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First Fermat factor of 2012!
On 4 Jan 2012 0:34:57 UTC, PrimeGrid's Proth Prime Search project found a prime Fermat divisor: 329 . 2^1246017+1 is a Factor of   F_1246013!!!.
The prime is 375,092 digits long and will enter Chris Caldwell's "The Largest Known Primes Database" ranked 6th for prime Fermat divisors and 522nd overall. It is the 1th divisor found in 2012 and 293rd overall.
The discovery was made by Bruce Dodson of the United States using an Intel Xeon MP @ 2.80GHz with 12 GB RAM running Linux. This computer took just over 3 hours and 25 minutes and 28 seconds to complete the primality test using LLR. Grzegorz is a member of the Sicituradastra Team.
The prime was verified on 6 January 2012 17:41:07 UTC, by Ovidiu Cioca of Canada using an Intel Core2 6700 @ 2.66GHz with 4 GB RAM running Windows XP. This computer took 29 minutes and 45 seconds to complete the primality test using LLR.
The credits for the discovery are as follows:
   1. Bruce Dodson (United States), discoverer
   2. PrimeGrid, et al.
   3. Srsieve, sieving program developed by Geoff Reynolds
   4. PSieve, sieving program developed by Ken Brazier and Geoff Reynolds
   5. LLR, primality program developed by Jean Penné
   6. OpenPFGW, a primality program developed by Chris Nash & Jim Fougeron with maintenance and improvements by Mark Rodenkirch
Congratulations go to Bruce and to the leading organizers of PrimeGrid!
- Nine Fermat factors found in 9 months! Will we be able to reach 12 this year?
On 9 Sep 2011 11:50:50 UTC, PrimeGrid's Proth Prime Search project found a prime Fermat divisor: 25 . 2^2141884+1 is a Factor of   F_2141872!!!.
The prime is 644,773 digits long and will enter Chris Caldwell's "The Largest Known Primes Database" ranked 5th for prime Fermat divisors and 88th overall. It is the 9th divisor found in 2011 and 292nd overall.
The discovery was made by Grzegorz Granowski of Poland using an Intel Xeon X5550 @ 2.67GHz with 12 GB RAM running Windows Vista x64. This computer took just over 58 minutes and 28 seconds to complete the primality test using LLR. Grzegorz is a member of the Polish National Team.
The prime was verified on 11 Sep 2011 12:02:18 UTC, by John R. H. Graham of Canada using an Intel i7 920 @ 2.67GHz with 12 GB RAM running Windows 7 x64. This computer took about 1 hour and 47 minutes to complete the primality test using LLR. John is a member of Team Canada.
The credits for the discovery are as follows:
   1. Grzegorz Granowski (Poland), discoverer
   2. PrimeGrid, et al.
   3. Srsieve, sieving program developed by Geoff Reynolds
   4. PSieve, sieving program developed by Ken Brazier and Geoff Reynolds
   5. LLR, primality program developed by Jean Penné
   6. OpenPFGW, a primality program developed by Chris Nash & Jim Fougeron with maintenance and improvements by Mark Rodenkirch
Congratulations go to Grzegorz and to the leading organizers of PrimeGrid!
- News from the download page!
New PFGW for Windows, MAC and Linux, and fermfact 2.0 added today.
- Another Fermat factor from PrimeGrid!
On 8th July 2011 02:22:20 UTC, PrimeGrid's Proth Prime Search project, through PRPNet, found a prime Fermat divisor: 4479 . 2²²⁶⁶¹⁸+1 is a Factor of   F₂₂₆₆₁₄!!!.
The prime is 68,223 digits long. It is the 8th divisor found in 2011 and 291th overall.
The discovery was made by Peter Doggart of the United Kingdom using an AMD Phenom 9600 X4 @ 2.3 GHz with 3 GB RAM running 32 bit Windows 7. This computer took 78 seconds to complete the primality test using LLR.
The credits for the discovery are as follows:
   1. Peter Doggart (United Kingdom), discoverer
   2. PrimeGrid, et al.
   3. Srsieve, sieving program developed by Geoff Reynolds
   4. PSieve, sieving program developed by Ken Brazier and Geoff Reynolds
   5. LLR, primality program developed by Jean Penné
   6. OpenPFGW, a primality program developed by Chris Nash and Jim Fougeron with maintenance and improvements by Mark Rodenkirch
Congratulations go to Peter and to the leading organizers of PrimeGrid!
- Seven Fermat factors found in 7 months!
43714055 . 2³³³⁷+1 is a Factor of   F₃₃₃₅!!!.
The factor was discovered by Nikolay Kamenyuk of Ukraine, and is the seventh factor of this year. We now have 250 Fermat numbers known to be composite, and "10 to go" to reach 300 prime factors overall.
Nikolay found his factor while testing N=3001-4000 and k=40,000,000-100,000,000.
Congratulations Nikolay!
- PrimeGrid strikes again!
