Search for GFN factors: Overall Limits (reactivated in February 2017) Complete Update: 5 September 2021 Reservations at the end of this page -------------------------------------------- n Limit for k 2-4 complete 5-8 10*10^9 9 1000*10^9 10-12 2400*10^9 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 21-23 10*10^12 24-100 60*10^12 101-140 4500*10^9 141-200 4500*10^9 201-300 4000*10^9 301-400 1200*10^9 401-500 800*10^9 501-600 600*10^9 601-700 400*10^9 701-800 300*10^9 801-900 200*10^9 901-1000 100*10^9 1001-1100 60*10^9 1101-1200 40*10^9 1201-1400 32*10^9 1401-1600 6*10^9 1601-1800 16*10^9 1801-2000 12*10^9 2001-2200 4*10^9 [ ] 50*10^9-60*10^9 2201-2400 3*10^9 2401-2500 3*10^9 [ ] 30*10^9-40*10^9 2501-2600 3*10^9 [ ] 20*10^9-40*10^9 2601-3000 3*10^9 [ ] 20*10^9-25*10^9 3001-3500 1550*10^6 [ ] 15*10^9-18*10^9 3501-3600 1550*10^6 [ ] 11*10^9-12*10^9 3601-4000 1550*10^6 [ ] 10*10^9-12*10^9 4001-4500 1000*10^6 [ ] 5*10^9-8*10^9 4501-5000 1000*10^6 [ ] 6*10^9-7*10^9 5001-5100 300*10^6 [ ] 1200*10^6-2800*10^6 [ ] 3500*10^6-4500*10^6 5101-5500 300*10^6 [ ] 3500*10^6-4500*10^6 5501-5600 300*10^6 [ ] 3*10^9-4*10^9 5601-5700 300*10^6 [ ] 1200*10^6-2500*10^6 [ ] 3*10^9-4*10^9 5701-5800 300*10^6 5801-6000 300*10^6 [ ] 3*10^9-4*10^9 6001-6150 3000*10^6 6151-6200 200*10^6 [ ] 800*10^6-3000*10^6 6201-6300 200*10^6 [ ] 900*10^6-1000*10^6 [ ] 2100*10^6-3000*10^6 6301-6500 200*10^6 [ ] 2*10^9-3*10^9 6501-7000 120*10^6 [ ] 1500*10^6-2000*10^6 7001-8000 100*10^6 [ ] 1000*10^6-1500*10^6 8001-9000 85*10^6 [ ] 350*10^6-400*10^6 [ ] 600*10^6-1000*10^6 9001-9200 50*10^6 [ ] 270*10^6-300*10^6 [ ] 450*10^6-750*10^6 9201-10000 60*10^6 [ ] 270*10^6-300*10^6 [ ] 450*10^6-750*10^6 10001-11000 30*10^6 [ ] 100*10^6-550*10^6 11001-12000 30*10^6 [ ] 160*10^6-350*10^6 12001-14000 20*10^6 [ ] 100*10^6-200*10^6 14001-14500 10*10^6 [ ] 20*10^6-30*10^6 [ ] 100*10^6-160*10^6 14501-15000 10*10^6 [ ] 40*10^6-70*10^6 [ ] 100*10^6-160*10^6 15001-16000 10*10^6 [ ] 70*10^6-160*10^6 16001-18000 5*10^6 [ ] 30*10^6-90*10^6 18001-19000 5*10^6 [ ] 30*10^6-75*10^6 19001-20000 3*10^6 [ ] 20*10^6-75*10^6 20001-22000 1*10^6 [ ] 2*10^6-3*10^6 [ ] 20*10^6-48*10^6 22001-23000 1*10^6 [ ] 9*10^6-32*10^6 23001-24000 1*10^6 [ ] 8*10^6-32*10^6 24001-25000 1*10^6 [ ] 8*10^6-24*10^6 25001-26000 3*10^6 [ ] 6*10^6-24*10^6 26001-30000 1500*10^3 [ ] 6*10^6-15*10^6 30001-35000 1000*10^3 [ ] 3*10^6-10*10^6 35001-40000 500*10^3 [ ] 2*10^6-6*10^6 40001-43000 300*10^3 [ ] 1000*10^3-4*10^6 43001-44000 300*10^3 [ ] 1000*10^3-1200*10^3 [ ] 1400*10^3-4*10^6 44001-45000 300*10^3 [ ] 1000*10^3-4*10^6 45001-46000 200*10^3 [ ] 1000*10^3-3*10^6 46001-47000 200*10^3 [ ] 1200*10^3-3*10^6 47001-50000 200*10^3 [ ] 1000*10^3-3*10^6 50001-55000 170*10^3 [ ] 