## PRP Records

### Probable Primes Top 10000

#### (295158 PRPs in the top)

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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See the Latest PRPs
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 1-250 251-500 501-750 751-1000 1001-1250 1251-1500 1501-1750 1751-2000 2001-2250 2251-2500 2501-2750 2751-3000 3001-3250 3251-3500 3501-3750 3751-4000 4001-4250 4251-4500 4501-4750 4751-5000 5001-5250 5251-5500 5501-5750 5751-6000 6001-6250 6251-6500 6501-6750 6751-7000 7001-7250 7251-7500 7501-7750 7751-8000 8001-8250 8251-8500 8501-8750 8751-9000 9001-9250 9251-9500 9501-9750 9751-10000

 Rank Probable prime Digits (> 50000) Who ? When ? 7001 (19*10^103907+77)/3 103908 Robert Price 05/2019 7002 (78557*2^345163+1)/78589 103905 Lelio R Paula 07/2014 7003 2^345106-112181 103888 Enzo Doria 06/2014 7004 (2^345105+1326)/2 103887 Stefano Morozzi 02/2021 7005 2^345079+99 103880 Lelio R Paula 09/2011 7006 (2^345034+1198)/2 103866 Stefano Morozzi 09/2020 7007 11^99736-1500 103865 Enzo Doria 12/2012 7008 (569^37699-1)/568 103863 Serge Batalov 06/2022 7009 (2^345010+2082)/2 103859 Stefano Morozzi 09/2020 7010 23263^23784-23784^23263 103857 Norbert Schneider 01/2020 7011 3*10^103844+31 103845 Robert Price 06/2021 7012 444*33^68368+19 103821 Eric Chen 05/2023 7013 23927^21814+21814^23927 103813 Hans Havermann 09/2020 7014 2^344842-20157 103808 Enzo Doria 06/2013 7015 (47*2^344822+1)/1071 103801 Lelio R Paula 05/2015 7016 2^344802-20765 103796 Enzo Doria 06/2013 7017 2^344794-3821 103794 Yves Minet 05/2011 7018 2^344782-109103 103790 Enzo Doria 04/2014 7019 3^217521-112292 103784 Enzo Doria 06/2014 7020 2^344759-3505 103783 Lelio R Paula 11/2016 7021 2^344735-147 103776 Lelio R Paula 09/2011 7022 L(496533)-p(496533) 103770 Robert Price 02/2018 7023 2*10^103749-69 103750 Robert Price 03/2018 7024 (55459*2^344617+1)/3 103745 Lelio R Paula 07/2014 7025 2^344607-108891 103738 Enzo Doria 03/2014 7027 (2^344608+3798)/2 103738 Stefano Morozzi 02/2021 7026 (1097^34123-1)/1096 103738 Serge Batalov 06/2022 7028 2^344560+22411 103723 Enzo Doria 09/2023 7029 (148*10^103718-1)/3 103720 Robert Price 03/2020 7030 2^344541-19561 103718 Enzo Doria 05/2013 7031 (1017*2^344529-1)/569 103714 Lelio R Paula 05/2015 7032 (8896^26263-1)/8895 103714 Serge Batalov 06/2022 7033 (2^344503+1758)/2 103706 Stefano Morozzi 09/2020 7034 (4*10^103703-1)/3 103704 Serge Batalov 08/2009 7035 2^344444-455 103688 Yves Minet 03/2012 7036 (4*10^103678-43)/3 103679 Robert Price 01/2022 7037 (13*53^238539*617^9)/10^307661 103673 Hans Havermann 06/2017 7038 (2^344367+2738)/2 103665 Stefano Morozzi 01/2021 7040 2^344317-109933 103650 Enzo Doria 04/2014 7039 26055^9508+9508^26055 103650 Hans Havermann 