Search for GFN factors: Overall Limits -------------------------------------- (Reservations at the end of this page) n Limit for k 1-4 complete 5-8 10*10^9 9-12 1*10^12 13-16 2^44 > 17*10^12 17 2^45 > 35*10^12 18 2^46 > 70*10^12 19 2^45 > 35*10^12 20 2^44 > 17*10^12 21 2^43 > 8.7*10^12 22 2^42 > 4.3*10^12 23 2^41 > 2.1*10^12 24-50 2*10^12 51-100 1*10^12 101-200 100*10^9 201-500 10*10^9 501-1000 1*10^9 1001-2000 1020*10^6 2001-2800 50*10^6 2801-3000 60*10^6 3001-4000 100*10^6 4001-5000 50*10^6 5001-6000 2*10^6 6001-6100 16*10^6 6101-8000 10*10^6 8001-9000 7*10^6 9001-12000 5*10^6 12001-20000 2*10^6 20001-24000 1*10^6 24001-25000 500*10^3 25001-30000 200*10^3 30001-33000 300*10^3 33001-50000 200*10^3 50001-55000 100*10^3 55001-60000 50*10^3 60001-61000 100*10*3 61001-70000 20*10^3 70001-73000 30*10^3 73001-80000 20*10^3 80001-210000 10*10^3 210001-1000000 1200 1000001-1400000 40 Limits of original B & R paper 1998 ----------------------------------- n Limit for k 2-100 1*10^9 1994 101-1000 3*10^6 1996 1001-3000 21*10^3 1996 3001-5000 10*10^3 1996 5001-10000 1200 1996 10001-12000 220 1996 12001-20000 120 1996 20001-50000 64 1996 50001-100000 32 1996 15-700 2003 Verified by Fougeron 301-12000 2003 Verified by Melo 12001-50000 2003 Verified by Melo & Keller 50001-100000 2003 Verified by Melo & ProthSearch Subsequent additions and verifications -------------------------------------- n Interval for k 10001-12000 220 to 1000 2001 Melo 12001-20000 120 to 1000 2001 Melo 20001-32000 64 to 600 2001 Melo 32001-48000 64 to 300 2001 Melo 1001-2000 1 to 100*10^3 2002 Keller 2001-5000 1 to 100*10^3 2002 Keller & McLean 301-500 1 to 30*10^6 2003 Melo 501-1000 1 to 10*10^6 2003 Melo 1001-2000 1 to 5*10^6 2003 Melo 2001-7000 1 to 1*10^6 2005 Melo 7001-7600 1 to 10*10^6 2006 Melo 5001-8000 1 to 20*10^3 2003 Melo & Keller 8001-20000 1 to 1600 2003 Melo & Keller 20001-40000 1 to 1200 2003 Melo & Keller 40001-100000 1 to 600 2003 Melo & ProthSearch 16-25 1 to 60*10^9 2004 Fougeron 26 1 to 2^36 2004 Fougeron 27 1 to 2^35 2004 Fougeron 28 1 to 2^34 2004 Fougeron 29-49 1 to 10*10^9 2004 Fougeron 50-100 1 to 5*10^9 2004 Fougeron 101-200 3*10^6 to 1*10^9 2004 Fougeron 201-300 3*10^6 to 100*10^6 2004 Fougeron 301-500 30*10^6 to 100*10^6 2004 Fougeron 501-1000 10*10^6 to 20*10^6 2004 Fougeron 501-1000 20*10^6 to 30*10^6 2004 Kokales 5001-8000 20*10^3 to 100*10^3 2004 Kokales 8001-10000 1600 to 100*10^3 2004 Kokales 10001-11000 1600 to 50*10^3 2004 Kokales 2001-4000 1*10^6 to 2*10^6 2008 Harvey 4001-5000 1*10^6 to 2*10^6 2005 Harvey 4001-5000 2*10^6 to 3*10^6 2008 Harvey 5001-7000 1*10^6 to 2*10^6 2008 Harvey 6501-7000 2*10^6 to 2^21 2008 Harvey 6501-7000 2^21 to 2.5*10^6 2005 Harvey 6501-7000 2.5*10^6 to 4*10^6 2008 Harvey 7001-8000 100*10^3 to 300*10^3 2008 Harvey 7600-8000 300*10^3 to 2*10^6 2008 Harvey 8001-10000 100*10^3 to 370*10^3 2005 Harvey 8001-10000 370*10^3 to 500*10^3 2006 Harvey 8001-10000 500*10^3 to 1*10^6 2008 Harvey 10001-12000 1000 to 200*10^3 2005 Harvey 10001-11000 200*10^3 