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Thursday, January 8, 2004: An Happy New Year for Yves Gallot who discovered the 5^{th} Generalized Fermat prime of the form b^{131072}+1: 572186^{217}+1 (754,652 digits). Monday, September 22, 2003: Just one month later, Daniel Heuer beat his own record. He found the new largest known Generalized Fermat prime: 1372930^{217}+1! This 804,474 digit number is now the 5^{th} largest known prime. In just about 10 months, the massive sieving effort of Generalized Fermat Numbers already found 4 primes in the top 10 largest known primes. Friday, August 22, 2003: Congratulations to Daniel Heuer who discovered the largest known Generalized Fermat prime: 1176694^{217} +1! This 795,695 digit number is now the 5^{th} largest known prime. Thanks to the massive sieving effort, the 3 largest primes found by the Generalized Fermat Prime Search (all found this year) have more than 600,000 digits! Saturday, July 12, 2003: Congratulations to Michael Angel who discovered the second known prime of the form b^{217}+1: 130816^{131072}+1! This 670,651 digit number is now the 5^{th} largest known prime. Michael "PRPed" this number on a P4Xeon using an asm optimized GeneFer under Linux. He proved primality with Proth . It is the second success for the massive sieving effort and Generalized Fermat Prime Search that already did several GHz years on the 131072 range. Saturday, April 19, 2003: The war is finished, the search just started again. Saturday, March 29, 2003: The search is suspended during the war: the search for prime numbers is an amazing project, but that amazement is overshadowed by the behaviour of some people who, while they consider themselves to be the pinnacle of civilisation, are deliberately killing those who they were not under threat from, and are endangering the lives of their own children. If you want to continue the search, first contribute to the most important thing that should be done today : STOP THE WAR! Wednesday, March 26, 2003: Franz Hagel discovered the 20^{th} Generalized Fermat prime of the form b^{65536}+1 (which is not a prime of the form b^{131072}+1) : 357868^{65536}+1 (363,969 digits). He already found the 10^{th} on July 2002! Friday, February 21, 2002: The whole range 22200000 is completed for exponent 32768. 35 primes were found in this range and the estimate for it was 29 primes. Thanks to Arlin Anderson and Don Robinson, Michael Angel, Göran Axelsson, Ray Ballinger, Yves Bellefeuille, Klaus Bodenstein, Phil Carmody, Gary Chaffey, Greg Childers, Peter Crickman, Rick Cummings, Chad Davis, Patrick Fossano, Yves Gallot, Tim Grubert, Franz Hagel, David Hanson, Steven Harvey, Leonard Hemsen, Daniel Heuer, Yary Hluchan, Paul Kecskes, Johnson Lau, Loïc Mottier, Jevgeni Muischnek, Michael Paepcke, Andy Penrose, Hans Rosenthal, Björn Rösner, Nathan Russell, Peter Shaw, Peter von Steht, Pavlos Saridis, Steve Scott, David Underbakke and Frank Welsch ! Sunday, February 16, 2003: Congratulations to Michael Angel who discovered the first known prime of the form b^{217}+1: 62722^{131072}+1! This 628,808 digit number is now the 5^{th} largest known prime. Michael "PRPed" this number on a P4 using an asm optimized GeneFer under Linux. He proved primality with Proth on an Athlon. Phil Carmody is leading the massive sieving effort that already did several GHz years on the 131072 range. He also together with Bernhard Frey made great strides in the GFN sieving algorithm. David Underbakke wrote AthGFNSieve using Phil's algorithm, and is as a result by far the fastest GFN sieving program. It is the cornerstone of Phil's GFN Sieving effort. Monday, January 6, 2003: An Happy New Year from Daniel Heuer who beat his own record! He discovered the largest known Generalized Fermat prime 1483076^{65536}+1 (404,434 digits), with GFNSieve+Proth. This number is the new largest known prime which is not a Mersenne prime, and the 6^{th} largest known prime. Monday, December 9, 2002: The first success for the
prefiltering of GFN organized by Phil Carmody: three new Generalized
Fermat primes! 291726^{65536}+1 (358,153 digits) and 292550^{65536}+1
(358,233 digits), both found by Yary Hluchan with
Proth. And 440846^{65536}+1 (369,904 digits), found by Michael