09/2020 7041 2^344309-1852033 103648 Enzo Doria 08/2015 7042 25729^10672+10672^25729 103643 Hans Havermann 09/2020 7043 (2^344289+1166)/2 103642 Stefano Morozzi 09/2020 7044 3*10^103637+61 103638 Robert Price 09/2020 7045 (2^344246+1614)/2 103629 Stefano Morozzi 09/2020 7046 2^344213-21253 103619 Enzo Doria 06/2013 7047 2^344196-465 103614 Lelio R Paula 11/2016 7048 2^344187-20001 103611 Enzo Doria 06/2013 7049 (117191#+(355573#)/(117191#))/(200233679) 103602 Makoto Morimoto 10/2017 7050 (237^43627-1)/236 103601 Serge Batalov 06/2022 7051 20^79621-19^79621 103590 Jean-Louis Charton 03/2011 7052 Phi(155391,10)/1243129 103586 Maksym Voznyy 09/2015 7053 (9^108553-2^108553)/7 103586 Jon Grantham 07/2023 7054 2^344085-20365 103580 Enzo Doria 06/2013 7055 5^148169+54 103566 Lelio R Paula 11/2016 7056 2^344017-108795 103560 Enzo Doria 03/2014 7057 (2^343974+2670)/2 103547 Stefano Morozzi 09/2020 7058 2^343971-5077 103546 Lelio R Paula 09/2011 7059 (7*10^103531+71)/3 103532 Robert Price 05/2018 7060 2^343899+141 103524 Lelio R Paula 08/2011 7061 (2^343933+1)/(3*98294339989393) 103520 Gord Palameta 08/2018 7062 6^133029-67 103517 Lelio R Paula 11/2016 7063 (17*2^343877+1)/13625 103515 Lelio R Paula 12/2013 7064 66*10^103507+7 103509 Robert Price 07/2020 7065 26297^8614+8614^26297 103485 Hans Havermann 09/2020 7066 (2^343764+2658)/2 103483 Stefano Morozzi 09/2020 7067 26499^8036+8036^26499 103480 Hans Havermann 09/2020 7068 (136*10^103474-1)/9 103476 Serge Batalov 12/2014 7069 5^148014-24 103458 Lelio R Paula 11/2016 7070 28316^4503+4503^28316 103453 Hans Havermann 09/2020 7071 (22*10^103450+53)/3 103451 Robert Price 07/2019 7072 2^343604+9931 103436 Yves Minet 01/2011 7073 2^343601-21189 103435 Enzo Doria 06/2013 7074 (10^103423+173)/3 103423 Robert Price 05/2021 7075 2^343508-115229 103407 Enzo Doria 06/2015 7076 (8766^26227-1)/8765 103404 Serge Batalov 06/2022 7077 (509203*2^343491-1)/16147 103403 Lelio R Paula 05/2015 7078 3^216685-113056 103386 Enzo Doria 07/2014 7079 24829^14580+14580^24829 103382 Hans Havermann 08/2020 7080 91355!4+1024 103381 Robert Price 09/2019 7081 44^62903-43^62903 103379 Jean-Louis Charton 08/2012 7082 11^99262-20 103371 Lelio R Paula 12/2016 7083 (509203*2^343357-1)/5 103366 Lelio R Paula 05/2015 7084 (2^343363+3570)/2 103363 Stefano Morozzi 09/2020 7085 2^343356-2791889 103361 Enzo Doria 03/2016 7086 (25*10^103360-241)/9 103361 Robert Price 05/2018 7087 Phi(104989,10)/2939693 103350 Maksym Voznyy 09/2015 7088 (371*33^68040-19)/32 103321 Eric Chen 05/2023 7089 24826^14511+14511^24826 103319 Hans Havermann 09/2020 7090 2^343182-171 103309 Lelio R Paula 08/2011 7091 (23619^23619+23620^23620)/7187 103294 David Broadhurst 09/2009 7092 (16487^24649-1)/(16487^157-1) 103287 Ryan