Information taken from GFNsrch.html suitably rearranged
Latest update: 24 January 2022
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2-100 1 to 1*10^9 1994 Bjoern & Riesel
5-16 1 to 10*10^9 2008 Keller
9-12 10*10^9 to 1*10^12 2010 Reynolds
13-15 10*10^9 to 2^44 2008 Reynolds
16-25 1 to 60*10^9 2004 Fougeron
16 60*10^9 to 2^44 2008 Reynolds
17 60*10^9 to 2^45 2008 Reynolds
18 60*10^9 to 2^45 2008 Reynolds
18 2^45 to 2^46 2010 Reynolds
19 60*10^9 to 2^45 2008 Reynolds
20 60*10^9 to 2^44 2008 Reynolds
21 60*10^9 to 2^43 2008 Reynolds
21 2^43 to 10*10^12 2012 Reynolds
22 60*10^9 to 2^42 2008 Reynolds
22 2^42 to 10*10^12 2012 Reynolds
23 60*10^9 to 2^41 2008 Reynolds
23 2^41 to 10*10^12 2012 Reynolds
24 60*10^9 to 2^40 2008 Reynolds
24 2^40 to 2*10^12 2010 Rajala
24 2*10^12 to 10*10^12 2012 Reynolds
25 60*10^9 to 1*10^12 2008 Reynolds
25 1*10^12 to 2*10^12 2010 Rajala
25 2*10^12 to 10*10^12 2012 Reynolds
26 1 to 2^36 2004 Fougeron
26 2^36 to 2^38 2008 Reynolds
26 2^38 to 1*10^12 2010 Reynolds
26 1*10^12 to 2*10^12 2010 Rajala
27 1 to 2^35 2004 Fougeron
27 2^35 to 2^37 2008 Reynolds
27 2^37 to 1*10^12 2010 Reynolds
27 1*10^12 to 2*10^12 2010 Rajala
28 1 to 2^34 2004 Fougeron
28 2^34 to 2^36 2008 Reynolds
28 2^36 to 1*10^12 2010 Reynolds
28 1*10^12 to 2*10^12 2010 Rajala
29-49 1 to 10*10^9 2004 Fougeron
29-49 10*10^9 to 1*10^12 2008 Reynolds
50 1 to 5*10^9 2004 Fougeron
50 5*10^9 to 1*10^12 2008 Reynolds
29-50 1*10^12 to 2*10^12 2010 Rajala
51-100 1 to 5*10^9 2004 Fougeron
51-100 5*10^9 to 1*10^12 2008 Reynolds
Summary as of 2012: n = 5-8 k < 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
Extended since 2020:
24-25 10*10^12 to 100*10^12 2021 Doescher
26-30 2*10^12 to 4000*10^9 2020 Gostin
26-30 4000*10^9 to 100*10^12 2021 Doescher
31-35 2*10^12 to 3500*10^9 2020 Gostin
31-35 3500*10^9 to 60*10^12 2021 Doescher
36-40 2*10^12 to 3500*10^9 2020 Gostin
36-40 3500*10^12 to 60*10^12 2021 Doescher
41-50 2*10^12 to 3000*10^9 2020 Gostin
41-50 3000*10^12 to 60*10^12 2021 Doescher
51-60 1*10^12 to 2700*10^9 2020 Gostin
51-60 2700*10^9 to 60*10^12 2021 Doescher
61-80 1*10^12 to 2300*10^9 2020 Gostin
61-80 2300*10^9 to 60*10^12 2021 Doescher
81-100 1*10^12 to 2000*10^9 2020 Gostin
81-100 2000*10^9 to 60*10^12 2021 Doescher
Updated Summary: n = 21-23 k < 10*10^12
24-30 100*10^12
31-100 60*10^12
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101-1000 1 to 3*10^6 1996 Bjoern & Riesel
101-200 3*10^6 to 1*10^9 2004 Fougeron
101-200 1*10^9 to 100*10^9 2008 Reynolds
201-300 3*10^6 to 100*10^6 2004 Fougeron
301-500 1 to 30*10^6 2003 Melo
301-500 30*10^6 to 100*10^6 2004 Fougeron
201-500 100*10^6 to 1*10^9 2008 Wesolowski
201-500 1*10^9 to 10*10^9 2008 Reynolds
501-1000 1 to 10*10^6 2003 Melo
501-1000 10*10^6 to 20*10^6 2004 Fougeron
501-1000 20*10^6 to 30*10^6 2004 Kokales
501-1000 30*10^6 to 110*10^6 2008 Pacher
501-1000 110*10^6 to 1*10^9 2009 Reynolds
501-600 1*10^9 to 2*10^9 2012 Kamenyuk
601-1000 1*10^9 to 2*10^9 2012 Reynolds
201-300 10*10^9 to 15*10^9 2013 Kamenyuk
Summary as of 2013: n = 101-200 k < 100*10^9
201-300 15*10^9
301-500 10*10^9
501-1000 2*10^9
Completely redone and extended since 2020:
101-130 1 to 1000*10^9 2020 Gostin
101-130 1000*10^9 to 3000*10^12 2021 Doescher
101-130 3000*10^9 to 4000*10^9 2021 Gostin
101-130 4000*10^9 to 10*10^12 2021 Doescher
131-140 1 to 1000*10^9 2020 Gostin
131-140 1000*10^9 to 3000*10^9 2021 Doescher
131-140 3000*10^9 to 4000*10^9 2021 Gostin
131-140 3500*10^9 to 10*10^12 2021 Doescher
141-200 1 to 600*10^9 2020 Gostin
