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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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
7002 | 2^341190-20577 | 102709 | Enzo Doria | 06/2013 |
7001 | (27*2^341212+1)/84674449 | 102709 | Lelio R Paula | 12/2013 |
7003 | (25*10^102698+77)/3 | 102699 | Robert Price | 09/2022 |
7004 | 6^131976-65 | 102698 | Lelio R Paula | 10/2016 |
7005 | 2^341134+2533 | 102692 | Henri Lifchitz | 09/2005 |
7006 | 13^92184-54 | 102688 | Lelio R Paula | 10/2016 |
7007 | 2^341116-20873 | 102687 | Enzo Doria | 06/2013 |
7008 | 2^341094-19953 | 102680 | Enzo Doria | 06/2013 |
7009 | 23761^20950+20950^23761 | 102676 | Hans Havermann | 03/2019 |
7011 | 2^341053+129 | 102668 | Lelio R Paula | 08/2011 |
7010 | (4724^27943-1)/4723 | 102668 | Serge Batalov | 06/2022 |
7013 | (31*2^341006-1)/3 | 102655 | Lelio R Paula | 03/2014 |
7012 | 7^121471+94 | 102655 | Lelio R Paula | 10/2016 |
7015 | 2^341004-173 | 102653 | Lelio R Paula | 08/2011 |
7014 | 20^78901+3 | 102653 | Lelio R Paula | 10/2016 |
7016 | (2^341001+1674)/2 | 102652 | Stefano Morozzi | 09/2020 |
7017 | 5^146853-52 | 102646 | Lelio R Paula | 10/2016 |
7018 | 2^340969-216931 | 102642 | Enzo Doria | 05/2014 |
7019 | 122^49196+121 | 102641 | Norbert Schneider | 10/2018 |
7020 | 2^340952+1870021 | 102637 | Enzo Doria | 05/2016 |
7021 | 5*2^340940-3 | 102634 | Lelio R Paula | 08/2014 |
7022 | (6^131891+1)/7 | 102631 | Paul Bourdelais | 01/2010 |
7023 | (11*10^102629-23)/3 | 102630 | Robert Price | 09/2021 |
7024 | 3^215094+5*2^215094 | 102626 | Jon Grantham | 08/2023 |
7025 | 25876^9239+9239^25876 | 102615 | Hans Havermann | 02/2019 |
7026 | (4*10^102612+83)/3 | 102613 | Robert Price | 02/2018 |
7027 | 75^54717+74 | 102598 | Norbert Schneider | 01/2015 |
7028 | (17*10^102597+13)/3 | 102598 | Robert Price | 01/2019 |
7029 | 2^340806-20393 | 102593 | Enzo Doria | 06/2013 |
7030 | (2^340790+5)/138267 | 102583 | Lelio R Paula | 12/2013 |
7031 | 6^131821+77 | 102577 | Lelio R Paula | 10/2016 |
7032 | (203*10^102561-11)/3 | 102563 | Robert Price | 12/2020 |
7033 | 2^340688-29 | 102558 | Henri Lifchitz | 05/2005 |
7034 | 2^340685-109101 | 102557 | Enzo Doria | 04/2014 |
7035 | 65^56567-64 | 102552 | Norbert Schneider | 11/2014 |
7036 | 26230^8121+8121^26230 | 102550 | Hans Havermann | 03/2019 |
7037 | (64*10^102547+161)/9 | 102548 | Robert Price | 08/2022 |
7038 | (8*10^102541+49)/3 | 102542 | Robert Price | 05/2020 |
7039 | (536*10^102533-23)/9 | 102535 | Robert Price | 02/2020 |
7040 | 2^340547-108897 | 102515 | Enzo Doria | 03/2014 |