600*10^3-2400*10^3 55001-57000 130*10^3 [ ] 500*10^3-1200*10^3 57001-60000 125*10^3 [ ] 500*10^3-1200*10^3 60001-65000 200*10^3 [ ] 400*10^3-900*10^3 65001-70000 150*10^3 [ ] 300*10^3-900*10^3 70001-75000 130*10^3 [ ] 250*10^3-600*10^3 75001-80000 100*10^3 [ ] 200*10^3-500*10^3 80001-85000 130*10^3 [ ] 200*10^3-400*10^3 85001-90000 130*10^3 [ ] 200*10^3-300*10^3 90001-91000 70*10^3 [ ] 80*10^3-100*10^3 91001-92000 70*10^3 [ ] 80*10^3-100*10^3 [ ] 200*10^3-250*10^3 92001-93000 70*10^3 [ ] 80*10^3-100*10^3 [ ] 150*10^3-250*10^3 93001-94000 70*10^3 [ ] 80*10^3-100*10^3 [ ] 200*10^3-250*10^3 94001-99000 70*10^3 [ ] 80*10^3-100*10^3 [ ] 150*10^3-200*10^3 99001-100000 100*10^3 [ ] 150*10^3-200*10^3 100001-120000 120*10^3 120001-130000 60*10^3 130001-142000 50*10^3 142001-190000 30*10^3 190001-250000 20*10^3 250001-300000 12*10^3 300001-1640000* 10*10^3 *being extended by PrimeGrid 1640001-3070000* 1200 *being extended by PrimeGrid 3070001-9000000 50 extended by PrimeGrid 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 -------------------------------------- Individual contributions suitably rearranged at http://www.prothsearch.com/GFNcompilation.txt 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 Double-checked by Reynolds: 13-15 1*10^9 to 10*10^9 2008 Reynolds 16-25 1*10^9 to 60*10^9 2008 Reynolds 26 1*10^9 to 2^36 2008 Reynolds 27 1*10^9 to 2^35 2008 Reynolds 28 1*10^9 to 2^34 2008 Reynolds 29-49 1*10^9 to 10*10^9 2008 Reynolds 50-100 1*10^9 to 5*10^9 2008 Reynolds 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 8001-9000 350*10^6 to 400*10^6 2018 Rodenkirch 9001-10000 270*10^6 to 300*10^6 2018 Rodenkirch 10001-11000 100*10^6 to 300*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 30001-35000 300*10^3 to 500*10^3 2018 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 3001-4000 750*10^6 to 800*10^6 2015 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 5501-6000 220*10^6 to 300*10^6 2018 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 4001-4500 350*10^6 to 1000*10^6 2016 Nohara 4501-5000 350*10^6 to 1000*10^6 2020 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 10001-11000 2*10^6 to 5*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 13-15 10*10^9 to 2^44 2008 Reynolds 16 60*10^9 to 2^44 2008 Reynolds 17-19 60*10^9 to 2^45 2008 Reynolds 18 2^45 to 2^46 2010 Reynolds 20 60*10^9 to 2^44 2008 Reynolds 21 60*10^9 to 2^43 2008 Reynolds 22 60*10^9 to 2^42 2008 Reynolds 23 60*10^9 to 2^41 2008 Reynolds 24 60*10^9 to 2^40 2008 Reynolds 25 1*10^9 to 1*10^12 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 25 2*39 to 10*10^12 2012 Reynolds 26 2^36 to 1*10^12 2008 Reynolds 27 2^35 to 1*10^12 2008 Reynolds 28 2^34 to 1*10^12 2008 Reynolds 29-49 