141-200 600*10^9 to 3000*10^9 2021 Doescher
141-200 3000*10^9 to 3500*10^9 2021 Gostin
141-200 3500*10^9 to 10*10^12 2021 Doescher
201-300 1 to 300*10^9 2020 Gostin
201-300 300*10^9 to 2000*10^9 2021 Doescher
201-300 2000*10^9 to 2500*10^9 2021 Gostin
201-300 2500*10^9 to 10*10^12 2021 Doescher
301-400 1 to 200*10^9 2020 Gostin
301-400 200*10^9 to 1800*10^9 2021 Gostin
301-400 1800*10^9 to 3000*10^9 2022 Gostin
401-500 1 to 130*10^9 2020 Gostin
401-500 130*10^9 to 1200*10^9 2021 Gostin
401-500 1200*10^9 to 2000*10^9 2022 Gostin
501-600 1 to 80*10^9 2020 Gostin
501-600 80*10^9 tp 1000*10^9 2021 Gostin
601-800 1 to 30*10^9 2020 Gostin
601-700 30*10^9 to 800*10^9 2021 Gostin
701-800 30*10^9 to 600*10^9 2021 Gostin
801-1000 1 to 14*10^9 2020 Gostin
801-900 14*10^9 to 400*10^9 2021 Gostin
901-1000 14*10^9 to 250*10^9 2021 Gostin
Updated Summary: n = 101-300 k < 10*10^12
301-400 3000*10^9
401-500 2000*10^9
501-600 1000*10^9
601-700 800*10^9
701-800 600*10^9
801-900 400*10^9
901-1000 250*10^9
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1001-2000 1 to 5*10^6 2003 Melo
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
1001-1400 1 to 600*10^6 2020 Gostin
(1 missed factor found)
1001-1100 1550*10^6 to 5*10^9 2020 Gostin
1001-1100 1 to 5*10^9 2021 Gostin
1001-1100 5*10^9 to 120*10^9 2021 Gostin
1101-1400 1550*10^6 to 5*10^9 2020 Gostin
1101-1400 1 to 5*10^9 2021 Gostin
1101-1200 5*10^9 to 40*10^9 2021 Gostin
1101-1200 40*10^9 to 100*10^9 2022 Gostin
1201-1400 5*10^9 to 32*10^9 2021 Gostin
1201-1400 32*10^9 to 60*10^9 2022 Gostin
1401-1600 1550*10^6 to 3*10^9 2020 Gostin
1401-1600 1 to 24*10^9 2021 Gostin
1601-1800 1550*10^6 to 3*10^9 2020 Gostin
1601-1800 1 to 16*10^9 2021 Gostin
1801-2000 1550*10^6 to 3*10^9 2020 Gostin
1801-2000 3*10^6 to 12*10^9 2021 Gostin
Summary n = 1001-1100 k < 120*10^9
1101-1200 100*10^9
1201-1400 60*10^9
1401-1600 24*10^9
1601-1800 16*10^9
1801-2000 12*10^9
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2001-3000 1 to 1*10^6 2005 Melo
2001-3000 1*10^6 to 2*10^6 2008 Harvey
2001-3000 2*10^6 to 50*10^6 2011 Kamenyuk
2001-2800 50*10^6 to 60*10^6 2012 Kamenyuk
2801-3000 50*10^6 to 60*10^6 2010 Dubrovin
2001-3000 60*10^6 to 400*10^6 2012 Nohara
2001-3000 400*10^6 to 500*10^6 2020 Gostin
2001-3000 500*10^6 to 1000*10^9 2013 Nohara
2001-3000 1000*10^6 to 1500*10^6 2014 Nohara
2001-2100 1500*10^6 to 2000*10^6 2014 Nordin
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
Summary: n = 2001-2200 k < 4*10^9
2201-3000 3*10^9
Beyond these limits:
2000-2200 50*10^9 to 60*10^9 2021 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
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3001-4000 1 to 1*10^6 2005 Melo
3001-4000 1*10^6 to 2*10^6 2008 Harvey
3001-4000 2*10^6 to 35*10^6 2011 Kamenyuk
3001-4000 35*10^6 to 40*10^6 2010 Choliy
3001-4000 40*10^6 to 100*10^6 2011 Kamenyuk
3001-3400 100*10^6 to 400*10^6 2012 Nohara
3401-4000 100*10^6 to 200*10^6 2013 Pacher
3401-4000 200*10^6 to 400*10^6 2012 Nohara
3001-4000 400*10^6 to 500*10^6 2013 Pacher
3001-4000 500*10^6 to 750*10^6 2014 Nohara
3001-4000 750*10^6 to 800*10^6 2015 Pacher
3001-4000 800*10^6 to 1500*10^6 2015 Nohara
3001-4000 1500*10^6 to 1600*10^6 2021 Doescher
Summary: n = 3001-4000 k < 1600*10^6
Beyond these limits:
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
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4001-5000 1 to 1*10^6 2005 Melo
4001-5000 1*10^6 to 2*10^6 2005 Harvey
4001-5000 2*10^6 to 3*10^6 2008 Harvey
4001-5000 3*10^6 to 50*10^6 2011 Kamenyuk
4001-4500 50*10^6 to 200*10^6 2012 Nohara
