by PrimeGrid

bdodson 2012-01-08 07:46

[QUOTE=rogue;285145]329*2^1246017+1 Divides F(1246013), discovered by PrimeGrid[/QUOTE]
Completed "Proth Prime searches" --- 1,871,042 with 313 positive
llr tests, for my first Fermat factor. Found on one of the old 32-bit
xeons; it's amazing that I didn't get DC credit instead. And note
the k = 329, with only 1/329 chance of a Proth giving a Fermat divisor.

Currently the 6th largest. -bdodson*

bdodson 2012-01-09 23:51

PrimeGrid observation
 
[QUOTE=bdodson;285366]Completed "Proth Prime searches" --- 1,871,042 with 313 positive
llr tests, for my first Fermat factor. ... And note
the k = 329, with only 1/329 chance of a Proth giving a Fermat divisor.

Currently the 6th largest. -bdodson*[/QUOTE]
John Blazek, of PrimeGrid, points to a link at the Prime Pages to the effect that
[QUOTE]
your prime ranks first among "weighted" Fermat primes

[url]http://primes.utm.edu/top20/page.php?id=8#weighted[/url]
[/QUOTE]
where Caldwell remarks about the ranking
[code]
For purposes of amusement only, we decided to try to rank [Fermat] divisors
based on the facts that

(1) large primes are harder to find than small ones; and
(2) the probability that N = k*2^n+1 divides a Fermat numbers
appears to be O(1/k). [/code]
As a factoring person, I won't argue with Caldwell on this prime!

Stargate38 2012-01-13 00:22

I wonder if PrimeGrid will ever find a factor to F(8675309). They probably can if they found a megabit prime factor for F(1246013). It wouldn't take very long if they have enough people connected. It would be one of the 20 largest known primes. :smile:

rogue 2012-02-07 16:46

PrimeGrid finds another one:

131*2^1494099+1 Divides F(1494096)

pinhodecarlos 2012-02-07 19:15

[QUOTE=rogue;288555]PrimeGrid finds another one:

131*2^1494099+1 Divides F(1494096)[/QUOTE]

It was found by Rob Derrera and not by Primegrid. Why do you insist the fermat factors were found by Primegrid?

rogue 2012-02-07 19:43

[QUOTE=pinhodecarlos;288562]It was found by Rob Derrera and not by Primegrid. Why do you insist the fermat factors were found by Primegrid?[/QUOTE]

I would prefer that you took a more civil tone. I could have specified that he found it while working on PrimeGrid's Proth Prime Search project, but to indicate that he found it without help from PrimeGrid would not be correct either.

As I understand how the project works, his computer found the prime, but PrimeGrid runs the Fermat divisibility test on the prime. Fermat divisibility testing is done by pfgw and there is no support for pfgw in BOINC.

pinhodecarlos 2012-02-07 19:49

[QUOTE=rogue;288564]I would prefer that you took a more civil tone. [/QUOTE]
I expect the same for you too.

[QUOTE=rogue;288564]
I could have specified that he found it while working on PrimeGrid's Proth Prime Search project, but to indicate that he found it without help from PrimeGrid would not be correct either.

As I understand how the project works, his computer found the prime, but PrimeGrid runs the Fermat divisibility test on the prime. Fermat divisibility testing is done by pfgw and there is no support for pfgw in BOINC.[/QUOTE]

So it was his machine who found it and he his a member of Primegrid...I see...

rajula 2012-02-08 06:24

[QUOTE=pinhodecarlos;288562]It was found by Rob Derrera and not by Primegrid. Why do you insist the fermat factors were found by Primegrid?[/QUOTE]

Saying that it was "found by Primegrid" is also the easiest short way of providing a large amount of information and source for it. If Derrera was to be mentined, how could have rogue left out the information on programs (or main programmers) and on the sieving effort?

Saying that it was found by Primegrid tells you exactly where to find the information. It is also factually correct. (I agree with you that) the combination "main contributor to the individual test" + "project name" would have been nicer. Still, if one is to drop one of those, it should be the first one as the second one gives it easily.