Propper 11/2023 7093 (10680^25639-1)/10679 103285 Serge Batalov 06/2022 7094 (7427^26683-1)/7426 103282 Serge Batalov 06/2022 7095 2^343079-1835611 103278 Enzo Doria 05/2015 7096 2^343063-1147 103273 Yves Minet 06/2013 7097 24741^14930+14930^24741 103271 Hans Havermann 09/2020 7098 (16*10^103255-73)/3 103256 Robert Price 07/2020 7099 (219^44119-1)/218 103256 Serge Batalov 06/2022 7100 9*6^132689+7 103254 Lelio R Paula 11/2014 7101 2^342979-18085 103247 Enzo Doria 05/2013 7102 (16*10^103244-31)/3 103245 Robert Price 03/2019 7103 2^342966-16995 103244 Lelio R Paula 11/2016 7104 23797^21774+21774^23797 103230 Hans Havermann 09/2020 7105 25388^11637+11637^25388 103224 Hans Havermann 09/2020 7106 (2^342876+2086)/2 103216 Stefano Morozzi 09/2020 7107 (16*10^103214-31)/3 103215 Robert Price 03/2019 7109 (37*10^103211+611)/9 103212 Robert Price 11/2018 7108 (238*10^103210-1)/3 103212 Robert Price 04/2020 7110 5^147650+16 103203 Lelio R Paula 11/2016 7111 gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809) 103201 Serge Batalov 04/2015 7112 2^342817+2707067 103199 Enzo Doria 03/2016 7113 43^63177-42 103198 Theodore Burton 02/2007 7114 2^342805-21025 103195 Enzo Doria 06/2013 7115 24129^18890+18890^24129 103182 Hans Havermann 09/2020 7116 (622*10^103171-1)/9 103173 Robert Price 11/2021 7117 2^342714+12285 103168 Lelio R Paula 11/2016 7118 (2*10^103161-17)/3 103161 Serge Batalov 11/2022 7119 18^82178-4481 103156 Enzo Doria 03/2013 7120 2^342665-17349 103153 Enzo Doria 05/2013 7121 30408^2467+2467^30408 103150 Hans Havermann 09/2020 7122 (5^147571-3^147571)/2 103148 Kellen Shenton 05/2022 7123 (2^342615+3090)/2 103138 Stefano Morozzi 09/2020 7124 2^342612+175 103137 Lelio R Paula 08/2011 7125 5*2^342585-3 103130 Lelio R Paula 09/2014 7126 (16*10^103127+77)/3 103128 Robert Price 03/2019 7127 (2^342527+3774)/2 103111 Stefano Morozzi 02/2021 7128 2^342503-19209 103104 Enzo Doria 05/2013 7129 (2^342484+2586)/2 103098 Stefano Morozzi 09/2020 7130 2^342476+51 103096 Lelio R Paula 08/2011 7131 2^342460-18885 103091 Enzo Doria 05/2013 7132 (2^342442+862)/2 103086 Stefano Morozzi 02/2021 7133 (194*10^103074-17)/3 103076 Robert Price 09/2020 7134 7^121968+82 103075 Lelio R Paula 10/2016 7135 2^342392-108863 103071 Enzo Doria 03/2014 7136 (2^342389+806)/2 103070 Stefano Morozzi 01/2021 7137 3^216014+28 103065 Lelio R Paula 11/2016 7138 2^342353-108879 103059 Enzo Doria 03/2014 7139 10^103055+276081 103056 Patrick De Geest 12/2016 7140 10^103055-53 103055 Lelio R Paula 11/2016 7141 (58*10^103046+419)/9 103047 Robert Price 05/2019 7142 7^121933+4 103046 Lelio R Paula 11/2014 7143 (71*10^103028-143)/9 103029 Robert Price 10/2021 7144 (2^342235+3618)/2 103023 Stefano Morozzi 09/2020 7145 19^80560-68 103017 Lelio R