4501-5000 50*10^6 to 200*10^6 2012 Rajala
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
Summary: n = 4001-5000 k < 1000*10^6
Beyond these limits:
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
4500-5000 6500*10^6 to 7000*10^6 2021 Morelli
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5001-6000 1 to 1*10^6 2005 Melo
5001-6000 1*10^6 to 2*10^6 2008 Harvey
5001-6000 2*10^6 to 5*10^6 2012 Kamenyuk
5001-6000 5*10^6 to 100*10^6 2012 Nohara
5001-6000 100*10^6 to 120*10^6 2015 Pacher
5001-6000 120*10^6 to 200*10^6 2014 Nohara
5001-5500 200*10^6 to 300*10^6 2020 Gostin
5501-6000 200*10^6 to 220*10^6 2016 Pacher
5501-6000 220*10^6 to 300*10^6 2018 Pacher
Summary: n = 5001-6000 k < 300*10^6
Beyond these limits:
5000-5100 1200*10^6 to 2500*10^6 2018 Rodenkirch
5000-5100 2500*10^6 to 2800*10^6 2021 Paula (DC)
5000-5100 3500*10^6 to 4500*10^6 2020 Gostin
5100-5500 3500*10^6 to 4500*10^6 2020 Gostin
5500-5600 3000*10^6 to 4000*10^6 2020 Gostin
5600-5700 1200*10^6 to 2500*10^6 2019 Morelli
5600-5700 3000*10^6 to 4000*10^6 2020 Gostin
5700-5800 3000*10^6 to 4000*10^6 2021 Gostin
5800-6000 3000*10^6 to 4000*10^6 2020 Gostin
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6001-7000 1 to 1*10^6 2005 Melo
6001-7000 1*10^6 to 2*10^6 2008 Harvey
6001-6050 100*10^3 to 16*10^6 2004 Nohara
6001-6050 16*10^6 to 20*10^6 2012 Kamenyuk
6001-6050 20*10^6 to 50*10^6 2012 Nohara
6001-6050 50*10^6 to 2500*10^6 2013 Tervooren & Bertels
6001-6050 2500*10^6 to 3000*10^6 2020 Gostin
6051-6100 100*10^3 to 8*10^6 2004 Nohara
6051-6100 8*10^6 to 16*10^6 2010 Morelli
6051-6100 16*10^6 to 20*10^6 2012 Kamenyuk
6051-6100 20*10^6 to 50*10^6 2012 Nohara
6051-6100 50*10^6 to 2500*10^6 2013 Tervooren & Bertels
6051-6100 2500*10^6 to 3000*10^6 2020 Gostin
6101-6150 100*10^3 to 8*10^6 2004 Nohara
6101-6150 8*10^6 to 10*10^6 2010 Kamenyuk
6101-6150 10*10^6 to 50*10^6 2012 Nohara
6101-6150 50*10^6 to 2500*10^6 2013 Tervooren & Bertels
6101-6150 2500*10^6 to 3000*10^6 2020 Gostin
6151-6400 100*10^3 to 8*10^6 2004 Nohara
6151-6400 8*10^6 to 10*10^6 2010 Kamenyuk
6151-6400 10*10^6 to 50*10^6 2012 Nohara
6151-6400 50*10^6 to 200*10^6 2014 Nohara
6151-6200 200*10^6 to 800*10^6 2022 Gostin
6151-6200 800*10^6 to 900*10^6 2017 Hermanns
6151-6200 900*10^6 to 2500*10^6 2018 Meekins
6151-6200 2500*10^6 to 3000*10^6 2020 Gostin
6401-6500 2*10^6 to 2^21 2010 Morelli
6401-6500 2^21 to 2^22 2008 Kitchen
6401-6500 4*10^6 to 10*10^6 2010 Morelli
6401-6500 10*10^6 to 50*10^6 2012 Nohara
6401-6500 50*10^6 to 200*10^6 2014 Nohara
6501-7000 2*10^6 to 2^21 2008 Harvey
6501-7000 2^21 to 2500*10^3 2005 Harvey
6501-7000 2500*10^3 to 4000*10^3 2008 Harvey
6501-7000 4*10^6 to 10*10^6 2010 Morelli
6501-7000 10*10^6 to 50*10^6 2012 Nohara
6501-7000 50*10^6 to 80*10^6 2014 Pacher
6501-7000 80*10^6 to 100*10^6 2014 Nohara
6501-7000 100*10^6 to 120*10^6 2020 Gostin
Summary: n = 6001-6200 k < 3000*10^6
6201-6500 200*10^6
6501-7000 120*10^6
Beyond these limits:
6200-6300 900*10^6 to 1000*10^6 2018 Rodenkirch
6200-6300 2100*10^6 to 3000*10^6 2020 Gostin
6300-6500 2000*10^6 to 3000*10^6 2020 Gostin
6500-7000 1500*10^6 to 2000*10^6 2020 Gostin
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7001-8000 1 to 20*10^3 2003 Melo & Keller
7001-8000 20*10^3 to 100*10^3 2004 Kokales
7001-8000 100*10^3 to 300*10^3 2008 Harvey
7001-7600 1 to 10*10^6 2006 Melo
7601-8000 300*10^3 to 2*10^6 2008 Harvey
7601-8000 2*10^6 to 10*10^6 2010 Choliy
7001-7200 10*10^6 to 50*10^6 2013 Nohara
7201-8000 10*10^6 to 20*10^6 2012 Batalov
7201-8000 20*10^6 to 50*10^6 2013 Nohara