Also, saying that "the factor was found by Rob Derrera and not by Primegrid" is simply wrong and even insulting to the people involved in the background work.

jmblazek 2012-02-10 20:19

[QUOTE=rogue;288564]As I understand how the project works, his computer found the prime, but PrimeGrid runs the Fermat divisibility test on the prime. Fermat divisibility testing is done by pfgw and there is no support for pfgw in BOINC.[/QUOTE]
This is correct. The server performs the Fermat divisibility test and it uses pfgw.

Maybe a simple link to the [URL="http://www.primegrid.com/download/PPS-F1494096.pdf"]official announcement[/URL] would suffice. It credits the project and its founders, the prime finder and host, the verifier and host, the software and its developers, and the thousands of others who participated in helping reach this discovery. However, a quick search at the Prime Pages for [URL="http://primes.utm.edu/primes/page.php?id=104247"]131*2^1494099+1[/URL] will provide the link as well. :smile:

But then again, maybe it falls short. For instance, the following are absent from the credits:[INDENT] the manufacturers of all the hardware
the creators of the code used in the development of the programs
the "helper" software used within the programs
the server that actually ran the Fermat divisibility test
the parents who conceived all those involved
ad absurdum
...the big bang.
[/INDENT](whew)

Scratch all that. I like rajula's comment better: "Saying that it was "found by Primegrid" is also the easiest short way of providing a large amount of information and source for it."

ET_ 2012-03-11 19:44

New fermat factor found by Fermatsearch!
 
March 11, 2012
Seventh Fermat factor found by Takahiro Nohara!
238451805 . 2[sup]2608[/sup]+1 is a Factor of F[sub]2606[/sub]!!!.
The factor was discovered by Takahiro Nohara of Japan, and is the third factor of this year.
He used NewPGen.exe by Paul Jobling for sieving and OpenPFGW.exe for PRP test and xGFN divisibility test. Takahiro found his factor while testing N=2005-2999 and k=60,000,000-400,000,000 exactly on the first anniversary of the earthquake and tsunami disaster that triggered also a nuclear accident in Fukushima..
Congratulations form the team of FermatSearch!

Luigi

wreck 2012-03-29 15:19

On March 28, 2012, Andriy Sen discovered a new Fermat factor.
4785972759 · 2^954 + 1 divides F943.

rogue 2012-03-29 15:34

[QUOTE=wreck;294656]On March 28, 2012, Andriy Sen discovered a new Fermat factor.
4785972759 · 2^954 + 1 divides F943.[/QUOTE]

Cool! What software was used?

wreck 2012-03-30 10:29

[QUOTE=rogue;294660]Cool! What software was used?[/QUOTE]
The factor was discovered by Andriy Sen of Ukraine, and is the fourth factor of this year.
He used GMP-Fermat.exe on a Windows Server 2008 R2 Standard x64, Intel Core2 CPU 6600 @ 2.40 GHz to test it. Andriy found his factor while testing N=900-989 and k=4,000,000,000-5,000,000,000.

ET_ 2012-03-30 14:40

[QUOTE=wreck;294806]The factor was discovered by Andriy Sen of Ukraine, and is the fourth factor of this year.
He used GMP-Fermat.exe on a Windows Server 2008 R2 Standard x64, Intel Core2 CPU 6600 @ 2.40 GHz to test it. Andriy found his factor while testing N=900-989 and k=4,000,000,000-5,000,000,000.[/QUOTE]

Yup, and that should be the second Fermat factor found with Mark's software... :smile:

Luigi

rogue 2012-03-30 16:29

[QUOTE=ET_;294838]Yup, and that should be the second Fermat factor found with Mark's software... :smile:[/QUOTE]

I noticed that. Now I just need to find one myself.

Note that this could be a screamer app if run on a GPU. I've thought about it, but I just don't have the time necessary for it.

ET_ 2012-03-30 16:42

[QUOTE=rogue;294856]I noticed that. Now I just need to find one myself.

Note that this could be a screamer app if run on a GPU. I've thought about it, but I just don't have the time necessary for it.[/QUOTE]

I did the same, and have some very rough code to start with. And the correct GMP libraries to implement mp math on CUDA...

What I desperately lack is time. :sad:

Luigi

rogue 2012-03-30 18:26

[QUOTE=ET_;294857]I did the same, and have some very rough code to start with. And the correct GMP libraries to implement mp math on CUDA...[/QUOTE]

I would suggest aiming for OpenCL for the main reason that one wouldn't be locked into using NVIDIA. Most Macs have ATI cards, which can't run CUDA.

