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Five in a row! Michael Vang (USA) found a new Fermat factor: 17353230210429594579133099699123162989482444520899 . 2¹⁵+1 is a Factor of   F₁₂!!!.
Mike found this factor after 5200 curves ran on F12.
Software used: GMP-ECM 6.2. The cofactor is still composite.
He used two AMD Phenom X4 9550 quad core boxes with 6GiB RAM each, running on Debian Linux.
Congratulations Mike!
- Third Fermat factor from GIMPS! David Bessel found a new Fermat factor: 3853959202444067657533632211 . 2²⁴+1 is a Factor of   F₂₂!!!.
The factor has been discovered by David Bessell from St Michael's Collegiate School in Australia using Prime95, while testing some ECM curves on F22.
It is the seconf Fermat factor discovered by David Bessell in less than one year, after more than 15,500 GHz-Days.
The cofactor is still composite...
Congratulations to Mr. David Bessell!
- PFGW 3.3.3 for Windows, Linux and MAC is out!!!.
Mark Rodenkirch released another, faster, version of PFGW for Windows, Linux and MAC, based on v25.14 of gwnum library.
The major change in this release is that it has been updated to use gwnum 25.14, which addresses the following issues:
* Gwnum would lose the /d in some (k*b^n+c)/d cases. This happened primarily in cases where the number was between 300 and 350 bits.
* The final conversion from gwnum to binary could fail in cases where generic reduction was used. The larger the number the less likely the bug would occur.
* Zero padded FFTs of length 80 and 112 could fail.
* More conservative in selecting an FFT length for non-base-2 cases.
This release also goes back to using rational FFTs, which are slightly faster than irrational FFTs.
With these changes to gwnum, there will be fewer roundoff errors with PFGW. These changes also address primality tests that silently fail. "Silently fail" refers to tests that do not trigger roundoff errors, yet have an incorrect result. It is highly recommended to update your clients to this release.
The new executable can be found on the Download page. Wonderful job, Mark, thank you!
- Another factor comes from FermatSearch! Cedric Vonck found a new Fermat factor: 81909357657279 . 2⁵⁴+1 is a Factor of   F₅₂!!!.
Cedric found this factor while testing his first range, how lucky!
Software used: Fermat.exe
The new factor is the third Fermat factor discovered in 2010.
Congratulations to Mr. Cedric Vonck!
- GIMPS strikes again! Tapio Rajala (Department of Mathematics and Statistics - University of Jyväskylä, Finland) found a new Fermat factor: 1784180997819127957596374417642156545110881094717 . 2¹⁶+1 is a Factor of   F₁₄!!!.
Tapio found this factor after approximately 750 curves ran on F14 with B1=110M.
Software used: Prime95
Note that F14 was the first Fermat number without known factors. The cofactor, C4880, is composite.
The new factor is the second Fermat factor discovered in 2010, and the second discovered by GIMPS using Elliptic Curves Method.
Congratulations to Mr. Tapio Rajala!
- Sergei Maiorov found a new Fermat factor: 84977118993 . 2⁵²⁰+1 is a Factor of   F₅₁₇!!!.
"It's my first Fermat factor, and also the first one of 2010!"
Software used: Fermat.exe 4.4
Congratulations to Mr. Sergei Maiorov!
- PFGW 3.3.0 for Linux and MAC, and 3.3.1 for WIndows are out!!!.
Mark Rodenkirch released another, faster, version of PFGW for Windows, Linux and MAC, based on v25.13 of gwnum library.
The new executable can be found on the Download page. Wonderful job, Mark, thank you!
- PFGW 3.2.3 is out!!!.
Mark Rodenkirch released a new, enhanced and bug-free version of PFGW for Windows, Linux and MAC, based on v25.13 of gwnum library.
The new executable can be found on the Download page. Thank you Mark!
- Takahiro Nohara found a new Fermat factor: 1814649 . 2¹²⁸²⁷+1 is a Factor of   F₁₂₈₂₅!!!.
"After six month since my previous report of a factor of the Fermat number, I'm able to tell you following one.
I also accumulated dozens of xGFN factors since my previous report.
Software
Fermfact.exe for sieving
LLR.exe for proth test
pfgw.exe to test xGFN divisibility (with -a2 or -a1 switch)"
Congratulations to Mr. Takahiro Nohara!
- George Woltman announced today that a new factor of F19 has been found: 8962167624028624126082526703 . 2²²+1 is a Factor of   F₁₉!!!.
The factor has been discovered by David Bessell from St Michael's Collegiate School in Australia using Prime95, while testing some ECM curves on F19.