7001-7200 50*10^6 to 100*10^6 2014 Nohara
7201-8000 50*10^6 to 100*10^6 2014 Nohara
Summary: n = 7001-8000 k < 100*10^6
Beyond these limits:
7000-8000 1000*10^6 to 1200*10^6 2020 Gostin
7000-8000 1200*10^6 to 1500*10^6 2021 Gostin
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8001-10000 1 to 1600 2003 Melo & Keller
8001-10000 1600 to 100*10^3 2004 Kokales
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
8001-9000 1*10^6 to 5*10^6 2010 Nohara
8001-9000 5*10^6 to 7*10^6 2011 Kamenyuk
8001-9000 7*10^6 to 15*10^6 2012 Batalov
8001-9000 15*10^6 to 30*10^6 2013 Nohara
8001-9000 30*10^6 to 50*10^6 2014 Nohara
8001-9000 50*10^6 to 85*10^6 2020 Gostin
9001-10000 1*10^6 to 5*10^6 2010 Nohara
9001-10000 5*10^6 to 10*10^6 2012 Batalov
9001-10000 10*10^6 to 30*10^6 2013 Nohara
9001-10000 30*10^6 to 50*10^6 2014 Nohara
9001-9200 50*10^6 to 60*10^6 2022 Gostin
9201-10000 50*10^6 to 60*10^6 2021 Nordin (DC)
Summary: n = 8001-9000 k < 85*10^6
9001-10000 60*10^6
Beyond these limits:
8000-9000 350*10^6 to 400*10^6 2018 Rodenkirch
8000-9000 600*10^6 to 800*10^6 2020 Gostin
8000-9000 800*10^6 to 1000*10^6 2021 Gostin
9000-10000 270*10^6 to 300*10^6 2018 Rodenkirch
9000-10000 450*10^6 to 600*10^6 2020 Gostin
9000-10000 600*10^6 to 750*10^6 2021 Gostin
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10001-20000 1 to 1600 2003 Melo & Keller
10001-11000 1000 to 200*10^3 2005 Harvey
10001-11000 200*10^3 to 400*10^3 2008 Harvey
10001-11000 400*10^3 to 1*10^6 2009 Kamenyuk
10001-11000 1*10^6 to 2*10^6 2010 Nohara
10001-11000 2*10^6 to 5*10^6 2010 Nohara
10001-11000 5*10^6 to 10*10^6 2012 Batalov
10001-11000 10*10^6 to 20*10^6 2013 Nohara
10001-11000 20*10^6 to 30*10^6 2015 Nohara
11001-12000 1000 to 200*10^3 2005 Harvey
11001-12000 200*10^3 to 330*10^3 2008 Harvey
11001-12000 330*10^3 to 1*10^6 2009 Kamenyuk
11001-12000 1*10^6 to 2*10^6 2010 Nohara
11001-12000 2*10^6 to 5*10^6 2011 Nohara
11001-12000 5*10^6 to 10*10^6 2012 Batalov
11001-12000 10*10^6 to 20*10^6 2013 Nohara
11001-12000 20*10^6 to 30*10^6 2015 Nohara
12001-13000 1600 to 100*10^3 2005 Harvey
12001-13000 100*10^3 to 200*10^3 2008 Harvey
12001-13000 200*10^3 to 2*10^6 2009 Nohara
12001-13000 2*10^6 to 5*10^6 2012 Rajala
12001-13000 5*10^6 to 10*10^6 2012 Batalov
12001-13000 10*10^6 to 20*10^6 2015 Nohara
13001-13500 1000 to 50*10^3 2005 Harvey
13001-13500 100*10^3 to 200*10^3 2008 Harvey
13001-13500 200*10^3 to 400*10^3 2010 Nohara
13001-13500 400*10^3 to 1*10^6 2010 Choliy
13001-13500 1*10^6 to 2*10^6 2010 Nohara
13001-13500 2*10^6 to 10*10^6 2012 Batalov
13001-13500 10*10^6 to 20*10^6 2015 Nohara
13501-14000 1000 to 50*10^3 2005 Harvey
13501-14000 50*10^3 to 100*10^3 2008 Samidoost
13501-14000 100*10^3 to 200*10^3 2008 Harvey
13501-14000 200*10^3 to 2*10^6 2010 Nohara
13501-14000 2*10^6 to 10*10^6 2012 Batalov
13501-14000 10*10^6 to 20*10^6 2015 Nohara
14001-15000 1000 to 50*10^3 2005 Harvey
14001-15000 50*10^3 to 100*10^3 2008 Samidoost
14001-15000 100*10^3 to 200*10^3 2008 Harvey
14001-15000 200*10^3 to 2*10^6 2010 Nohara
14001-15000 2*10^6 to 10*10^6 2012 Batalov
14001-14500 10*10^6 to 20*10^6 2022 Gostin
14001-14500 20*10^6 to 30*10^6 2017 Morelli
14501-15000 10*10^6 to 40*10^6 2022 Gostin
14501-15000 40*10^6 to 70*10^6 2018 Rodenkirch
15001-16000 1600 to 50*10^3 2005 Harvey
15001-16000 50*10^3 to 100*10^3 2008 Samidoost
15001-16000 100*10^3 to 200*10^3 2008 Harvey
15001-16000 200*10^3 to 2*10^6 2010 Nohara
15001-16000 2*10^6 to 10*10^6 2012 Batalov
16001-16350 1600 to 40*10^3 2006 Harvey