10*10^9 to 1*10^12 2008 Reynolds 50 5*10^9 to 1*10^12 2008 Reynolds 51-100 5*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 99000-100000 10*10^3 to 100*10^3 2021 Samidoost (DC) 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 60000-61000 100*10^3 to 125*10^3 2020 Larouche (DC) 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 4501-5000 6500*10^6 to 7000*10^6 2021 Morelli 5601-5700 1200*10^6 to 2500*10^6 2019 Morelli 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 19000-20000 2*10^6 to 3*10^6 2020 Morelli 30000-33000 3500*10^3 to 4000*10^3 2020 Morelli 33000-35000 3*10^6 to 4*10^6 2020 Morelli 35000-36000 300*10^3 to 500*10^3 2020 Morelli 36000-40000 200*10^3 to 500*10^3 2020 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 80000-85000 300*10^3 to 400*10^3 2021 Morelli 90001-100000 10*10^3 to 30*10^3 2013 Morelli 100001-110000 1200 to 10*10^3 2010 Morelli 160000-170000 15*10^3 to 20*10^3 2020 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*10^3 2011 Choliy 27001-30000 100*10^3 to 200*10^3 2011 Choliy 73001-74000 10*10^3 to 20*10^3 2010 Choliy 74001-80000 10*10^3 to 20*10^3 2011 Choliy 140000-142000 30*10^3 to 50*10^3 2021 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 62001-70000 100*10^3 to 110*10^3 2017 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 9201-10000 50*10^6 to 60*10^6 2021 Nordin (DC) 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 80001-81000 70*10^3 to 80*10^3 2021 Nordin (DC) 81001-82000 70*10^3 to 80*10^3 2015 Nordin 80001-90000 80*10^3 to 90*10^3 2017 Nordin 180001-181743 13*10^3 to 30*10^3 2017 Nordin 6151-6200 800*10^6 to 900*10^6 2017 Hermanns 181744-190000 13*10^3 to 30*10^3 2020 Hermanns 6151-6200 900*10^6 to 2500*10^6 2018 Meekins 9001-9100 450*10^6 to 500*10^6 2019 Delgado 60001-61000 400*10^3 to 450*10^3 2019 Delgado 70001-71000 250*10^3 to 350*10^3 2019 Delgado 92001-93000 150*10^3 to 170*10^3 2019 Delgado 92001-93000 170*10^3 to 200*10^3 2020 Delgado 5000-5100 2500*10^6 to 2800*10^6 2021 Paula (DC) 22000-23000 9*10^6 to 16*10^6 2021 Paula (DC) 10-13 1 to 2400*10^9 2020 Gostin 26-30 2*10^12 to 4000*10^9 2020 Gostin 31-40 2*10^12 to 3500*10^9 2020 Gostin 41-50 2*10^12 to 3000*10^9 2020 Gostin 51-60 1*10^12 to 2700*10^9 2020 Gostin 61-80 1*10^12 to 2300*10^9 2020 Gostin 81-100 1*10^12 to 2000*10^9 2020 Gostin 101-140 1 to 1000*10^9 2020 Gostin 101-140 3000*10^9 to 4000*10^9 2021 Gostin 141-200 1 to 600*10^9 2020 Gostin 141-200 3000*10^9 to 3500*10^9 2021 Gostin 201-300 1 to 300*10^9 2020 Gostin 201-300 2000*10^9 to 2500*10^9 2021 Gostin 301-400 1 to 200*10^9 2020 Gostin 301-400 200*10^9 to 1200*10^9 2021 Gostin 401-500 1 to 130*10^9 2020 Gostin 401-500 130*10^9 to 800*10^9 2021 Gostin 501-600 1 to 80*10^9 