ET_ 2012-07-09 10:11

300th Fermat factor found!
 
July 7th, 2012
300th Fermat factor found!
20018578522347 . 2[sup]88[/sup]+1 is a Factor of F[sub]86[/sub]!!!.
The factor was discovered by Michael Dangler of USA, using Mark Rodenkirch's program GMP-Factor, and is the ninth factor discovered this year.
The factor was found using this environment:
[LIST][*]Windows 7 Home Premium 64-bit Operating System[*]Toshiba Satellite P775[*]Intel(R)Core(TM)i7-2670QM CPU @2.20GHZ 6.00 GB Memory[/LIST]
Michael found the factor on its eleventh test-range, after only a few months of testing.
Congratulations from the team of FermatSearch!
-

ET_ 2012-07-10 16:04

July 10th, 2012
New Fermat factor after 3 days!
2674670937447 . 2[sup]171[/sup]+1 is a Factor of F[sub]166[/sub]!!!.
The factor was discovered by Roman Maznichenko from Russia using a AMD FX-8120 @3800MHz and his version of Mark Rodenkirch's GMP-Fermat. This is the fourth factor found by GMP-Fermat, and the second found by Roman Maznichenko.
We have discovered 9 factors in less than 7 months, the same total of the whole 2011, and we keep going!


Luigi

Batalov 2012-09-26 06:07

[COLOR=Green](branched the GFNs to a separate, eponymous, thread)[/COLOR]

I do however hope that this thread, too, will get extended soon, any day now. I am still searching for the word "has"!

rajula 2012-10-09 13:13

Not with mmff (this was with newpgen + pfgw), but still:

143918649*2^4654+1 is a Factor of F4652.

ET_ 2012-10-09 13:22

:groupwave::bow wave::bow wave::bounce wave::party:[QUOTE=rajula;314060]Not with mmff (this was with newpgen + pfgw), but still:

143918649*2^4654+1 is a Factor of F4652.[/QUOTE]

:bow wave::bounce wave::bounce wave::party:

Batalov 2012-10-09 17:26

yay!

LaurV 2012-10-10 05:12

Yarrrr! Two thumbs up! kotgw!
Our factor is cornered, we will catch him soon...

rogue 2012-11-07 00:06

I see that this wasn't posted:

1207*2^410108+1 divides F410105

discovered by Scott Brown via [URL="http://prpnet.mine.nu:12000/user_gfns.html"]PrimeGrid's PPSElow project on PRPNet[/URL]

Batalov 2012-11-07 00:37

I was wondering why there was that gap in W.Keller's reservations:
[CODE]...
73001-80000 20*10^3
80001-390000 10*10^3 Updated!
390001-450000 1200
450000-925000 10*10^3 Updated!
...
[/CODE]
Now, it is clear.

Nice find! (and just at the border of the interval)

c10ck3r 2012-11-07 01:39

[QUOTE=rogue;317300]I see that this wasn't posted:

1207*2^410108+1 divides F410105

discovered by Scott Brown via [URL="http://prpnet.mine.nu:12000/user_gfns.html"]PrimeGrid's PPSElow project on PRPNet[/URL][/QUOTE]

"We" realize this was found 7 years ago, right?

rogue 2012-11-07 02:06

[QUOTE=c10ck3r;317322]"We" realize this was found 7 years ago, right?[/QUOTE]

Sorry, I hadn't looked it up.

Batalov 2012-11-07 02:12

PPSE low found some xGFs, too and they (except one) also seem to be known.
[CODE]> awk '$5>390000 && $5<450000 && $4>1000' GFNfacs.
8 1 417447 1257 417451 2007 Benson
10 1 395563 3021 395564 2012 Matillek
12 5 417896 1949 417897 2008 Harvey
12 5 440260 1473 440261 2008 Harvey

However this one appears to be new:
+---------------------------------------------------------+
| GFN Divisors for User SysadmAtNbg |
|---------------------------------------------------------|
| Tested Number | Divides GFN | Date Reported ||
|---------------+---------------+------------------------+|
|4869*2^413322+1|xGF(413321,7,6)|2012-10-01 00:26:51 GMT ||
|---------------------------------------------------------|
| User SysadmAtNbg has found 1 GFN divisor |
+---------------------------------------------------------+
[/CODE]