7041 | (2^340536+778)/2 | 102512 | Stefano Morozzi | 09/2020 |
7042 | 25592^10119+10119^25592 | 102500 | Hans Havermann | 02/2019 |
7043 | (5*10^102492-23)/9 | 102492 | Serge Batalov | 11/2022 |
7044 | 7^121268+82 | 102484 | Lelio R Paula | 10/2016 |
7045 | (6883*2^340443-1)/162401 | 102483 | Lelio R Paula | 05/2015 |
7046 | 2^340434-5955 | 102481 | Lelio R Paula | 11/2016 |
7047 | (7*10^102480-19)/3 | 102481 | Robert Price | 10/2020 |
7048 | (2^340381+47)/7 | 102465 | Lelio R Paula | 12/2013 |
7049 | 111^50095+110 | 102461 | Norbert Schneider | 04/2017 |
7050 | 2^340291-20301 | 102438 | Enzo Doria | 06/2013 |
7051 | 12^94915+89 | 102431 | Lelio R Paula | 10/2016 |
7052 | (106*10^102422+17)/3 | 102424 | Robert Price | 04/2021 |
7053 | 24466^15349+15349^24466 | 102417 | Hans Havermann | 03/2019 |
7054 | 2^340212+111546435 | 102415 | Paul Bourdelais | 10/2021 |
7055 | 2^340208-20373 | 102413 | Enzo Doria | 06/2013 |
7056 | 6^131598-17273 | 102404 | Enzo Doria | 02/2013 |
7057 | (2^340132+1182)/2 | 102390 | Stefano Morozzi | 09/2020 |
7058 | (2^340133+1166)/2 | 102390 | Stefano Morozzi | 09/2020 |
7059 | 2^340115-21181 | 102385 | Enzo Doria | 06/2013 |
7060 | (55459*2^340090+1)/1591 | 102379 | Lelio R Paula | 07/2014 |
7061 | (2^340064+3630)/2 | 102370 | Stefano Morozzi | 09/2020 |
7062 | 89^52511-88^52511 | 102365 | Robert Price | 06/2015 |
7063 | 3^214539-112756 | 102362 | Enzo Doria | 07/2014 |
7064 | 23159^23450-23450^23159 | 102353 | Norbert Schneider | 12/2019 |
7065 | 2^340000-19877 | 102351 | Enzo Doria | 06/2013 |
7066 | 2^339990-114845 | 102348 | Enzo Doria | 05/2015 |
7067 | (3^214516-2)/51383 | 102346 | Lelio R Paula | 12/2013 |
7068 | 20^78661-99 | 102341 | Lelio R Paula | 09/2016 |
7070 | 2^339951-19585 | 102336 | Enzo Doria | 05/2013 |
7069 | (17*10^102335-167)/3 | 102336 | Robert Price | 05/2022 |
7071 | (13*2^339943+1)/45 | 102333 | Lelio R Paula | 12/2013 |
7072 | (236282#+121441)/(121441*25499429) | 102332 | Makoto Morimoto | 08/2020 |
7073 | 5*10^102323-91 | 102324 | Robert Price | 03/2021 |
7075 | 2^339889+29327 | 102317 | Yves Minet | 06/2010 |
7074 | (167*10^102315-17)/3 | 102317 | Robert Price | 03/2020 |
7076 | 26348^7641+7641^26348 | 102314 | Hans Havermann | 03/2019 |
7077 | Phi(239414,10)/6333218543 | 102303 | Makoto Kamada | 08/2019 |
7078 | 2^339834-109493 | 102301 | Enzo Doria | 04/2014 |
7079 | (16*10^102299-19)/3 | 102300 | Robert Price | 02/2019 |
7080 | (11^98221-5^98221)/6 | 102286 | Robert Price | 01/2013 |
7081 | 3^214365+1820 | 102279 | Lelio R Paula | 10/2016 |
7082 | 31978^1579+1579^31978 | 102278 | Hans Havermann | 03/2019 |