Paula 10/2016 7146 2^342209+76607 103016 Enzo Doria 05/2016 7148 328^40945+40945^328 103013 Norbert Schneider 12/2014 7147 12^95454-91 103013 Lelio R Paula 10/2016 7149 25833^9716+9716^25833 103009 Hans Havermann 01/2019 7150 (893*10^103004+7)/9 103006 Robert Price 06/2021 7151 (1475^32503-1)/1474 102993 Serge Batalov 06/2022 7152 65^56809-64^56809 102990 Robert Price 08/2013 7153 5^147338-6 102985 Lelio R Paula 11/2014 7154 2^342084-112739 102978 Enzo Doria 06/2014 7155 9*6^132330+7 102974 Lelio R Paula 11/2014 7156 2^342034-16737 102963 Enzo Doria 05/2013 7157 (9787*2^342011-1)/25 102959 Lelio R Paula 05/2015 7158 (3^215802-5)/124343756 102956 Lelio R Paula 12/2013 7159 2^341991-17421 102950 Enzo Doria 05/2013 7160 2^341969-112225 102943 Enzo Doria 06/2014 7161 (9787*2^341864-1)/3 102915 Lelio R Paula 05/2015 7162 2^341859+1869413 102910 Enzo Doria 05/2016 7163 10^102909+61 102910 Lelio R Paula 11/2016 7164 10^102909-67049 102909 Patrick De Geest 12/2016 7165 23814^20935+20935^23814 102898 Hans Havermann 02/2019 7166 28345^4264+4264^28345 102888 Hans Havermann 02/2019 7167 25665^10204+10204^25665 102886 Hans Havermann 02/2019 7168 26288^8181+8181^26288 102860 Hans Havermann 02/2019 7169 2^341659+1836773 102850 Enzo Doria 03/2016 7170 2^341608-110639 102835 Enzo Doria 05/2014 7171 10^102824+49 102825 Lelio R Paula 11/2016 7172 10^102824-168011 102824 Patrick De Geest 12/2016 7173 11^98708-8 102794 Lelio R Paula 10/2016 7174 2^341466+4429 102792 Lelio R Paula 09/2011 7175 2^341460-107 102790 Lelio R Paula 08/2011 7176 (2^341388+47)/21014943 102761 Lelio R Paula 12/2013 7177 2^341355+21 102759 Lelio R Paula 08/2011 7178 (6496^26947-1)/6495 102736 Serge Batalov 06/2022 7179 2^341246+40755 102726 Lelio R Paula 11/2016 7180 (2^341256-5)/991699 102723 Lelio R Paula 12/2013 7181 7^121547+78 102720 Lelio R Paula 10/2016 7182 2^341223-461197 102719 Enzo Doria 06/2015 7183 27838^4893+4893^27838 102711 Hans Havermann 03/2019 7185 2^341190-20577 102709 Enzo Doria 06/2013 7184 (27*2^341212+1)/84674449 102709 Lelio R Paula 12/2013 7186 (25*10^102698+77)/3 102699 Robert Price 09/2022 7187 6^131976-65 102698 Lelio R Paula 10/2016 7188 2^341134+2533 102692 Henri Lifchitz 09/2005 7189 13^92184-54 102688 Lelio R Paula 10/2016 7190 2^341116-20873 102687 Enzo Doria 06/2013 7191 2^341094-19953 102680 Enzo Doria 06/2013 7192 23761^20950+20950^23761 102676 Hans Havermann 03/2019 7194 2^341053+129 102668 Lelio R Paula 08/2011 7193 (4724^27943-1)/4723 102668 Serge Batalov 06/2022 7196 (31*2^341006-1)/3 102655 Lelio R Paula 03/2014 7195 7^121471+94 102655 Lelio R Paula 10/2016 7198 2^341004-173 102653 Lelio R Paula 08/2011 7197 20^78901+3 102653 Lelio R Paula 10/2016 7199 (2^341001+1674)/2 102652 Stefano Morozzi 09/2020 7200 