Angel with a binary of GeneFer for Linux . Tuesday, October 31, 2002: Proth 7.1: Performance increase on the P4. The new code is 1015% faster on this processor. It's now about as fast on a P4 as on a Athlon XP at the same clock (see benchmarks). An option "Don't use SSE2" was added: it slows down the program on the P4 but 80bit calculations of the x86 FPU allow the test of some ranges that cannot be checked with 64bit SSE2 code. Tuesday, October 8, 2002: Congratulations to Daniel Heuer who discovered the largest known Generalized Fermat prime 1478036^{65536}+1 (404,337 digits), with GFNSieve+Proth. This number is the new largest known prime which is not a Mersenne prime, and the 6^{th} largest known prime. The 20 largest known Generalized Fermat primes have all more than 200,000 digits! And now there are 12 GF primes in the 20 largest known primes (all of them have more than 300,000 digits). Sunday, September 15, 2002: David Underbakke took the torch from Jim Fougeron, and implemented the most uptodate algorithm for GFN sieving in his Athlon and P4optimised AthGFNSieve. This is the only software is used currently for the prefiltering of GFN organized by Phil Carmody. Tuesday, July 30, 2002: Franz Hagel discovered the 10^{th} Generalized Fermat prime of the form b^{65536}+1: 255694^{65536}+1 (354,401 digits). Today, there are 10 GF primes in the 20 largest known primes (all of them have more than 300,000 digits) and 35 GF primes in the top 50 (all of them have more than 180,000 digits). Thursday, July 4, 2002: Andy Penrose discovered the largest known Generalized Fermat prime 1361846^{65536}+1 (402,007 digits), with GFNSieve+Proth. This number is the first +400,000 digit GF prime, the largest known prime which is not a Mersenne prime, and the 6^{th} largest known prime. Thursday, June 27, 2002: Richard Kapek discovered a 8^{th} Generalized Fermat prime of the form b^{65536}+1: 189590^{65536}+1 (345,887 digits). Wednesday, June 26, 2002: A new revision of "A problem on the conjecture concerning the distribution of generalized Fermat prime numbers (a new method for the search for large primes)" is available for download. Monday, June 10, 2002: The version 1.2 of the C source code of "GeneFer" is available. The test of GFN is now faster on Sun, Alpha and SGI workstations and you can check directly a presieved range with it. Sunday, April 21, 2002: Kimmo Herranen joined Phil Carmody to sieve the Generalized Fermat Numbers for exponent 65536. Now, you can download presieved ranges for this exponent too! Saturday, April 13, 2002: The Stat page was updated. The conjecture on the distribution of the Generalized Fermat primes is now fully indicated and some very recent results from Peter Moree and Yves Gallot about the computation of the C_{n} are reported. Saturday, April 13, 2002: The whole range 22700000 is completed for exponent 16384. 89 primes were found in this range and the estimate for it was 96 primes. Thanks to Arlin Anderson and Don Robinson, Michael Angel, Klaus Bodenstein, Greg Childers, Peter Crickman, Patrick Fossano, Jim Fougeron, Yves Gallot, David Hanson, Steven Harvey, Kimmo Herranen, Daniel Heuer, Greg Hewgill, Johnson Lau, Jevgeni Muischnek, Andy Penrose, Jose Plaza, Martin Raab, Mike Reed, Hans Rosenthal, Steve Scott, Peter Shaw, Peter von Steht, David Underbakke and Frank Welsch! Friday, April 12, 2002: Phil Carmody is a superquintillious! Recently, Phil found a new algorithm for sieving more efficiently the Generalized Fermat Numbers and Jim Fougeron implemented it in GFNSieve. Today, the entire range for exponents 131072 and 262144 has been sieved to 1,000,000,000,000,000. Wednesday, April 3, 2002: Ludwig Berndt discovered a 7^{th} Generalized Fermat prime of the form b^{65536}+1: 141146^{65536}+1 (337,489 digits). Friday, March 22, 2002: Proth 7.0 : 1 Performance increase on the P4. The code was translated and use SSE2 instructions. The new code is typically 1.4 times faster on this processor. 2 The maximum error of all the transforms, involved in the primality test, is computed and printed to the screen and log file. These errors occur when, after every iteration, floating point values are rounded back to integers. It allows the control of possible hardware errors during the search. 