7083 | (89*10^102262-467)/9 | 102263 | Robert Price | 04/2022 |
7084 | (11*2^339705-1)/183 | 102261 | Lelio R Paula | 03/2014 |
7085 | 2^339694-16995 | 102259 | Lelio R Paula | 09/2016 |
7086 | (56*10^102255+691)/9 | 102256 | Robert Price | 05/2019 |
7087 | 122^49008+121 | 102249 | Norbert Schneider | 10/2018 |
7088 | (2^339652+3178)/2 | 102246 | Stefano Morozzi | 09/2020 |
7089 | 7^120985-38 | 102245 | Lelio R Paula | 10/2016 |
7090 | 10^102244+122961 | 102245 | Patrick De Geest | 12/2016 |
7091 | 10^102244-27 | 102244 | Lelio R Paula | 09/2016 |
7092 | 7^120982-62 | 102242 | Lelio R Paula | 10/2016 |
7093 | (2^339640+2670)/2 | 102242 | Stefano Morozzi | 09/2020 |
7094 | 4*6^131382-5 | 102236 | Lelio R Paula | 11/2014 |
7095 | (2^339607+3290)/2 | 102232 | Stefano Morozzi | 02/2021 |
7096 | 2^339586-1091 | 102226 | Yves Minet | 11/2012 |
7097 | 11^98161-3072000 | 102225 | Enzo Doria | 12/2012 |
7098 | 9*7^120961-4 | 102225 | Lelio R Paula | 11/2014 |
7099 | 5*3^214250+2 | 102224 | Serge Batalov | 10/2010 |
7100 | 12^94713-59 | 102213 | Lelio R Paula | 10/2016 |
7101 | 12^94705+89 | 102204 | Lelio R Paula | 10/2016 |
7102 | 2^339407-177 | 102172 | Lelio R Paula | 08/2011 |
7103 | 4*10^102163-57 | 102164 | Robert Price | 10/2018 |
7104 | 2^339355+65 | 102157 | Lelio R Paula | 07/2011 |
7105 | (28*10^102142-31)/3 | 102143 | Robert Price | 12/2019 |
7106 | (2^339323+47)/880715 | 102141 | Lelio R Paula | 12/2013 |
7107 | (2^339268+1758)/2 | 102130 | Stefano Morozzi | 09/2020 |
7108 | s(178551) | 102122 | Robert Price | 05/2020 |
7109 | (797*10^102112-23)/9 | 102114 | Robert Price | 01/2022 |
7110 | (5*10^102107+7)/3 | 102108 | Tyler Busby | 02/2023 |
7111 | (2^339175+2790)/2 | 102102 | Stefano Morozzi | 02/2021 |
7113 | 2^339168+21 | 102100 | Lelio R Paula | 07/2011 |
7114 | 2^339167-108807 | 102100 | Enzo Doria | 03/2014 |
7112 | (2^339169+42)/2 | 102100 | Stefano Morozzi | 09/2020 |
7115 | 2^339156+163 | 102097 | Lelio R Paula | 08/2011 |
7116 | (2^339149+746)/2 | 102094 | Stefano Morozzi | 09/2020 |
7117 | (25*10^102076-67)/3 | 102077 | Robert Price | 06/2019 |
7118 | 2^339081-4543 | 102074 | Yves Minet | 03/2019 |
7119 | (3435^28867-1)/3434 | 102069 | Serge Batalov | 06/2022 |
7120 | 2*10^102062+77 | 102063 | Robert Price | 08/2020 |
7122 | 24327^15668+15668^24327 | 102053 | Hans Havermann | 02/2019 |
7121 | 10^102052+66793 | 102053 | Patrick De Geest | 09/2022 |
7123 | 10^102052-7000001 | 102052 | Robert Price | 06/2021 |
7124 | 10^102052-618623 | 102052 | Patrick De Geest | 09/2022 |
