Search for GFN factors: Overall Limits -------------------------------------- Reservations at the end of this page (reactivated in February 2017) Updated 25 Jul 2018 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 21-25 10*10^12 26-50 2*10^12 51-100 1*10^12 101-200 100*10^9 201-300 15*10^9 301-500 10*10^9 501-1000 2*10^9 1001-2000 1550*10^6 2001-2200 400*10^6 [ ] 500*10^6-4*10^9 2201-3000 400*10^6 [ ] 500*10^6-3*10^9 3001-4000 750*10^6 [ ] 800*10^6-1500*10^6 4001-5000 350*10^6 5001-5100 200*10^6 [ ] 1200*10^6-2500*10^6 5101-5500 200*10^6 5501-6000 220*10^6 6001-6150 2500*10^6 6151-6200 200*10^6 [ ] 800*10^6-900*10^6 6201-6300 200*10^6 [ ] 800*10^6-1000*10^6 6301-6500 200*10^6 [ ] 800*10^6-900*10^6 6501-8000 100*10^6 8001-9000 50*10^6 9001-10000 50*10^6 [ ] 270*10^6-300*10^6 10001-11000 30*10^6 [ ] 100*10^6-269*10^6 11001-12000 30*10^6 12001-14000 20*10^6 14001-14500 10*10^6 [ ] 20*10^6-30*10^6 14501-15000 10*10^6 [ ] 40*10^6-70*10^6 15001-16000 10*10^6 16001-18000 5*10^6 18001-20000 2*10^6 20001-25000 1*10^6 25001-26000 3*10^6 26001-28000 1*10^6 28001-30000 1500*10^3 30001-35000 300*10^3 [ ] 500*10^3-1*10^6 35001-36000 300*10^3 36001-40000 200*10^3 40001-45000 300*10^3 45001-50000 200*10^3 50001-55000 125*10^3 55001-57000 130*10^3 57001-60000 125*10^3 60001-61000 100*10^3 61001-62000 60*10^3 [ ] 100*10^3-125*10^3 62001-70000 60*10^3 71001-80000 30*10^3 [ ] 50*10^3-60*10^3 80001-81000 60*10^3 [ ] 80*10^3-100*10^3 81001-82000 60*10^3 [ ] 70*10^3-90*10^3 82001-90000 60*10^3 [ ] 80*10^3-90*10^3 90001-100000 60*10^3 100001-114000 40*10^3 114001-120000 100*10^3 120001-130000 20*10^3 [ ] 30*10^3-40*10^3 130001-140000 30*10^3 140001-160000 20*10^3 160001-390000 10*10^3 390001-450000 1200 450000-925000 10*10^3 925000-1500000 1200 1500001-2000000 100 2000001-2500000 32 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 5001-5100 1200*10^6 to 2500*10^6 2018 Rodenkirch 6201-6300 900*10^6 to 1000*10^6 2018 Rodenkirch 9001-10000 270*10^6 to 300*10^6 2018 Rodenkirch 10001-11000 100*10^6 to 269*10^6 2018 Rodenkirch 14501-15000 40*10^6 to 70*10^6 2018 Rodenkirch 16351-20000 100*10^3 to 500*10^3 2005 Rodenkirch 114001-120000 40*10^3 to 100*10^3 2017 Rodenkirch 120001-130000 30*10^3 to 40*10^3 2017 Rodenkirch 130001-140000 20*10^3 to 30*10^3 2017 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 1150*10^6 2011 Pacher 1001-2000 1150*10^6 to 1550*10^6 2012 Pacher 3001-4000 400*10^6 to 500*10^6 2013 Pacher 3401-4000 100*10^6 to 200*10^6 2013 Pacher 5001-6000 100*10^6 to 120*10^6 2015 Pacher 5501-6000 200*10^6 to 220*10^6 2016 Pacher 6501-7000 50*10^6 to 80*10^6 2014 Pacher 2001-3000 60*10^6 