2020 Gostin 501-600 80*10^9 tp 600*10^9 2021 Gostin 601-800 1 to 30*10^9 2020 Gostin 601-700 30*10^9 to 400*10^9 2021 Gostin 701-800 30*10^9 to 300*10^9 2021 Gostin 801-1000 1 to 14*10^9 2020 Gostin 801-900 14*10^9 to 200*10^9 2021 Gostin 901-1000 14*10^9 to 100*10^9 2021 Gostin 1001-1400 1550*10^6 to 5*10^9 2020 Gostin 1001-1100 5*10^9 to 60*10^9 2021 Gostin 1101-1200 5*10^9 to 40*10^9 2021 Gostin 1201-1400 5*10^9 to 32*10^9 2021 Gostin 1401-2000 1550*10^6 to 3*10^9 2020 Gostin 1401-1600 3*10^9 to 6*10^9 2021 Gostin 1601-1800 3*10^9 to 16*10^9 2021 Gostin 1801-2000 3*10^9 to 12*10^9 2021 Gostin 2000-2200 50*10^9 to 60*10^9 2021 Gostin 2001-3000 400*10^6 to 500*10^6 2020 Gostin 2400-2500 30*10^9 to 40*10^9 2021 Gostin 2500-2600 20*10^9 to 40*10^9 2021 Gostin 2600-3000 20*10^9 to 25*10^9 2021 Gostin 3000-3500 15*10^9 to 18*10^9 2021 Gostin 3500-3600 11*10^9 to 12*10^9 2021 Gostin 3600-4000 10*10^9 to 12*10^9 2021 Gostin 4000-4500 5000*10^6 to 7500*10^6 2020 Gostin 4000-4500 7500*10^6 to 8000*10^6 2021 Gostin 4500-5000 6000*10^6 to 6500*10^6 2020 Gostin 5000-5500 200*10^6 to 300*10^6 2020 Gostin 5000-5500 3500*10^6 to 4500*10^6 2020 Gostin 5500-5700 3000*10^6 to 4000*10^6 2020 Gostin 5800-6000 3000*10^6 to 4000*10^6 2020 Gostin 6000-6200 2500*10^6 to 3000*10^6 2020 Gostin 6200-6300 2100*10^6 to 3000*10^6 2020 Gostin 6300-6500 2000*10^6 to 3000*10^6 2020 Gostin 6500-7000 80*10^6 to 120*10^6 2020 Gostin 6500-7000 1500*10^6 to 2000*10^6 2020 Gostin 7000-8000 1000*10^6 to 1200*10^6 2020 Gostin 7000-8000 1200*10^6 to 1500*10^6 2021 Gostin 8000-9000 50*10^6 to 85*10^6 2020 Gostin 8000-9000 600*10^6 to 800*10^6 2020 Gostin 8000-9000 800*10^6 to 1000*10^6 2021 Gostin 9000-10000 450*10^6 to 600*10^6 2020 Gostin 9000-10000 600*10^6 to 750*10^6 2021 Gostin 10000-11000 300*10^6 to 420*10^6 2020 Gostin 10000-11000 420*10^6 to 550*10^6 2021 Gostin 11000-12000 160*10^6 to 250*10^6 2020 Gostin 11000-12000 250*10^6 to 350*10^6 2021 Gostin 12000-14000 100*10^6 to 150*10^6 2020 Gostin 12000-14000 150*10^6 to 200*10^6 2021 Gostin 14000-15000 100*10^6 to 120*10^6 2020 Gostin 15000-16000 70*10^6 to 120*10^6 2020 Gostin 14000-16000 120*10^6 to 160*10^6 2021 Gostin 16000-18000 30*10^6 to 60*10^6 2020 Gostin 16000-18000 60*10^6 to 90*10^6 2021 Gostin 18000-19000 30*10^6 to 50*10^6 2020 Gostin 19000-20000 20*10^6 to 50*10^6 2020 Gostin 18000-20000 50*10^6 to 75*10^6 2021 Gostin 20000-22000 2*10^6 to 3*10^6 2020 Gostin 20000-22000 20*10^6 to 40*10^6 2020 Gostin 20000-22000 40*10^6 to 48*10^6 2021 Gostin 22000-25000 8*10^6 to 9*10^6 2021 Gostin 22000-23000 16*10^6 to 32*10^6 2020 Gostin 23000-25000 9*10^6 to 20*10^6 2020 Gostin 23000-24000 20*10^6 to 32*10^6 2021 Gostin 24000-25000 20*10^6 to 24*10^6 2021 