16001-16350 40*10^3 to 100*10^3 2008 Samidoost
16001-16350 100*10^3 to 200*10^3 2008 Harvey
16001-16350 200*10^3 to 500*10^3 2010 Nohara
16001-16350 500*10^3 to 2*10^6 2010 Nohara
16001-16350 2*10^6 to 5*10^6 2012 Batalov
16001-16350 5*10^6 to 6*10^6 2021 Baur
16351-17000 1600 to 40*10^3 2006 Harvey
16351-17000 40*10^3 to 100*10^3 2008 Samidoost
16351-17000 100*10^3 to 500*10^3 2005 Rodenkirch
16351-17000 500*10^3 to 2*10^6 2010 Nohara
16351-17000 2*10^6 to 5*10^6 2012 Batalov
16351-17000 5*10^6 to 6*10^6 2021 Baur
17001-18000 1000 to 40*10^3 2006 Harvey
17001-18000 40*10^3 to 100*10^3 2008 Samidoost
17001-18000 100*10^3 to 500*10^3 2005 Rodenkirch
17001-18000 500*10^3 to 1*10^6 2010 Nohara
17001-18000 1*10^6 to 2*10^6 2011 Nohara
17001-18000 2*10^6 to 5*10^6 2012 Batalov
18001-19000 1000 to 30*10^3 2006 Harvey
18001-19000 30*10^3 to 100*10^3 2008 Samidoost
18001-19000 100*10^3 to 500*10^3 2005 Rodenkirch
18001-19000 500*10^3 to 1*10^6 2010 Nohara
18001-19000 1*10^6 to 2*10^6 2011 Nohara
18001-19000 2*10^6 to 5*10^6 2020 Baur
19001-20000 1000 to 20*10^3 2006 Harvey
19001-20000 20*10^3 to 100*10^3 2008 Wesolowski
19001-20000 100*10^3 to 500*10^3 2005 Rodenkirch
19001-20000 500*10^3 to 1*10^6 2010 Nohara
19001-20000 1*10^6 to 2*10^6 2011 Nohara
19001-20000 2*10^6 to 3*10^6 2020 Morelli
Summary: n = 10001-12000 k < 30*10^6
12001-14000 20*10^6
14001-14500 30*10^6
14501-15000 70*10^6
15001-16000 10*10^6
16001-17000 6*10^6
17001-19000 5*10^6
19001-20000 3*10^6
Beyond these limits:
10000-11000 100*10^6 to 300*10^6 2018 Rodenkirch
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
14000-15000 120*10^6 to 160*10^6 2021 Gostin
15000-16000 70*10^6 to 120*10^6 2020 Gostin
15000-16000 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
18000-19000 50*10^6 to 75*10^6 2021 Gostin
19000-20000 20*10^6 to 50*10^6 2020 Gostin
19000-20000 50*10^6 to 75*10^6 2021 Gostin
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20001-30000 1 to 1200 2003 Melo & Keller
20001-21000 1200 to 15*10^3 2006 Harvey
20001-21000 15*10^3 to 100*10^3 2008 Wesolowski
20001-21000 100*10^3 to 1*10^6 2011 Nohara
20001-21000 1*10^6 to 2*10^6 2022 Gostin
20001-21000 2*10^6 to 3*10^6 2020 Gostin
21001-22000 1200 to 15*10^3 2006 Harvey
21001-22000 15*10^3 to 100*10^3 2008 Bock
21001-22000 100*10^3 to 500*10^3 2010 Choliy
21001-22000 500*10^3 to 1*10^6 2011 Nohara
21001-22000 1*10^6 to 2*10^6 2022 Gostin
21001-22000 2*10^6 to 3*10^6 2020 Gostin
22001-23000 1200 to 15*10^3 2006 Harvey
22001-23000 15*10^3 to 100*10^3 2008 Wesolowski
22001-23000 100*10^3 to 200*10^3 2010 Choliy
22001-23000 200*10^3 to 1*10^6 2011 Nohara
23001-24000 1200 to 15*10^3 2006 Harvey
23001-24000 15*10^3 to 100*10^3 2008 Wesolowski
23001-24000 100*10^3 to 500*10^3 2010 Choliy
23001-24000 500*10^3 to 1*10^6 2011 Rajala
24001-25000 1200 to 10*10^3 2006 Harvey
24001-25000 10*10^3 to 100*10^3 2008 Wesolowski
24001-25000 100*10^3 to 200*10^3 2011 Choliy
24001-25000 200*10^3 to 500*10^3 2011 Choliy
24001-25000 500*10^3 to 1*10^6 2012 Nohara
25001-30000 1200 to 10*10^3 2006 Harvey
25001-30000 10*10^3 to 100*10^3 2008 Wesolowski
25001-30000 100*10^3 to 200*10^3 2011 Choliy
25001-28000 200*10^3 to 500*10^3 2012 Nohara
28001-30000 200*10^3 to 500*10^3 2012 Rajala
25001-27000 500*10^3 to 1*10^6 2013 Le Foulher
27001-30000 500*10^3 to 1*10^6 2013 Le Foulher
25001-26000 1000*10^3 to 1100*10^3 2014 Nordin
25001-26000 1100*10^3 to 3000*10^3 2015 Nordin
26001-28000 1000*10^3 to 1500*10^3 2020 Gostin
28001-30000 1000*10^3 to 1500*10^3 2015 Rajala
Summary: n = 20001-22000 k < 3*10^6