Batalov 2012-11-09 16:55

5505161*2^9449+1 is a Factor of F9447

(newpgen+pfgw, 9000<N<=10000, 5e6<k<10e6; popped out tonight)

ATH 2012-11-10 00:41

Congratulations!! Very nice find. :bow: :cool: :lol: :wacky: :bounce:
Amazing the next factor is found with newpgen and pfgw after all the recent factoring with mmff :big grin: :big grin:

Batalov 2012-11-10 00:48

I can only repeat after Gary Player:
"The more I practice, the luckier I get."

I am not giving up on mmff (especially, the 147<N<177 range)!

philmoore 2012-11-12 21:02

Congratulations, Serge! Looks like this is your first Fermat factor. I'm betting it won't be your last.

LaurV 2012-11-13 01:43

Very good job Batalov! Congrats and kutgw!

Batalov 2012-11-13 16:53

one more!
 
30967*2^106436+1 is a Factor of F106432

(from the next range for GFN:
100000<N<=120000, 20000<k<40000)

firejuggler 2012-11-13 17:14

i'm jealous...
so far, 2 fermat, one wich is already know
11925*2^80011+1 is a Factor of GF(80004,12)!!!!
23705*2^80025+1 is a Factor of xGF(80024,10,3)!!!!

aketilander 2012-11-13 17:16

[QUOTE=Batalov;318174]30967*2^106436+1 is a Factor of F106432

(from the next range for GFN:
100000<N<=120000, 20000<k<40000)[/QUOTE]

Its increadible that you found another one in such a short time!!

Congratulations!!! Did you use mmff this time?

:curtisc::curtisc::curtisc::curtisc::curtisc::curtisc::curtisc::curtisc::curtisc::curtisc::curtisc::curtisc::curtisc::curtisc::curtisc::curtisc::curtisc::curtisc::curtisc::curtisc::curtisc::curtisc::curtisc::curtisc::curtisc:

Jatheski 2012-11-13 17:36

[QUOTE=Batalov;318174]30967*2^106436+1 is a Factor of F106432

(from the next range for GFN:
100000<N<=120000, 20000<k<40000)[/QUOTE]

I'm curious, how many cores do you use ?

And congratulations for your two finds !!

philmoore 2012-11-13 17:50

Woo-hoo!

:bow wave::bow wave::bow wave:

:party::party::party::party::party:

:bounce wave::bounce wave::bounce wave:

ixfd64 2012-11-20 05:08

[QUOTE=philmoore;318086]Congratulations, Serge! Looks like this is your first Fermat factor. [I]I'm betting it won't be your last.[/I][/QUOTE]

The prophecy has been fulfilled.

Batalov 2012-11-21 19:26

3860269*2^17750+1 is a Factor of F17748

:sirrobin:

rajula 2012-11-21 21:17

Batalov: with this speed you will factorize all the Fermat numbers before Christmas! :skiing:

rajula 2012-12-07 16:16

mmff finally found one!

2864929972774011*2^41+1 is a Factor of F39!

[CODE]F39 has a factor: 6300047635658008393597059073 [TF:92:93:mmff 0.26 mfaktc_barrett96_F32_63gs][/CODE]

Jatheski 2012-12-07 16:21

Congratulations :beer:

ET_ 2012-12-07 16:43

Well done, Tapio!

Though I'm still waiting for mine...

Luigi

Prime95 2012-12-07 17:08

[QUOTE=rajula;320865]mmff finally found one![/QUOTE]

Woohoo!! I was beginning to worry we'd never find one.

Jatheski 2012-12-07 17:56

[QUOTE=rajula;320865]mmff finally found one!