It's the first factor of a Fermat number of index < 30 since the turn of the century, and only the fourth of index < 80.
The 35 digits factor has been proven prime, a 157,770-digit composite cofactor remains. The cofactor has been proven composite by independent users, with different software.
The known factorization of F19 is now 70525124609.646730219521.37590055514133754286524446080499713.C157770 Congratulations to GIMPS distributed ECM effort!
- PFGW 1.3 for Windows is out!!!.
Mark Rodenkirch did the magic, and re-engineered PFGW with George Woltman's GWNUM 25.10 library.
The new executable can be found on the Download page. Enhancements to: v1.3 Release Candidate 1
- Updated to v25.10 of George Woltman's gwnum library
- Ported to MacIntel
- Addressed inconsistent handling of switches as some require parameters, some require parameters of specific values, and others have optional parameters
- Print leading zeros on residues so that they are always 16 characters
- Added -k for terse output, useful when running multiple files through PFGW in succession
- Takahiro Nohara strikes again! He found today the fourth Fermat factor of 2009:
71007 . 2⁴⁹⁴⁹⁰+1 is a Factor of   F₄₉₄₈₈!!!.
Takahiro found the factor and two new xGF factors too, using Fermfact for sienving, LLR for Proth tests and OpenPFGW for checking xGFN divisibily test.
Congratulations go to Takahiro Nohara!
- Congratulations to Eric Embling, the discoverer of PrimeGrid's third Fermat divisor in the Proth Prime Search project: 659 . 2⁶¹⁷⁸¹⁵+1 is a Factor of   F₆₁₇₈₁₃!!!.
It is the 3rd found Fermat divisor of 2009 and 273nd overall. The prime is 185,984 digits long and is the 6th largest Fermat Number divisor in Chris Caldwell's “The Largest Known Primes Database”. Incidentally, it is a new record for "weighted" Fermat Number divisors.
The discovery was made by Eric Embling (Eric E) of the United States using an Intel C2D E6750 @ 2.66GHz with 4 GB RAM. This computer took about 8 minutes 31 seconds to test. Eric is a member of team [H]ard|OCP.
The credits for the discovery are as follows:
1. Eric Embling (USA), discoverer
2. PrimeGrid, et al.
3. Srsieve, sieving program developed by Geoff Reynolds
4. LLR, primality program developed by Jean Penné.
- Congratulations to Senji Yamashita, the discoverer of PrimeGrid's second Fermat divisor in the Proth Prime Search project: 519 . 2⁵⁶⁷²³⁵+1 is a Factor of   F₅₆₇₂₃₃!!!.
It is only the 2nd found Fermat divisor of 2009 and 272nd overall. The prime is 170,758 digits long and is the 7th largest Fermat Number divisor in Chris Caldwell's “The Largest Known Primes Database”.
The discovery was made by Senji Yamashita (s-yama) of the Japan using an Intel C2Q Q9450 @ 2.66GHz with 2 GB RAM. This computer took about 8 minutes to test. Senji is a member of team Tamagawa Data Center.
The credits for the discovery are as follows:
1. Senji Yamashita (Japan), discoverer
2. PrimeGrid, et al.
3. Srsieve, sieving program developed by Geoff Reynolds
4. LLR, primality program developed by Jean Penné.
- Takahiro Nohara found today the first Fermat factor of 2009:
177795 . 2³⁸⁹⁶⁹+1 is a Factor of   F₃₈₉₆₇!!!.
Takahiro found the factor and two new xGF factors too.
Congratulations go to Takahiro Nohara!
- Geoffrey Reynolds recoded part of his assembly routines in Mark Rodenkirch's program up to 768 bit, and released binaries of GMP-Factor for both Linux 32 bit and Linux 64 bit platforms!
You can find updated binaries on the Download page.
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FermatSearch passed 1000 CPU years of Pentium II/400 ! Thanks to all the researchers that joined the project!
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it is with a great deal of sadness that I heard that Oliver Atkin died on December 28 from pneumonia. He had suffered a fall and a fractured vertebrae, and contracted pneumonia while in the hospital.
He was a truly great computational number theorist and deserves a note on this forum.
- Congratulations to Eric Ueda, the discoverer of PrimeGrid's first Fermat divisor in the Proth Prime Search project: 651 . 2⁴⁷⁶⁶³²+1 is a Factor of   F₄₇₆₆₂₄!!!.
It is only the 6th found Fermat divisor of 2008 and 270th overall. The prime is 143,484 digits long and is the 8th largest Fermat divisor in Chris Caldwell's “The Largest Known Primes Database”.