7125 | 2^339000-175635 | 102050 | Stefano Morozzi | 12/2021 |
7126 | 2^339000-151667 | 102050 | Stefano Morozzi | 12/2021 |
7127 | 2^338999+79289 | 102049 | Stefano Morozzi | 01/2022 |
7128 | 2^338998-63897 | 102049 | Stefano Morozzi | 12/2022 |
7129 | 2^338997+99659 | 102049 | Stefano Morozzi | 02/2023 |
7130 | 2^338994+188757 | 102048 | Stefano Morozzi | 05/2022 |
7131 | 2^338995+70785 | 102048 | Stefano Morozzi | 11/2022 |
7132 | 2^338994-12183 | 102048 | Stefano Morozzi | 12/2022 |
7133 | 2^338992+181591 | 102047 | Stefano Morozzi | 01/2022 |
7134 | 2^338992+136171 | 102047 | Stefano Morozzi | 03/2022 |
7135 | 2^338991-109435 | 102047 | Stefano Morozzi | 04/2022 |
7136 | 2^338991+193611 | 102047 | Stefano Morozzi | 09/2022 |
7137 | 2^338988-134619 | 102046 | Stefano Morozzi | 04/2022 |
7138 | 2^338987-62557 | 102046 | Stefano Morozzi | 12/2022 |
7139 | 2^338986-60141 | 102045 | Stefano Morozzi | 06/2022 |
7140 | 2^338986+98209 | 102045 | Stefano Morozzi | 11/2022 |
7141 | 2^338981+106391 | 102044 | Stefano Morozzi | 01/2022 |
7142 | 2^338982+34069 | 102044 | Stefano Morozzi | 03/2022 |
7143 | 2^338982-58781 | 102044 | Stefano Morozzi | 04/2022 |
7144 | 2^338980+70833 | 102044 | Stefano Morozzi | 11/2022 |
7145 | 2^338982-92111 | 102044 | Stefano Morozzi | 02/2023 |
7146 | 2^338977+83007 | 102043 | Stefano Morozzi | 02/2022 |
7147 | 2^338979-83601 | 102043 | Stefano Morozzi | 04/2022 |
7148 | 2^338975+28355 | 102042 | Stefano Morozzi | 01/2022 |
7149 | 2^338973+134619 | 102042 | Stefano Morozzi | 03/2022 |
7150 | 2^338974+183777 | 102042 | Stefano Morozzi | 03/2022 |
7151 | 2^338975+69293 | 102042 | Stefano Morozzi | 09/2022 |
7159 | 25080^11711+11711^25080 | 102041 | Hans Havermann | 02/2019 |
7152 | 2^338972+152343 | 102041 | Stefano Morozzi | 12/2021 |
7153 | 2^338972-180623 | 102041 | Stefano Morozzi | 02/2022 |
7154 | 2^338972+84441 | 102041 | Stefano Morozzi | 03/2022 |
7155 | 2^338971+64875 | 102041 | Stefano Morozzi | 05/2022 |
7156 | 2^338971+44985 | 102041 | Stefano Morozzi | 11/2022 |
7157 | 2^338971+145065 | 102041 | Stefano Morozzi | 11/2022 |
7158 | 2^338972-16635 | 102041 | Stefano Morozzi | 01/2023 |
7160 | 2^338968+53461 | 102040 | Stefano Morozzi | 01/2022 |
7161 | 2^338969+160175 | 102040 | Stefano Morozzi | 03/2022 |
7162 | 2^338967+13409 | 102040 | Stefano Morozzi | 04/2022 |
7163 | 2^338969+67635 | 102040 | Stefano Morozzi | 09/2022 |
7164 | 2^338969-15913 | 102040 | Stefano Morozzi | 01/2023 |
7165 | 2^338963-127455 | 102039 | Stefano Morozzi | 12/2021 |
7166 | 2^338963+132195 | 102039 | Stefano Morozzi | 02/2022 |