3 The possible algebraic factorizations of Generalized Fermat numbers are detected and displayed: for example, the factor 2^{16384}+1 is found during the test of 8^{16384}+1. Friday, February 15, 2002: Manfred Toplic discovered a 6^{th} Generalized Fermat prime of the form b^{65536}+1: 671600^{65536}+1 (381,886 digits). Thursday, January 31, 2002: David Underbakke discovered the largest known Generalized Fermat prime 1266062^{65536}+1 (399,931 digits), with his own sieve program and Proth. This number is the largest known prime which is not a Mersenne prime, and the 6^{th} largest known prime. Monday, January 21, 2002: If you don't yet use a sieve for your search, read a sound piece of advice from David Underbakke. Saturday, January 12, 2002: Phil Carmody and David Underbakke started the systematic sieve of all ranges for exponents 131072, 262144 and 524288. You can speed up your search for huge primes by downloading them! Wednesday, January 2, 2002: Yves Gallot discovered again the largest known Generalized Fermat prime 857678^{65536}+1 (388,847 digits), with the combo GFNSieve+Proth. This number is the largest known prime, which is not a Mersenne prime, and the 6^{th} largest known prime. Today, there are 4 GF primes in the 10 largest known primes (all of them have more than 300,000 digits) and 55 GF primes in the top 100 (all of them have more than 100,000 digits). Friday, October 26, 2001: Yves Gallot discovered the largest known Generalized Fermat prime 843832^{65536}+1 (388,384 digits!), with the powerful combo GFNSieve+Proth. This number is the largest known prime, which is not a Mersenne prime, and the 5^{th} largest known prime. Friday, October 5, 2001: Proth 6.8 : this new release uses a different transform on the Athlon and Duron processors which speeds up the code by 10% for N=16384, by 30% for N=65536 and by 80% for N=262144. The CPUs with L2 cache on die (new PIII and Celeron, P4) and with large L1 cache (Athlon and Duron) are also detected and a different memory layout speeds up the program. Monday, September 17, 2001: Klaus Bodenstein discovered the largest known Generalized Fermat prime 108368^{65536}+1 (329,968 digits!). This number is the largest known prime, which is not a Mersenne prime, and the 6^{th} largest known prime. Thursday, August 16, 2001: The whole range 22600000 is completed for exponent 8192. 190 primes were found in this range and the estimate for it was 196 primes. Thanks to Michael Angel, Ray Ballinger, Michael Bell, Klaus Bodenstein, Kenneth Brazier, JeanYves Canart, Greg Childers, Peter Crickman, Jim Fougeron, Yves Gallot, David Hanson, Kimmo Herranen, Daniel Heuer, Johnson Lau, Jose Plaza, Eric Prestemon, Pavlos Saridis, Peter Shaw and Manfred Toplic, Bateman and Horn conjecture was for the first time verified for a polynomial of degree 8192. Monday, August 13, 2001: 70906^{32768}+1 is the smallest prime of the form b^{215}+1. Saturday, August 4, 2001: More than half of the 100 largest known primes are GF primes. Saturday, July 14, 2001: The test of the C source code of "GeneFer" on different Unix workstations was succesful: it implements a probable test of GFN. A page was created to collect the timings of Proth and GeneFer for various machines. Friday, July 13, 2001: Eleven of the twenty largest known primes are GF primes: all of them have more than 170,000 digits! Sunday, May 21, 2001: The ten largest known GF primes have more than 100,000 digits. Congratulations to Steve Scott (48594^{65536}+1, 999236^{32768}+1), Yves Gallot (1041870^{32768}+1, 167176^{32768}+1), Greg Hewgill (553602^{32768}+1), Johnson Lau (524552^{32768}+1), Michael Angel (321164^{32768}+1), David Hanson (204462^{32768}+1), Pavlos Saridis (70906^{32768}+1), Jim Fougeron (1514888^{16384}+1) and all the others who are searching and have not yet found. Sunday, May 21, 2001: The first public release of Jim Fougeron's GFNSieve is available. This program will quickly trial factor GFN candidates eliminating composite numbers. Download it to speed up your search! Thursday, May 17, 2001: The article: Harvey Dubner and Yves Gallot, Distribution of generalized Fermat prime numbers, Math. Comp. was electronically published. Friday, April 27, 2001: Greg Hewgill discovered the prime 553602^{32768}+1 (188,194 digits) running Proth.exe under Linux with Wine. Tuesday, June 6, 2000: Steve Scott discovered the largest known Generalized Fermat prime 48594^{65536}+1 (307,140 digits!) This number is the largest known prime, which is not a Mersenne prime, and the 6^{th} largest known prime. 