2864929972774011*2^41+1 is a Factor of F39!
[/QUOTE]

I'm jealous :cry:

[CODE]From N To N From k To k Researcher Status
41 41 600,000,000,000,000 1,000,000,000,000,000 Fabrice Le Foulher factoring
41 41 1,000,000,000,000,000 2,000,000,000,000,000 Serge Batalov Reserved
41 41 2,000,000,000,000,000 3,000,000,000,000,000 Tapio Rajala factoring
41 41 3,000,000,000,000,000 4,000,000,000,000,000 Fabrice Le Foulher Reserved[/CODE]

Fabrice

philmoore 2012-12-07 19:24

[QUOTE=Prime95;320875]Woohoo!! I was beginning to worry we'd never find one.[/QUOTE]

We'll find another one soon, don't worry.

Congratulations, to George and the whole project. 15 new Fermat factors in all this year, the most since 2001 when 22 new factors were discovered. And the year is not over yet...

LaurV 2012-12-08 05:43

Congratulation man!

We wish that your next factor be a split of F20 or F24 :D
(save F33 for us...:whistle:)

edit: now[URL="http://www.prothsearch.net/fermat.html"] this [/URL]would need and update...

ET_ 2012-12-08 12:13

I already emailed Wilfrid Keller about the discovery.

Let him the time to read and update... :smile:

Luigi

Batalov 2012-12-27 00:38

A factor of F1132
 
GMP_Fermat saiz:
"Found factor 10111717305*2^1136+1 of 2^2^1132+1"

No exclamation points, though (the famous "!!!!")

c10ck3r 2012-12-27 03:53

Congrats on the factor!!!
How big of Fermat numbers (if any) is P-1 viable for?
This could be found with B1=9 B2=225M iirc.

axn 2012-12-27 04:09

[QUOTE=c10ck3r;322782]Congrats on the factor!!!
How big of Fermat numbers (if any) is P-1 viable for?
This could be found with B1=9 B2=225M iirc.[/QUOTE]

F31 ~= M(2^31) is about the upper limit of "viable" P-1/ECM.

ET_ 2012-12-27 08:44

[QUOTE=Batalov;322768]GMP_Fermat saiz:
"Found factor 10111717305*2^1136+1 of 2^2^1132+1"

No exclamation points, though (the famous "!!!!")[/QUOTE]

You deserve the exclamation!

Luigi

philmoore 2012-12-28 04:12

[QUOTE=Batalov;322768]GMP_Fermat saiz:
"Found factor 10111717305*2^1136+1 of 2^2^1132+1"

No exclamation points, though (the famous "!!!!")[/QUOTE]

It was a very good year!!!! 15 Fermat factors so far.

Xyzzy 2012-12-28 04:38

F[sub]12[/sub] continues to mock us. We stopped running curves a few months ago. We have run T55 thrice.

:mike:

ET_ 2012-12-28 08:12

[QUOTE=Xyzzy;322892]F[sub]12[/sub] continues to mock us. We stopped running curves a few months ago. We have run T55 thrice.

:mike:[/QUOTE]

I am continuing, from time to time...

:et_:

literka 2012-12-28 12:38

[QUOTE=ET_;322907]I am continuing, from time to time...

:et_:[/QUOTE]


Yes, it is a big question about F12. But I started to be interested in Fermat numbers with discovery of a factor of F14.
Is it known, if there is not a prime factor between 5 known prime factors of F12 and a 54 digits prime factor? Is it known that factor of F14 found by Rajula and others is the smallest one?

henryzz 2012-12-28 12:49

[QUOTE=literka;322928]Yes, it is a big question about F12. But I started to be interested in Fermat numbers with discovery of a factor of F14.
Is it known, if there is not a prime factor between 5 known prime factors of F12 and a 54 digits prime factor? Is it known that factor of F14 found by Rajula and others is the smallest one?[/QUOTE]

If 3t55 have been run on F12 then there isn't a very large chance of a <54 digit factor.
I think 1-e^-3 =5% for 55 digits or less(and that's forgetting what everyone else has done)

c10ck3r 2012-12-28 15:12

Is it safe to say that all Riesel primes reported [URL="http://mersenneforum.org/showthread.php?t=8621"]here[/URL], [URL="http://www.mersenneforum.org/showthread.php?t=1767"]here,[/URL]and [URL="http://www.mersenneforum.org/showthread.php?t=13180"]here[/URL] (et al.) are tested for division into Fermat numbers?