7167 | 2^338966+137919 | 102039 | Stefano Morozzi | 04/2022 |
7168 | 2^338963-87529 | 102039 | Stefano Morozzi | 12/2022 |
7169 | 2^338963-116859 | 102039 | Stefano Morozzi | 02/2023 |
7176 | (2^338982-7)/1754517 | 102038 | Lelio R Paula | 12/2013 |
7170 | 2^338960+53935 | 102038 | Stefano Morozzi | 01/2022 |
7171 | 2^338962+83157 | 102038 | Stefano Morozzi | 02/2022 |
7172 | 2^338961+12341 | 102038 | Stefano Morozzi | 04/2022 |
7173 | 2^338960+63933 | 102038 | Stefano Morozzi | 05/2022 |
7174 | 2^338960+170791 | 102038 | Stefano Morozzi | 11/2022 |
7175 | 2^338962+21679 | 102038 | Stefano Morozzi | 11/2022 |
7177 | 2^338959-30919 | 102037 | Stefano Morozzi | 02/2022 |
7178 | 2^338959+164769 | 102037 | Stefano Morozzi | 05/2022 |
7179 | 2^338958-43161 | 102037 | Stefano Morozzi | 02/2023 |
7180 | 2^338954-177003 | 102036 | Stefano Morozzi | 12/2021 |
7181 | 2^338954+154207 | 102036 | Stefano Morozzi | 01/2022 |
7182 | 2^338956+182493 | 102036 | Stefano Morozzi | 02/2022 |
7183 | 2^338954+162715 | 102036 | Stefano Morozzi | 04/2022 |
7184 | 2^338955-158241 | 102036 | Stefano Morozzi | 04/2022 |
7185 | 2^338956-33395 | 102036 | Stefano Morozzi | 04/2022 |
7186 | 2^338954+190915 | 102036 | Stefano Morozzi | 06/2022 |
7187 | 2^338955+41643 | 102036 | Stefano Morozzi | 09/2022 |
7188 | 2^338954+194427 | 102036 | Stefano Morozzi | 09/2022 |
7189 | 2^338956+117967 | 102036 | Stefano Morozzi | 09/2022 |
7190 | 2^338956+195495 | 102036 | Stefano Morozzi | 11/2022 |
7191 | 2^338954-186371 | 102036 | Stefano Morozzi | 12/2022 |
7192 | 2^338950+175077 | 102035 | Stefano Morozzi | 12/2021 |
7193 | 2^338951-51687 | 102035 | Stefano Morozzi | 12/2021 |
7194 | 2^338951+66123 | 102035 | Stefano Morozzi | 06/2022 |
7195 | 2^338950+19317 | 102035 | Stefano Morozzi | 09/2022 |
7196 | 2^338951-161479 | 102035 | Stefano Morozzi | 12/2022 |
7197 | 2^338950-66335 | 102035 | Stefano Morozzi | 01/2023 |
7198 | 2^338951-41611 | 102035 | Stefano Morozzi | 02/2023 |
7199 | 2^338952-142887 | 102035 | Stefano Morozzi | 02/2023 |
7200 | 2^338949+85449 | 102034 | Stefano Morozzi | 03/2022 |
7201 | 2^338949-184585 | 102034 | Stefano Morozzi | 04/2022 |
7202 | 2^338949-88555 | 102034 | Stefano Morozzi | 12/2022 |
7203 | 2^338948+49393 | 102034 | Stefano Morozzi | 02/2023 |
7204 | 2^338949-17601 | 102034 | Stefano Morozzi | 02/2023 |
7205 | 2^338943+127103 | 102033 | Stefano Morozzi | 12/2021 |
7206 | 2^338944-84003 | 102033 | Stefano Morozzi | 04/2022 |
7207 | 2^338945+138605 | 102033 | Stefano Morozzi | 05/2022 |
7208 | 2^338943+95133 | 102033 | Stefano Morozzi | 11/2022 |