22001-25000 1*10^6
25001-26000 3*10^6
26001-30000 1500*10^3
Beyond these limits:
20000-22000 20*10^6 to 40*10^6 2020 Gostin
20000-22000 40*10^6 to 64*10^6 2021 Gostin
22000-23000 8*10^6 to 9*10^6 2021 Gostin
22000-23000 9*10^6 to 16*10^6 2021 Paula (DC)
22000-23000 16*10^6 to 32*10^6 2020 Gostin
22000-23000 32*10^6 to 48*10^6 2020 Gostin
23000-24000 8*10^6 to 9*10^6 2021 Gostin
23000-24000 9*10^6 to 20*10^6 2020 Gostin
23000-24000 20*10^6 to 32*10^6 2021 Gostin
23000-24000 32*10^6 to 48*10^6 2021 Gostin
24000-25000 8*10^6 to 9*10^6 2021 Gostin
24000-25000 9*10^6 to 20*10^6 2020 Gostin
24000-25000 20*10^6 to 24*10^6 2021 Gostin
24000-25000 24*10^6 to 36*10^6 2022 Gostin
25000-26000 6*10^6 to 12*10^6 2020 Gostin
25000-26000 12*10^6 to 24*10^6 2021 Gostin
25000-26000 24*10^6 to 36*10^6 2022 Gostin
26000-30000 6*10^6 to 12*10^6 2020 Gostin
26000-30000 12*10^6 to 15*10^6 2021 Gostin
26000-30000 15*10^6 to 20*10^6 2022 Gostin
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30001-40000 1 to 1200 2003 Melo & Keller
30001-35000 1200 to 5*10^3 2006 Harvey
35001-36000 1200 to 5*10^3 2007 Keller
36001-38000 1200 to 5*10^3 2006 Harvey
38001-39000 1200 to 5*10^3 2007 Keller
30001-40000 1*10^3 to 10*10^3 2008 Samidoost
30001-31000 10*10^3 to 100*10^3 2008 Wesolowski
30001-31000 100*10^3 to 300*10^3 2009 Nohara
31001-32000 10*10^3 to 200*10^3 2008 Keiser
31001-32000 200*10^3 to 300*10^3 2009 Nohara
32001-33000 10*10^3 to 100*10^3 2008 Wesolowski
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 2008 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
34001-38000 100*10^3 to 200*10^3 2008 Nohara
38001-40000 100*10^3 to 200*10^3 2009 Nohara
33001-35000 200*10^3 to 300*10^3 2013 Rajala
35001-36000 200*10^3 to 250*10^3 2012 Gautier
35001-36000 250*10^3 to 300*10^3 2013 Rajala
30001-35000 300*10^3 to 500*10^3 2018 Rodenkirch
30001-35000 500*10^3 to 1*10^6 2013 Nohara
35001-36000 300*10^3 to 500*10^3 2020 Morelli
36001-40000 300*10^3 to 500*10^3 2020 Morelli
Summary: n = 30001-35000 k < 1*10^6
35001-40000 500*10^3
Beyond these limits:
30000-33000 3000*10^3 to 3500*10^3 2020 Gostin
30000-33000 3500*10^3 to 4000*10^3 2020 Morelli
33000-35000 3*10^6 to 4*10^6 2020 Morelli
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
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40001-50000 1 to 600 2003 Melo & ProthSearch
40001-50000 600 to 1200 2006 Keller & Axelsson
40001-50000 1*10^3 to 10*10^3 2008 Samidoost
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
40001-45000 100*10^3 to 200*10^3 2011 Rajala
45001-50000 100*10^3 to 200*10^3 2011 Morelli
40001-45000 200*10^3 to 300*10^3 2015 Rajala
Summary: n = 40001-45000 k < 300*10^3
45001-50000 200*10^3
Beyond these limits:
40000-43000 1000*10^3 to 3000*10^3 2020 Gostin
43000-44000 1000*10^3 to 1200*10^3 2020 Gostin
43001-44000 1200*10^3 to 1400*10^3 2022 Gostin
43000-44000 1400*10^3 to 3000*10^3 2020 Gostin
44000-45000 1000*10^3 to 3000*10^3 2020 Gostin
40000-45000 3000*10^3 to 4000*10^3 2021 Gostin
45000-46000 1000*10^3 to 2200*10^3 2020 Gostin
46001-47000 1000*10^3 to 1200*10^3 2019 Rodenkirch
46000-47000 1200*10^3 to 2200*10^3 2020 Gostin
47000-50000 1000*10^3 to 2200*10^3 2020 Gostin
45000-50000 2200*10^3 to 3000*10^3 2021 Gostin
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50001-60000 1 to 600 2003 Melo & ProthSearch
50001-60000 600 to 1200 2006 Keller & Axelsson
50001-60000 1*10^3 to 10*10^3 2008 Samidoost
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
50001-55000 100*10^3 to 125*10^3 2014 Rajala