On 1 July 2011 02:59:41 UTC, PrimeGrid's Proth Prime Search project, through PRPNet, found a prime Fermat divisor: 3771 . 2²²¹⁶⁷⁶+1 is a Factor of   F₂₂₆₁₇₀!!!.
The prime is 66,736 digits long. It is the 6th divisor found in 2011 and 289th overall.
The discovery was made by Mark Doom of the United States using an AMD Phenom II X6 1090T with 2 GB RAM running Windows 7 x64. This computer took 40 seconds to complete the primality test using LLR.
The credits for the discovery are as follows:
   1. Mark Doom (United States), discoverer
   2. PrimeGrid, et al.
   3. Srsieve, sieving program developed by Geoff Reynolds
   4. PSieve, sieving program developed by Ken Brazier and Geoff Reynolds
   5. LLR, primality program developed by Jean Penné
   6. OpenPFGW, a primality program developed by Chris Nash and Jim Fougeron with maintenance and improvements by Mark Rodenkirch
Congratulations go to Mark and to the leading organizers of PrimeGrid!
- New Fermat factor discovered after 1 day!
7333 . 2¹³⁸⁵⁶⁰+1 is a Factor of   F₁₃₈₅₅₇!!!.
The factor was discovered by Dirk D'huyvetters of Belgium coadiuvated by the PrimeGrid team. This is the 288th known divisor fifth factor found this year.
This factor was the first of the three disconvered in March, but only during the recent double-checking for GFN divisibilities the factor was revealed, as the team was focused on Proth Primes and not Fermat factors.
Congratulations go to Dirk and to the leading organizers of PrimeGrid: John Blazek, Rytis Slatkevičius and Lennart Vogel!
- New record-size Fermat factor!
As part of PrimeGrid's Proth Prime Search, Scott Brown (USA) found the following new factor of a Fermat number: 9 . 2^2543551+1 is a Factor of   F_2543548!!!.
This factor 765,687 digits long exceeds in size the prime factor 3 . 2^2478785+1 of   F_2478782 discovered on October 10, 2003 and therefore is currently the largest known divisor of a Fermat number!
Congratulations to everyone involved in this remarkable discovery!!
- New Fermat factor after 5 days!
111318179143061 . 2⁴⁵+1 is a Factor of   F₄₂!!!.
The factor was discovered by Roman Maznichenko from Russia using Mark Rodenkirch's GMP-Factor. This is the first factor found by GMP-Factor.
Roman worked hard on ECM also, and we all hope he will find another factor soon.
Congratulation, Roman!
- Second Fermat factor of 2011!
14783975791554494074552473179612897725474511 . 2¹⁹+1 is a Factor of   F₁₇!!!.
The factor was discovered by David Bessell from St Michael's Collegiate School in Australia using Prime95. This is the third factor found by David while computing ECM curves on small Fermat numbers.
The cofactor of F17 has around 39,000 digits, and has been proven composite.
Congratulation, David!
- FermatSearch.org has a new server ! To guarantee better performances to our users, your webmaster has taken the opportunity to upgrade the old hardware and install a new more powerful one. Please let me know about every possible glitch that may have occurred during the migration of data.
- GMP-Fermat 2.1 for Windows 64 bit version has passed its checks!!!.
Thanks to Matt Anderson (who addressed the issue on MersenneForum) and Brian Gladman (who offered his programming skills), we now finally have a GMP-Fermat version with superfast assembly routines written by Geoff Reynolds and running on Windows 64-bit platforms!
The new executable can be found on the Download page. Wonderful job, Brian and Matt, thank you!
- First Fermat factor of 2011!
837747239 . 2¹²⁰³+1 is a Factor of   F₁₂₀₁!!!.
The factor was discovered by our old friend Maximilian Pacher, from Austria, using NewPGen, PRP and PFGW programs. Maxi could have found this factor seven years ago if his range were not limited to 1200.
This is his fourth Fermat factor"
Congratulation, Maxi!
- GMP-Fermat 2.1 for Windows 64 bit version is out!!!.
Thanks to Matt Anderson (who addressed the issue on a forum) and Brian Gladman (who offered his programming skills), we now finally have a GMP-Fermat version with superfast assembly routines written by Geoff Reynolds and running on Windows 64-bit platforms!
The new executable can be found on the Download page. Wonderful job, Brian and Matt, thank you!
- A second new Fermat factor has been found on November 20!
272392805475 . 2³⁰⁴+1 is a Factor of   F₂₉₉!!!.
The factor was discovered by Alexey Komkov, from Russia, using his own program written in Borland C++ builder. Alexey has been testing a huge range using 30 P4 computers in the last 6 months.
Congratulation, Alexey!
- A totally new Fermat factor has been found!
103257279 . 2²⁴²²+1 is a Factor of   F₂₄₂₀!!!.
The factor was discovered by Peter Strasser, from Austria, on November 7th, 2010. Peter was testing a huge range with his own program based on Mathematica.
Congratulation, Peter!
- 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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Compiled by Luigi Morelli