Gostin 25000-30000 6*10^6 to 12*10^6 2020 Gostin 25000-26000 12*10^6 to 24*10^6 2021 Gostin 26000-30000 12*10^6 to 15*10^6 2021 Gostin 26000-28000 1000*10^3 to 1500*10^3 2020 Gostin 30000-33000 3000*10^3 to 3500*10^3 2020 Gostin 30000-35000 4*10^6 to 8*10^6 2020 Gostin 30000-35000 8*10^6 to 10*10^6 2021 Gostin 35000-40000 2*10^6 to 4*10^6 2020 Gostin 35000-40000 4*10^6 to 6*10^6 2021 Gostin 40000-43000 1200*10^3 to 1400*10^3 2020 Gostin 40000-44000 1400*10^3 to 1800*10^3 2020 Gostin 44000-45000 1200*10^3 to 1800*10^3 2020 Gostin 40000-45000 1800*10^3 to 3000*10^3 2020 Gostin 40000-45000 3*10^6 to 4*10^6 2021 Gostin 40000-46000 1000*10^3 to 1200*10^3 2020 Gostin 45000-47000 1200*10^3 to 1400*10^3 2020 Gostin 47000-50000 1000*10^3 to 1400*10^3 2020 Gostin 45000-50000 1400*10^3 to 2200*10^3 2020 Gostin 45000-50000 2200*10^3 to 3000*10^3 2021 Gostin 50000-55000 125*10^3 to 170*10^3 2020 Gostin 50000-55000 600*10^3 to 1800*10^3 2020 Gostin 50000-55000 1800*10^3 to 2400*10^3 2021 Gostin 55000-60000 500*10^3 to 1200*10^3 2020 Gostin 60000-65000 150*10^3 to 200*10^3 2020 Gostin 60000-65000 500*10^3 to 900*10^3 2020 Gostin 65000-70000 300*10^3 to 400*10^3 2020 Gostin 65000-70000 400*10^3 to 700*10^3 2021 Gostin 61000-70000 60*10^3 to 100*10^3 2020 Gostin 60000-70000 125*10^3 to 150*10^3 2020 Gostin 62000-70000 110*10^3 to 125*10^3 2020 Gostin 60000-61000 450*10^3 to 500*10^3 2020 Gostin 61000-65000 400*10^3 to 500*10^3 2020 Gostin 70000-80000 30*10^3 to 50*10^3 2020 Gostin 70000-80000 60*10^3 to 100*10^3 2020 Gostin 70000-75000 100*10^3 to 130*10^3 2020 Gostin 70000-75000 350*10^3 to 600*10^3 2021 Gostin 71000-75000 250*10^3 to 350*10^3 2020 Gostin 75000-80000 200*10^3 to 300*10^3 2020 Gostin 75000-80000 300*10^3 to 500*10^3 2021 Gostin 80000-81000 100*10^3 to 130*10^3 2020 Gostin 80000-100000 60*10^3 to 70*10^3 2020 Gostin 82000-90000 70*10^3 to 80*10^3 2020 Gostin 81000-90000 90*10^3 to 130*10^3 2020 Gostin 81000-90000 250*10^3 to 300*10^3 2021 Gostin 80000-90000 200*10^3 to 250*10^3 2020 Gostin 90000-99000 80*10^3 to 100*10^3 2020 Gostin 91000-100000 200*10^3 to 250*10^3 2021 Gostin 94000-100000 150*10^3 to 200*10^3 2020 Gostin 100000-114000 40*10^3 to 100*10^3 2020 Gostin 100000-110000 100*10^3 to 120*10^3 2020 Gostin 110000-120000 100*10^3 to 110*10^3 2020 Gostin 120000-130000 20*10^3 to 30*10^3 2020 Gostin 120000-130000 40*10^3 to 60*10^3 2020 Gostin 130000-140000 30*10^3 to 50*10^3 2020 Gostin 140000-170000 20*10^3 to 30*10^3 2020 Gostin 160000-180000 10*10^3 to 15*10^3 2020 Gostin 170000-180000 15*10^3 to 30*10^3 2020 Gostin 180000-190000 10*10^3 to 13*10^3 2020 Gostin 190000-220000 10*10^3 to 20*10^3 2020 Gostin 220001-250000 10*10^3 to 15*10^3 2020 Gostin 250001-300000 10*10^3 