50001-55000 125*10^3 to 170*10^3 2020 Gostin
55001-60000 10*10^3 to 30*10^3 2010 Nohara
55001-60000 30*10^3 to 50*10^3 2009 Nohara
55001-60000 50*10^3 to 100*10^3 2012 Kamenyuk
55001-60000 100*10^3 to 125*10^3 2014 Rajala
55001-57000 125*10^3 to 130*10^3 2017 Nordin
Summary: n = 50001-55000 k < 170*10^3
55001-57000 130*10^3
57001-60000 125*10^3
Beyond these limits:
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
55000-60000 1200*10^3 to 1600*10^3 2021 Gostin
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60001-70000 1 to 600 2003 Melo & ProthSearch
60001-70000 600 to 1200 2006 Keller & Axelsson
60001-70000 1000 to 10*10^3 2008 Samidoost
60001-61000 10*10^3 to 20*10^3 2008 Larouche
60001-61000 20*10^3 to 100*10^3 2009 Larouche
61001-69000 10*10^3 to 20*10^3 2009 Keiser
69001-70000 10*10^3 to 20*10^3 2010 Morelli
61001-70000 20*10^3 to 30*10^3 2012 Morelli
61001-70000 30*10^3 to 50*10^3 2013 Le Foulher
61001-70000 50*10^3 to 60*10^3 2014 Rajala
61001-70000 60*10^3 to 100*10^3 2020 Gostin
60001-61000 100*10^3 to 125*10^3 2020 Larouche (DC)
61001-62000 100*10^3 to 125*10^3 2015 Nordin
62001-70000 100*10^3 to 110*10^3 2017 Batalov
62001-70000 110*10^3 to 125*10^3 2020 Gostin
60001-70000 125*10^3 to 150*10^3 2020 Gostin
60001-65000 150*10^3 to 200*10^3 2020 Gostin
60001-65000 200*10^3 to 400*10^3 2021 Doescher
60001-61000 400*10^3 to 450*10^3 2019 Delgado
60001-61000 450*10^3 to 500*10^3 2020 Gostin
61001-65000 400*10^3 to 500*10^3 2020 Gostin
60001-65000 500*10^3 to 900*10^3 2020 Gostin
60001-65000 900*10^3 to 1*10^6 2021 Doescher
65001-70000 150*10^3 to 300*10^3 2021 Doescher
65001-70000 300*10^3 to 400*10^3 2020 Gostin
65001-70000 400*10^3 to 700*10^3 2021 Gostin
65001-70000 700*10^3 to 1*10^6 2021 Doescher
Summary: n = 60001-70000 k < 1*10^6
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70001-80000 1 to 600 2003 Melo & ProthSearch
70001-80000 600 to 1200 2006 Keller & Axelsson
70001-80000 1*10^3 to 10*10^3 2008 Samidoost
70001-73000 10*10^3 to 30*10^3 2010 Morelli
73001-74000 10*10^3 to 20*10^3 2010 Choliy
74001-80000 10*10^3 to 20*10^3 2011 Choliy
73001-80000 20*10^3 to 30*10^3 2012 Morelli
70001-80000 30*10^3 to 50*10^3 2020 Gostin
70001-80000 50*10^3 to 60*10^3 2014 Rajala
70001-80000 60*10^3 to 100*10^3 2020 Gostin
70001-75000 100*10^3 to 130*10^3 2020 Gostin
Summary: n = 70001-75000 k < 130*10^3
75001-80000 100*10^3
Beyond these limits:
70000-71000 250*10^3 to 350*10^3 2019 Delgado
71000-75000 250*10^3 to 350*10^3 2020 Gostin
70000-75000 350*10^3 to 600*10^3 2021 Gostin
75000-80000 200*10^3 to 300*10^3 2020 Gostin
75000-80000 300*10^3 to 500*10^3 2021 Gostin
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80001-90000 1 to 600 2003 Melo & ProthSearch
80001-90000 600 to 1200 2006 Keller & Axelsson
80001-90000 1*10^3 to 10*10^3 2008 Samidoost
80001-90000 10*10^3 to 30*10^3 2013 Gautier
80001-90000 30*10^3 to 50*10^3 2012 Batalov
80001-90000 50*10^3 to 60*10^3 2014 Rajala
80001-90000 60*10^3 to 70*10^3 2020 Gostin
80001-81000 70*10^3 to 80*10^3 2021 Nordin (DC)
81001-82000 70*10^3 to 80*10^3 2015 Nordin
82001-90000 70*10^3 to 80*10^3 2020 Gostin
80001-90000 80*10^3 to 90*10^3 2017 Nordin
80001-81000 90*10^3 to 100*10^3 2017 Morelli
80001-81000 100*10^3 to 130*10^3 2020 Gostin
81001-90000 90*10^3 to 130*10^3 2020 Gostin
Summary: n = 80001-90000 k < 130*10^3
Beyond these limits:
80000-90000 200*10^3 to 250*10^3 2020 Gostin
80001-81000 250*10^3 to 300*10^3 2021 Delgado
81000-90000 250*10^3 to 300*10^3 2021 Gostin
80000-85000 300*10^3 to 400*10^3 2021 Morelli