to 400*10^6 2012 Nohara 2001-3000 500*10^6 to 1*10^9 2013 Nohara 2001-3000 1000*10^6 to 1500*10^6 2014 Nohara 2101-3000 1500*10^6 to 2000*10^6 2015 Nohara 2001-3000 2*10^9 to 3*10^9 2015 Nohara 2001-2200 3*10^9 to 4*10^9 2015 Nohara 3001-3400 100*10^6 to 400*10^6 2012 Nohara 3401-4000 200*10^6 to 400*10^6 2012 Nohara 3001-4000 500*10^6 to 750*10^6 2014 Nohara 3001-4000 800*10^6 to 1500*10^6 2015 Nohara 4001-4500 50*10^6 to 200*10^6 2012 Nohara 4001-5000 200*10^6 to 350*10^6 2014 Nohara 5001-6000 5*10^6 to 100*10^6 2012 Nohara 5001-6000 120*10^6 to 200*10^6 2014 Nohara 6001-6050 100*10^3 to 16*10^6 2004 Nohara 6051-6400 100*10^3 to 8*10^6 2004 Nohara 6151-6500 50*10^6 to 200*10^6 2014 Nohara 6001-6100 20*10^6 to 50*10^6 2012 Nohara 6101-7000 10*10^6 to 50*10^6 2012 Nohara 6501-7000 80*10^6 to 100*10^6 2014 Nohara 7001-7200 10*10^6 to 50*10^6 2013 Nohara 7201-8000 20*10^6 to 50*10^6 2013 Nohara 7001-8000 50*10^6 to 100*10^6 2014 Nohara 8001-9000 15*10^6 to 30*10^6 2013 Nohara 9001-10000 10*10^6 to 30*10^6 2013 Nohara 8001-11000 1*10^6 to 5*10^6 2010 Nohara 8001-10000 30*10^6 to 50*10^6 2014 Nohara 10001-12000 1*10^6 to 2*10^6 2010 Nohara 11001-12000 2*10^6 to 5*10^6 2011 Nohara 10001-12000 10*10^6 to 20*10^6 2013 Nohara 10001-12000 20*10^6 to 30*10^6 2015 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 12001-14000 10*10^6 to 20*10^6 2015 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 24001-25000 500*10^3 to 1*10^6 2012 Nohara 25001-28000 200*10^3 to 500*10^3 2012 Nohara 30001-35000 500*10^3 to 1*10^6 2013 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 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 21 2^43 to 10*10^12 2012 Reynolds 22 2^42 to 10*10^12 2012 Reynolds 23 2^41 to 10*10^12 2012 Reynolds 24-25 2*10^12 to 10*10^12 2012 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 601-1000 1*10^9 to 2*10^9 2012 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 201-300 10*10^9 to 15*10^9 2013 Kamenyuk 501-600 1*10^9 to 2*10^9 2012 Kamenyuk 1001-2000 810*10^6 to 820*10^6 2011 Kamenyuk 2001-3000 2*10^6 to 50*10^6 2011 Kamenyuk 2001-2800 50*10^6 to 60*10^6 2012 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 5001-6000 2*10^6 to 5*10^6 2012 Kamenyuk 6001-6100 16*10^6 to 20*10^6 2012 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 55001-60000 50*10^3 to 100*10^3 2012 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 14001-14500 20*10^6 to 30*10^6 2017 Morelli 45001-50000 100*10^3 to 200*10^3 2011 Morelli 69001-70000 10*10^3 to 20*10^3 2010 Morelli 61001-70000 20*10^3 to 30*10^3 2012 Morelli 70001-73000 10*10^3 to 30*10^3 2010 Morelli 73001-80000 