to 12*10^3 2020 Gostin Double-checked by Gostin: 14-19 1 to 1200*10^9 2020 Gostin 20-59 1 to 600*10^9 2020 Gostin 60-99 1 to 400*10^9 2020 Gostin 501-600 1 to 80*10^9 2021 Gostin 601-800 1 to 30*10^9 2021 Gostin 801-1000 1 to 14*10^9 2021 Gostin 1001-1400 1 to 600*10^6 2020 Gostin 1401-2000 1 to 200*10^6 2020 Gostin 1001-1400 1 to 5*10^9 2021 Gostin 1401-2000 1 to 3*10^9 2021 Gostin 2001-3000 1 to 50*10^6 2020 Gostin 3001-4000 1 to 27*10^6 2020 Gostin 4001-5000 1 to 15*10^6 2020 Gostin 5001-6000 1 to 10*10^6 2020 Gostin 6001-8000 1 to 2400*10^3 2020 Gostin 8001-10000 1 to 1300*10^3 2020 Gostin 10001-14000 1 to 300*10^3 2020 Gostin 14001-20000 1 to 80*10^3 2020 Gostin 20001-30000 1 to 20*10^3 2020 Gostin 18000-19000 2*10^6 to 5*10^6 2020 Baur 110001-120000 110*10^3 to 120*10^3 2021 Tarasov 24-25 10*10^12 to 60*10^12 2021 Doescher 26-30 4000*10^9 to 60*10^12 2021 Doescher 31-35 3500*10^9 to 60*10^12 2021 Doescher 36-50 3*10^12 to 60*10^12 2021 Doescher 51-60 2700*10^9 to 60*10^12 2021 Doescher 61-80 2300*10^9 to 60*10^12 2021 Doescher 81-100 2000*10^9 to 60*10^12 2021 Doescher 101-140 1000*10^9 to 3*10^12 2021 Doescher 101-140 4000*10^9 to 4500*10^9 2021 Doescher 141-200 600*10^9 to 3*10^12 2021 Doescher 141-200 3500*10^9 to 4500*10^9 2021 Doescher 201-300 300*10^9 to 2*10^12 2021 Doescher 201-300 2500*10^9 to 4000*10^9 2021 Doescher 3001-4000 1500*10^6 to 1550*10^6 2021 Doescher 65001-70000 700*10^3 to 900*10^6 2021 Doescher 220000-250000 15*10^3 to 20*10^3 2021 Doescher New (or confirmed) reservations, as of 5 September 2021: n Interval for k 24-30 60*10^12 to 100*10^12 04 Sep 2021 Doescher 101-140 4500*10^9 to 10*10^12 04 Sep 2021 Doescher 141-200 4500*10^9 to 10*10^12 04 Sep 2021 Doescher 201-300 4000*10^9 to 10*10^12 04 Sep 2021 Doescher 3001-4000 1550*10^6 to 1600*10^6 04 Sep 2021 Doescher 60001-65000 200*10^3 to 400*10^3 08 Aug 2021 Doescher 60001-65000 900*10^3 to 1*10^6 03 Aug 2021 Doescher 65001-70000 150*10^3 to 300*10^3 08 Aug 2021 Doescher 65001-70000 900*10^3 to 1*10^6 04 Sep 2021 Doescher 301-400 1200*10^9 to 1800*10^9 31 Jul 2021 Gostin 401-500 800*10^9 to 1200*10^9 31 Jul 2021 Gostin 501-600 600*10^9 to 1000*10^9 30 Aug 2021 Gostin 601-700 400*10^9 to 800*10^9 30 Aug 2021 Gostin 701-800 300*10^9 to 600*10^9 30 Aug 2021 Gostin 801-900 200*10^9 to 400*10^9 30 Aug 2021 Gostin 901-1000 100*10^9 to 250*10^9 30 Aug 2021 Gostin 1001-1100 60*10^9 to 120*10^9 30 Aug 2021 Gostin 1101-1200 40*10^9 to 80*10^9 30 Aug 2021 Gostin 1401-1600 6*10^9 to 24*10^9 12 Jul 2021 Gostin 7001-8000 800*10^6 to 1*10^9 13 Feb 2020 Pacher 20001-25000 1*10^6 to 2*10^6 03 Feb 2020 Kamenyuk 100001-120000 120*10^3 to 130*10^3 04 Jan 2021 Tarasov 142000-144000 30*10^3 to 50*10^3 05 Jun 2021 Choliy