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90001-100000 1 to 600 2003 Melo & ProthSearch
90001-100000 600 to 1200 2006 Keller & Axelsson
90001-100000 1*10^3 to 10*10^3 2008 Samidoost
90001-100000 10*10^3 to 30*10^3 2013 Morelli
90001-100000 30*10^3 to 50*10^3 2012 Batalov
90001-100000 50*10^3 to 60*10^3 2014 Rajala
90001-100000 60*10^3 to 70*10^3 2020 Gostin
90001-99000 70*10^3 to 80*10^3 2022 Gostin
90001-99000 80*10^3 to 100*10^3 2020 Gostin
99001-100000 10*10^3 to 100*10^3 2021 Samidoost (DC)
Summary: n = 90001-100000 k < 100*10^3
Beyond these limits:
90001-91000 200*10^3 to 250*10^3 2021 Delgado
91000-92000 200*10^3 to 250*10^3 2021 Gostin
92000-93000 150*10^3 to 170*10^3 2019 Delgado
92000-93000 170*10^3 to 200*10^3 2020 Delgado
92000-93000 200*10^3 to 250*10^3 2021 Gostin
93000-94000 150*10^3 to 200*10^3 2020 Delgado
93000-94000 200*10^3 to 250*10^3 2021 Gostin
94000-100000 150*10^3 to 200*10^3 2020 Gostin
94000-100000 200*10^3 to 250*10^3 2021 Gostin
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100001-150000 10*10^3 to 20*10^3 2012 Batalov
150001-160000 10*10^3 to 20*10^3 2013 Rajala
160001-170000 10*10^3 to 15*10^3 2020 Gostin
160001-170000 15*10^3 to 20*10^3 2020 Morelli
100001-120000 20*10^3 to 40*10^3 2012 Batalov
100001-114000 40*10^3 to 100*10^3 2020 Gostin
114001-120000 40*10^3 to 100*10^3 2017 Rodenkirch
100001-110000 100*10^3 to 120*10^3 2020 Gostin
110001-120000 100*10^3 to 110*10^3 2020 Gostin
110001-120000 110*10^3 to 120*10^3 2021 Tarasov
120001-130000 20*10^3 to 30*10^3 2020 Gostin
120001-130000 30*10^3 to 40*10^3 2017 Rodenkirch
120001-130000 40*10^3 to 60*10^3 2020 Gostin
130001-140000 20*10^3 to 30*10^3 2017 Rodenkirch
130001-140000 30*10^3 to 50*10^3 2020 Gostin
140001-170000 20*10^3 to 30*10^3 2020 Gostin
140001-144000 30*10^3 to 50*10^3 2021 Choliy
170001-180000 10*10^3 to 30*10^3 2020 Gostin
180001-190000 10*10^3 to 13*10^3 2020 Gostin
180001-181743 13*10^3 to 30*10^3 2017 Nordin
181744-190000 13*10^3 to 30*10^3 2020 Hermanns
190001-220000 10*10^3 to 20*10^3 2020 Gostin
220001-250000 10*10^3 to 15*10^3 2020 Gostin
220001-250000 15*10^3 to 20*10^3 2021 Doescher
250001-300000 10*10^3 to 12*10^3 2020 Gostin
Summary: n = 100001-120000 k < 120*10^3
120001-130000 60*10^3
130001-144000 50*10^3
144001-190000 30*10^3
190001-250000 20*10^3
250001-300000 12*10^3
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Compact Summary
n = 21-23 10*10^12
24-30 100*10^12
31-100 60*10^12
101-300 10*10^12
301-400 3*10^12
401-500 2*10^12
501-600 1*10^12
601-700 800*10^9
701-800 600*10^9
801-900 400*10^9
901-1000 250*10^9
1001-1100 120*10^9
1101-1200 100*10^9
1201-1400 60*10^9
1401-1600 24*10^9
1601-1800 16*10^9
1801-2000 12*10^9
2001-2200 4*10^9
2201-3000 3*10^9
3001-4000 1600*10^6
4001-5000 1000*10^6
5001-6000 300*10^6
6001-6200 3000*10^6
6201-6500 200*10^6
6501-7000 120*10^6
7001-8000 100*10^6
8001-9000 85*10^6
9001-10000 60*10^6
10001-12000 30*10^6
12001-14000 20*10^6
14001-14500 30*10^6
14501-15000 70*10^6
15001-16000 10*10^6
16001-17000 6*10^6
17001-19000 5*10^6
19001-22000 3*10^6
22001-25000 1*10^6
25001-26000 3*10^6
26001-30000 1500*10^3
30001-35000 1000*10^3
35001-40000 500*10^3
40001-45000 300*10^3
45001-50000 200*10^3
50001-55000 170*10^3
55001-57000 130*10^3
57001-60000 125*10^3
60001-70000 1*10^6
70001-75000 130*10^3
75001-80000 100*10^3
80001-90000 130*10^3
90001-100000 100*10^3
100001-120000 120*10^3
120001-130000 60*10^3
130001-144000 50*10^3
144001-190000 30*10^3
190001-250000 20*10^3
250001-300000 12*10^3
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