to 400*10^3 2008 Harvey 11001-12000 200*10^3 to 330*10^3 2008 Harvey 12001-13000 1600 to 100*10^3 2005 Harvey 12001-15000 100*10^3 to 200*10^3 2008 Harvey 15001-16350 100*10^3 to 200*10^3 2008 Harvey 13001-15000 1000 to 50*10^3 2005 Harvey 15001-16000 1600 to 50*10^3 2005 Harvey 16001-17000 1600 to 40*10^3 2006 Harvey 17001-18000 1000 to 40*10^3 2006 Harvey 18001-19000 1000 to 30*10^3 2006 Harvey 19001-20000 1000 to 20*10^3 2006 Harvey 20001-24000 1200 to 15*10^3 2006 Harvey 24001-30000 1200 to 10*10^3 2006 Harvey 30001-35000 1200 to 5*10^3 2006 Harvey 36001-38000 1200 to 5*10^3 2006 Harvey 110001-120000 1200 to 3*10^3 2009 Harvey 5-16 1 to 10*10^9 2008 Keller 35001-36000 1200 to 5*10^3 2007 Keller 38001-39000 1200 to 5*10^3 2007 Keller 40001-100000 600 to 1200 2006 Keller & Axelsson Partly done by Melo, completed by Keller: 100001-340000 1 to 600 2003 Melo & ProthSearch 2006 Keller & ProthSearch 2007 Keller & ProthSearch 16351-20000 100*10^3 to 500*10^3 2005 Rodenkirch 501-1000 30*10^6 to 110*10^6 2008 Pacher 1001-2000 5*10^6 to 6*10^6 2006 Pacher 1001-2000 6*10^6 to 30*10^6 2007 Pacher 1001-2000 30*10^6 to 50*10^6 2008 Pacher 1001-2000 50*10^6 to 70*10^6 2009 Pacher 1001-2000 70*10^6 to 110*10^6 2011 Pacher 1001-2000 110*10^6 to 215*10^6 2006 Pacher 1001-2000 215*10^6 to 350*10^6 2007 Pacher 1001-2000 350*10^6 to 410*10^6 2008 Pacher 1001-2000 410*10^6 to 570*10^6 2009 Pacher 1001-2000 570*10^6 to 810*10^6 2010 Pacher 1001-2000 810*10^6 to 1020*10^6 2011 Pacher 6001-6050 100*10^3 to 16*10^6 2004 Nohara 6051-6400 100*10^3 to 8*10^6 2004 Nohara 8001-11000 1*10^6 to 5*10^6 2010 Nohara 10001-12000 1*10^6 to 2*10^6 2010 Nohara 11001-12000 2*10^6 to 5*10^6 2011 Nohara 12001-13000 200*10^3 to 2*10^6 2009 Nohara 13001-13500 200*10^3 to 400*10^3 2010 Nohara 13001-13500 1*10^6 to 2*10^6 2010 Nohara 13501-16000 200*10^3 to 2*10^6 2010 Nohara 16001-16350 200*10^3 to 500*10^3 2010 Nohara 16001-17000 500*10^3 to 2*10^6 2010 Nohara 17001-20000 500*10^3 to 1*10^6 2010 Nohara 17001-20000 1*10^6 to 2*10^6 2011 Nohara 20001-21000 100*10^3 to 1*10^6 2011 Nohara 21001-22000 500*10^3 to 1*10^6 2011 Nohara 22001-23000 200*10^3 to 1*10^6 2011 Nohara 30001-31000 100*10^3 to 300*10^3 2009 Nohara 31001-32000 200*10^3 to 300*10^3 2009 Nohara 32001-33000 100*10^3 to 300*10^3 2009 Nohara 33001-34000 10*10^3 to 100*10^3 2008 Nohara 33001-34000 100*10^3 to 200*10^3 2009 Nohara 34001-35300 10*10^3 to 20*10^3 2010 Nohara 34001-35300 20*10^3 to 100*10^3 2008 Nohara 35301-40000 10*10^3 to 100*10^3 2008 Nohara 33001-38000 100*10^3 to 200*10^3 2008 Nohara 38001-40000 100*10^3 to 200*10^3 2009 Nohara 40001-49000 2^13 to 50*10^3 2008 Nohara 49001-50000 600 to 21*10^3 2007 Nohara 49001-50000 21*10^3 to 50*10^3 2008 Nohara 40001-50000 50*10^3 to 100*10^3 2009 Nohara 50001-55000 600 to 11*10^3 2007 Nohara 50001-55000 1200 to 50*10^3 2008 Nohara 50001-55000 50*10^3 to 80*10^3 2009 Nohara 50001-55000 80*10^3 to 100*10^3 2011 Nohara 55001-60000 10*10^3 to 20*10^3 2010 Nohara 55001-60000 20*10^3 to 30*10^3 