5^146853-52 102646 Lelio R Paula 10/2016 7201 2^340969-216931 102642 Enzo Doria 05/2014 7202 122^49196+121 102641 Norbert Schneider 10/2018 7203 2^340952+1870021 102637 Enzo Doria 05/2016 7204 5*2^340940-3 102634 Lelio R Paula 08/2014 7205 (6^131891+1)/7 102631 Paul Bourdelais 01/2010 7206 (11*10^102629-23)/3 102630 Robert Price 09/2021 7207 3^215094+5*2^215094 102626 Jon Grantham 08/2023 7208 25876^9239+9239^25876 102615 Hans Havermann 02/2019 7209 (4*10^102612+83)/3 102613 Robert Price 02/2018 7210 75^54717+74 102598 Norbert Schneider 01/2015 7211 (17*10^102597+13)/3 102598 Robert Price 01/2019 7212 2^340806-20393 102593 Enzo Doria 06/2013 7213 (2^340790+5)/138267 102583 Lelio R Paula 12/2013 7214 6^131821+77 102577 Lelio R Paula 10/2016 7215 (203*10^102561-11)/3 102563 Robert Price 12/2020 7216 2^340688-29 102558 Henri Lifchitz 05/2005 7217 2^340685-109101 102557 Enzo Doria 04/2014 7218 65^56567-64 102552 Norbert Schneider 11/2014 7219 26230^8121+8121^26230 102550 Hans Havermann 03/2019 7220 (64*10^102547+161)/9 102548 Robert Price 08/2022 7221 (8*10^102541+49)/3 102542 Robert Price 05/2020 7222 (536*10^102533-23)/9 102535 Robert Price 02/2020 7223 2^340547-108897 102515 Enzo Doria 03/2014 7224 (2^340536+778)/2 102512 Stefano Morozzi 09/2020 7225 25592^10119+10119^25592 102500 Hans Havermann 02/2019 7226 (5*10^102492-23)/9 102492 Serge Batalov 11/2022 7227 7^121268+82 102484 Lelio R Paula 10/2016 7228 (6883*2^340443-1)/162401 102483 Lelio R Paula 05/2015 7229 2^340434-5955 102481 Lelio R Paula 11/2016 7230 (7*10^102480-19)/3 102481 Robert Price 10/2020 7231 (2^340381+47)/7 102465 Lelio R Paula 12/2013 7232 111^50095+110 102461 Norbert Schneider 04/2017 7233 2^340291-20301 102438 Enzo Doria 06/2013 7234 12^94915+89 102431 Lelio R Paula 10/2016 7235 (106*10^102422+17)/3 102424 Robert Price 04/2021 7236 24466^15349+15349^24466 102417 Hans Havermann 03/2019 7237 2^340212+111546435 102415 Paul Bourdelais 10/2021 7238 2^340208-20373 102413 Enzo Doria 06/2013 7239 6^131598-17273 102404 Enzo Doria 02/2013 7240 (2^340132+1182)/2 102390 Stefano Morozzi 09/2020 7241 (2^340133+1166)/2 102390 Stefano Morozzi 09/2020 7242 2^340115-21181 102385 Enzo Doria 06/2013 7243 (55459*2^340090+1)/1591 102379 Lelio R Paula 07/2014 7244 (2^340064+3630)/2 102370 Stefano Morozzi 09/2020 7245 9348*31^68638+13 102369 Eric Chen 04/2024 7246 89^52511-88^52511 102365 Robert Price 06/2015 7247 3^214539-112756 102362 Enzo Doria 07/2014 7248 23159^23450-23450^23159 102353 Norbert Schneider 12/2019 7249 2^340000-19877 102351 Enzo Doria 06/2013 7250 2^339990-114845 102348 Enzo Doria 05/2015

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 27 2024 13:30 (Time in France)

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