rogue 2012-12-28 15:56

[QUOTE=c10ck3r;322934]Is it safe to say that all Riesel primes reported [URL="http://mersenneforum.org/showthread.php?t=8621"]here[/URL], [URL="http://www.mersenneforum.org/showthread.php?t=1767"]here,[/URL]and [URL="http://www.mersenneforum.org/showthread.php?t=13180"]here[/URL] (et al.) are tested for division into Fermat numbers?[/QUOTE]

Probably not. The reason is that Proth primes are tested, not Riesel primes.

c10ck3r 2012-12-28 16:10

[QUOTE=rogue;322941]Probably not. The reason is that Proth primes are tested, not Riesel primes.[/QUOTE]
Shoot. I can't believe I spaced that...
Are all the Proth primes found checked?
Also, which projects search for Proth primes?

Ralf Recker 2012-12-28 16:18

[QUOTE=c10ck3r;322942]Shoot. I can't believe I spaced that...
Are all the Proth primes found checked?
Also, which projects search for Proth primes?[/QUOTE]
PrimeGrid's Proth Prime Search searches for Proth primes. The project admins check if newly found prime numbers divide Fermat numbers.

[URL="http://www.primegrid.com/"]PrimeGrid's home page[/URL] lists some of their recent finds:

[QUOTE]25·2[SUP]2141884[/SUP]+1 (PPS): [URL="http://www.primegrid.com/download/pps-F2141884.pdf"]official announcement[/URL] | Fermat Divisor
329·2[SUP]1246017[/SUP]+1 (PPS): [URL="http://www.primegrid.com/download/pps-F1246013.pdf"]official announcement[/URL] | Fermat Divisor
519·2[SUP]567233[/SUP]+1 (PPS): [URL="http://www.primegrid.com/download/pps-F567233.pdf"]official announcement[/URL] | Fermat Divisor
651·2[SUP]476624[/SUP]+1 (PPS): [URL="http://www.primegrid.com/download/pps-F476624.pdf"]official announcement[/URL] | Fermat Divisor
4479·2[SUP]226618[/SUP]+1 (PPS): [URL="http://www.primegrid.com/download/pps-F226614.pdf"]official announcement[/URL] | Fermat Divisor
3771·2[SUP]221676[/SUP]+1 (PPS): [URL="http://www.primegrid.com/download/pps-F221670.pdf"]official announcement[/URL] | Fermat Divisor
7333·2[SUP]138560[/SUP]+1 (PPS): [URL="http://www.primegrid.com/download/pps-F138557.pdf"]official announcement[/URL] | Fermat Divisor[/QUOTE]

Batalov 2012-12-28 19:04

[URL]http://www.prothsearch.net/[/URL] also has some data.
[URL]http://www.prothsearch.net/status.html[/URL]

PGrid is of course one of the largest users. I've added some data for small k's recently (15, 21), but no Fermat factors yet (for small k's one is almost guaranteed to find GF and xGF factors for a consolation). Surely, I tested the three primes that I found like PGrid does (pfgw -a1 -gxo).

ET_ 2012-12-29 11:17

[QUOTE=Batalov;322945][URL]http://www.prothsearch.net/[/URL] also has some data.
[URL]http://www.prothsearch.net/status.html[/URL]

PGrid is of course one of the largest users. I've added some data for small k's recently (15, 21), but no Fermat factors yet (for small k's one is almost guaranteed to find GF and xGF factors for a consolation). Surely, I tested the three primes that I found like PGrid does (pfgw -a1 -gxo).[/QUOTE]

Is the "-a1" switch still needed with the new PFGW?

Luigi

rogue 2012-12-29 15:46

[QUOTE=ET_;323009]Is the "-a1" switch still needed with the new PFGW?[/QUOTE]

No. With George's help, the FFT selection for GFN divisibility testing is very solid. Even if it detects a MAXERR condition, pfgw will resize the FFT and try again.

Jatheski 2013-01-02 18:18

[QUOTE=rogue;323028]No. With George's help, the FFT selection for GFN divisibility testing is very solid. Even if it detects a MAXERR condition, pfgw will resize the FFT and try again.[/QUOTE]

Good to know, it's really faster without it.

Batalov 2013-01-19 17:30

First for 2013
 
Maximilian Pacher found his fifth new factor of a Fermat number: 406860969·2^3322 + 1 divides F3314


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