2010 Nohara 55001-60000 30*10^3 to 50*10^3 2009 Nohara 9-12 10*10^9 to 1*10^12 2010 Reynolds 13-20 1*10^9 to 2^44 2008 Reynolds 17-19 2^44 to 2^45 2008 Reynolds 18 2^45 to 2^46 2010 Reynolds 21 1*10^9 to 2^43 2008 Reynolds 22 1*10^9 to 2^42 2008 Reynolds 23 1*10^9 to 2^41 2008 Reynolds 24 1*10^9 to 2^40 2008 Reynolds 25-100 1*10^9 to 1*10^12 2008 Reynolds 101-200 1*10^9 to 100*10^9 2008 Reynolds 201-500 1*10^9 to 10*10^9 2008 Reynolds 501-1000 110*10^6 to 1*10^9 2009 Reynolds 10001-19000 10*10^3 to 100*10^3 2008 Samidoost 16001-100000 1*10^3 to 10*10^3 2008 Samidoost 21001-22000 15*10^3 to 100*10^3 2008 Bock 201-500 100*10^6 to 1*10^9 2008 Wesolowski 19001-20000 20*10^3 to 100*10^3 2008 Wesolowski 20001-21000 15*10^3 to 100*10^3 2008 Wesolowski 22001-24000 15*10^3 to 100*10^3 2008 Wesolowski 24001-31000 10*10^3 to 100*10^3 2008 Wesolowski 32001-33000 10*10^3 to 100*10^3 2008 Wesolowski 6401-6500 2^21 to 2^22 2008 Kitchen 60001-61000 10*10^3 to 20*10^3 2008 Larouche 60001-61000 20*10^3 to 100*10*3 2009 Larouche 31001-32000 10*10^3 to 200*10^3 2008 Keiser 61001-69000 10*10^3 to 20*10^3 2009 Keiser 110001-120000 3000 to 10*10^3 2009 Keiser 120001-130000 1200 to 5000 2009 Keiser 130001-150000 1200 to 3000 2009 Keiser 1001-2000 810*10^6 to 820*10^6 2011 Kamenyuk 2001-3000 2*10^6 to 50*10^6 2011 Kamenyuk 3001-4000 2*10^6 to 35*10^6 2011 Kamenyuk 3001-4000 40*10^6 to 100*10^6 2011 Kamenyuk 4001-5000 3*10^6 to 50*10^6 2011 Kamenyuk 6001-6400 8*10^6 to 10*10^6 2010 Kamenyuk 8001-9000 5*10^6 to 7*10^6 2011 Kamenyuk 10001-11000 400*10^3 to 1*10^6 2009 Kamenyuk 11001-12000 330*10^3 to 1*10^6 2009 Kamenyuk 6051-6100 8*10^6 to 16*10^6 2010 Morelli 6401-6500 2*10^6 to 2^21 2010 Morelli 6401-7000 4*10^6 to 10*10^6 2010 Morelli 45001-50000 100*10^3 to 200*10^3 2011 Morelli 69001-70000 10*10^3 to 20*10^3 2010 Morelli 70001-73000 10*10^3 to 30*10^3 2010 Morelli 100001-110000 1200 to 10*10^3 2010 Morelli 3001-4000 35*10^6 to 40*10^6 2010 Choliy 7601-8000 2*10^6 to 10*10^6 2010 Choliy 13001-13500 400*10^3 to 1*10^6 2010 Choliy 21001-22000 100*10^3 to 500*10^3 2010 Choliy 22001-23000 100*10^3 to 200*10^3 2010 Choliy 23001-24000 100*10^3 to 500*10^3 2010 Choliy 24001-27000 100*10^3 to 200*10^3 2011 Choliy 24001-25000 200*10^3 to 500*10^6 2011 Choliy 27001-30000 100*10^3 to 200*10^3 2011 Choliy 73001-74000 10*10^3 to 20*10^3 2010 Choliy 74001-77000 10*10^3 to 20*10^3 2011 Choliy 77001-80000 10*10^3 to 20*10^3 2011 Choliy 2801-3000 50*10^6 to 60*10^6 2010 Dubrovin 24 2^40 to 2*10^12 2010 Rajala 25-30 1*10^12 to 2*10^12 2010 Rajala 31-50 1*10^12 to 2*10^12 2010 Rajala 23001-24000 500*10^3 to 1*10^6 211 Rajala 40001-45000 100*10^3 to 200*10^3 2011 Rajala Reserved: 1001-2000 1020*10^6 to 1200*10^6 14 Jun 2011 Pacher 2001-2800 50*10^6 to 60*10^6 08 Jul 2011 Kamenyuk 6401-7000 4*10^6 to 10*10^6 13 Apr 2010 Morelli 24001-25000 500*10^3 to 1*10^6 09 Dec 2011 Nohara 25001-28000 200*10^3 to 500*10^3 09 Dec 2011 Nohara 55001-60000 50*10^3 to 100*10^3 23 Nov 2010 Kamenyuk Updated: January 7, 2012