20*10^3 to 30*10^3 2012 Morelli 80001-81000 90*10^3 to 100*10^3 2017 Morelli 90001-100000 10*10^3 to 30*10^3 2013 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 25-50 1*10^12 to 2*10^12 2010 Rajala 4501-5000 50*10^6 to 200*10^6 2012 Rajala 12001-13000 2*10^6 to 5*10^6 2012 Rajala 23001-24000 500*10^3 to 1*10^6 2011 Rajala 28001-30000 200*10^3 to 500*10^3 2012 Rajala 28001-30000 1000*10^3 to 1500*10^3 2015 Rajala 33001-35000 200*10^3 to 300*10^3 2013 Rajala 35001-36000 250*10^3 to 300*10^3 2013 Rajala 40001-45000 100*10^3 to 200*10^3 2011 Rajala 40001-45000 200*10^3 to 300*10^3 2015 Rajala 50001-60000 100*10^3 to 125*10^3 2014 Rajala 61001-100000 50*10^3 to 60*10^3 2014 Rajala 150001-160000 10*10^3 to 20*10^3 2013 Rajala 35001-36000 200*10^3 to 250*10^3 2012 Gautier 80001-90000 10*10^3 to 30*10^3 2013 Gautier 7201-8000 10*10^6 to 20*10^6 2012 Batalov 8001-9000 7*10^6 to 15*10^6 2012 Batalov 9001-10000 5*10^6 to 10*10^6 2012 Batalov 10001-13000 5*10^6 to 10*10^6 2012 Batalov 13001-14000 2*10^6 to 10*10^6 2012 Batalov 14001-16000 2*10^6 to 10*10^6 2012 Batalov 16001-17000 2*10^6 to 5*10^6 2012 Batalov 17001-18000 2*10^6 to 5*10^6 2012 Batalov 80001-100000 30*10^3 to 50*10^3 2012 Batalov 100001-150000 10*10^3 to 20*10^3 2012 Batalov 100001-120000 20*10^3 to 40*10^3 2012 Batalov 25001-27000 500*10^3 to 1*10^6 2013 Le Foulher 27001-30000 500*10^3 to 1*10^6 2013 Le Foulher 61001-70000 30*10^3 to 50*10^3 2013 Le Foulher 6001-6150 50*10^6 to 2500*10^6 2013 Tervooren & Bertels 2001-2100 1500*10^6 to 2000*10^6 2014 Nordin 25001-26000 1000*10^3 to 1100*10^3 2014 Nordin 25001-26000 1100*10^3 to 3000*10^3 2015 Nordin 55001-57000 125*10^3 to 130*10^3 2017 Nordin 61001-62000 100*10^3 to 125*10^3 2015 Nordin 81001-82000 70*10^3 to 80*10^3 2015 Nordin 80001-90000 80*10^3 to 90*10^3 2017 Nordin 6151-6200 800*10^6 to 900*10^6 2017 Hermanns Confirmed Reservations, as of Jul 18, 2018: n Interval for k 301-500 10*10^9 to 15*10^9 08 Feb 2017 Kamenyuk 501-1000 2*10^9 to 3*10^9 08 Feb 2017 Kamenyuk 2001-3000 400*10^6 to 500*10^6 08 Feb 2017 Kamenyuk 20001-25000 1*10^6 to 2*10^6 08 Feb 2017 Kamenyuk 30001-35000 300*10^3 to 500*10^3 09 Jun 2018 Jiahao He 81001-90000 90*10^3 to 130*10^3 05 Jan 2018 Batalov 4501-5000 350*10^6 to 1000*10^6 20 Feb 2016 Nohara Earlier Reservations (to be confirmed or removed): 3001-4000 750*10^6 to 800*10^6 22 Feb 2015 Pacher 5501-6000 220*10^6 to 300*10^6 26 Jun 2016 Pacher 7001-7100 2500*10^6 to 3000*10^3 26 Jan 2017 Nordin 80001-81000 70*10^3 to 80*10^3 05 Sep 2015 Nordin 70001-80000 30*10^3 to 50*10^4 04 Apr 2013 Le Foulher 18001-19000 2*10^6 to 5*10^6 11 Jan 2013 Batalov