7209 | 2^338943+147435 | 102033 | Stefano Morozzi | 11/2022 |
7210 | 2^338943-116067 | 102033 | Stefano Morozzi | 01/2023 |
7211 | 2^338940+78607 | 102032 | Stefano Morozzi | 01/2022 |
7212 | 2^338942-86687 | 102032 | Stefano Morozzi | 12/2022 |
7213 | 2^338939+151569 | 102031 | Stefano Morozzi | 12/2021 |
7214 | 2^338938+183975 | 102031 | Stefano Morozzi | 03/2022 |
7215 | 2^338937-33429 | 102031 | Stefano Morozzi | 04/2022 |
7216 | 2^338939-183259 | 102031 | Stefano Morozzi | 04/2022 |
7217 | 2^338937-139951 | 102031 | Stefano Morozzi | 01/2023 |
7218 | 2^338938-40151 | 102031 | Stefano Morozzi | 01/2023 |
7219 | 2^338938+74449 | 102031 | Stefano Morozzi | 02/2023 |
7220 | 2^338935+179999 | 102030 | Stefano Morozzi | 01/2022 |
7221 | 2^338936+84147 | 102030 | Stefano Morozzi | 03/2022 |
7222 | 2^338935+171261 | 102030 | Stefano Morozzi | 11/2022 |
7223 | 2^338936-41355 | 102030 | Stefano Morozzi | 01/2023 |
7224 | 2^338931+2349 | 102029 | Stefano Morozzi | 12/2021 |
7225 | 2^338933+79935 | 102029 | Stefano Morozzi | 01/2022 |
7226 | 2^338930+33819 | 102029 | Stefano Morozzi | 03/2022 |
7227 | 2^338931-31555 | 102029 | Stefano Morozzi | 03/2022 |
7228 | 2^338933+64169 | 102029 | Stefano Morozzi | 05/2022 |
7229 | 2^338932-184965 | 102029 | Stefano Morozzi | 06/2022 |
7230 | 2^338932+66943 | 102029 | Stefano Morozzi | 09/2022 |
7231 | 2^338932+92995 | 102029 | Stefano Morozzi | 09/2022 |
7232 | 2^338931+97001 | 102029 | Stefano Morozzi | 11/2022 |
7233 | 2^338932-165453 | 102029 | Stefano Morozzi | 01/2023 |
7234 | 2^338933-40899 | 102029 | Stefano Morozzi | 01/2023 |
7235 | 2^338928+2367 | 102028 | Stefano Morozzi | 12/2021 |
7236 | 2^338927+52779 | 102028 | Stefano Morozzi | 01/2022 |
7237 | 2^338927-79539 | 102028 | Stefano Morozzi | 02/2022 |
7238 | 2^338929+60819 | 102028 | Stefano Morozzi | 03/2022 |
7239 | 2^338928-156959 | 102028 | Stefano Morozzi | 03/2022 |
7240 | 2^338927-63919 | 102028 | Stefano Morozzi | 12/2022 |
7241 | 2^338925+106631 | 102027 | Stefano Morozzi | 01/2022 |
7242 | 2^338926+80235 | 102027 | Stefano Morozzi | 01/2022 |
7243 | 2^338926+41607 | 102027 | Stefano Morozzi | 09/2022 |
7244 | 2^338925+195435 | 102027 | Stefano Morozzi | 11/2022 |
7245 | 2^338924-92885 | 102027 | Stefano Morozzi | 02/2023 |
7246 | 2^338922-27291 | 102026 | Stefano Morozzi | 12/2021 |
7247 | 2^338919-103849 | 102025 | Stefano Morozzi | 01/2022 |
7248 | 2^338919+130221 | 102025 | Stefano Morozzi | 01/2022 |
7249 | 2^338918-91967 | 102025 | Stefano Morozzi | 02/2023 |
7250 | 2^338914-79121 | 102024 | Stefano Morozzi | 02/2022 |