The discovery was made by Eric Ueda of the United States using an Intel C2Q Q6600 @ 2.40 GHz with 1 GB RAM. This computer took almost 4 minutes 43 seconds to test. Eric is a member of TeAm AnandTech.
The credits for the discovery are as follows:
1. Eric Ueda (United States), discoverer
2. PrimeGrid, et al.
3. Srsieve, sieving program developed by Geoff Reynolds
4. LLR, primality program developed by Jean Penné.
- After the two Mersenne primes discovered between August and September, we have a new Fermat factor!
Martin Ptáček from Czech Republic found the fifth Fermat factor of 2008: 3334131633063 . 2¹⁰¹+1 is a Factor of   F₉₆!!!.
Martin found the factor using an AMD sempron LE-1200 2,1GHz and 2GB ram and Fermat.exe program.
Congratulations Martin!
- Your webmaster is back online, and the pending ranges have been updated. Thank to your cumulative effort, all the holes below N=250 have been filled. We are approaching 1000 CPU years of Pentium II/400 !
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Your webmaster will leave for a two weeks vacation Tuesday 4th, so if you have ranges to request or update, please send them to me before November 4th. Of course you have my permission to find out Fermat factors during this time...
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Payam Samidoost found the fourth Fermat number factor of the year!
6089 . 2⁷⁹²²³+1 is a Factor of   F₇₉₂₂₁!!!
"The sieve was done by Fougeron's FermFact up to 3T. It was found prime using Penne's LLRNET running over 30 clients. [07/31/08 22:46:50] 6089*2^79223+1 is prime! Finally Fougeron's pfgw revealed the Fermat divisiblity one night later. Unfortunately PFGW does not log the exact time."
Welcome back, Payam Samidoost!
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A new instrument to search for Fermat factors has been released.
GMP-Fermat, the creation of Mark Rodenkirch (aka rogue) is now available for all platforms. The source code may be compiled on DOS, Linux and Windows, as well as PowerPC, Sparc and all the architectures where GMP library can be installed. Geoffrey Reynolds provided its superfast assembly routines for modular multiplication and we may now download a 64-bit version compiled under Linux, faster than Fermat.exe for n>45.
A wonderful gift for researchers, offered by our collaborative effort.
- Caution about WinPFGW usage for Fermat factor searching.
In WInPFGW there is a risk to miss a Fermat factor.
For example, if you command as follows to calculate Fermat (or Generalized Fermat) numbers divisibility.
pfgw -q"9*2^461081+1" -go{2,2}{2,2} >> Fermat_div_test_out.txt
As you know, 9*2^461081+1 is a factor of F461076. But you will not get this result with winPFGW. This is probably caused by a error of FFT calculation in this software.
To get a correct result, use -a1 or -a2 switches.
-a1 command means use larger size of FFT than standard one.
Needless to say, it takes longer calculation time than normal also.
So far, I've faced at least other 4 examples like this. It is enough risky!
-a2 is much safer, so type -a2 is recommended. But I think -a1 is enough in normal usage.
Takahiro Nohara
- Wonderful news from Takahiro Nohara, who found the third Fermat factor of 2008!
"I found a new prime factor of the Fermat number today. (3rd May): 28949 . 2⁴⁸⁶²⁷+1 is a Factor of   F₄₈₆₂₄. I used FermFact.exe, LLR.exe and PFGW.exe to search this number. This is 3rd factor of Fermat number found by me and it has took close to five years since previuos report.".
Congratulations to Takahiro Nohara!
- Maximilian Pacher Strikes again! Maxi found the second Fermat factor of 2008!
"When I sent you my last Fermat-Factor of F1710. And you have written "a third factor could be near the corner". Now, one month later, I am of the opinion, that it is time to recover a new factor: 364182745 . 2¹⁷²⁴+1 is a Factor of   F₁₇₂₂!!!! I am very happy, that I have found this factor so shortly after my last one. This is my third Fermat-factor an the second in this year if I remember correctly. I used "NewPGen", "PRP" and "WinPFGW".
Congratulations again, Maximilian! Now we're waiting for the third!
- Maximilian Pacher found the first Fermat factor of 2008!
"After 7 years of searching, I'm very happy to announce my second Fermat factor: 351276975 . 2¹⁷¹⁹+1 divides   F₁₇₁₀! I have been searching for Fermat-factors since 2001 and this factor is my second one (my first one is 2018719057*2¹¹⁶²+1, that is a factor of F(1160)). I hope, it will not be the last one."
Maxi found this factor using "NewPGen", "PRP" and "WinPFGW" programs.
Congratulations, Maximilian!
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Compiled by Luigi Morelli