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 ? |
7001 | 18^85619-95 | 107476 | Lelio R Paula | 04/2017 |
7002 | (2^357013+2526)/2 | 107472 | Stefano Morozzi | 09/2020 |
7003 | 3^225248-130 | 107471 | Lelio R Paula | 03/2017 |
7004 | (5*2^356961+1)/143 | 107455 | Lelio R Paula | 03/2014 |
7005 | 27029^9448+9448^27029 | 107450 | Hans Havermann | 11/2020 |
7006 | 2^356935-18085 | 107449 | Enzo Doria | 05/2013 |
7007 | 55396^87+87^55396 | 107442 | Hans Havermann | 10/2020 |
7008 | (14*10^107439-137)/3 | 107440 | Robert Price | 04/2021 |
7009 | 164^48505-48505^164 | 107432 | Norman Luhn | 09/2024 |
7010 | 10^107409+37 | 107410 | Lelio R Paula | 02/2017 |
7011 | 10^107409-329633 | 107409 | Patrick De Geest | 03/2017 |
7012 | (2^356799+3134)/2 | 107407 | Stefano Morozzi | 09/2020 |
7013 | 2^356787-109027 | 107404 | Enzo Doria | 04/2014 |
7014 | (2^356767+78557)/5 | 107397 | Lelio R Paula | 12/2013 |
7015 | 3*10^107389+77 | 107390 | Robert Price | 09/2018 |
7016 | (11*10^107385+61)/9 | 107386 | Tyler Busby | 01/2023 |
7017 | 5^153622-42 | 107378 | Lelio R Paula | 02/2017 |
7018 | 2^356699-97305 | 107378 | Lelio R Paula | 03/2017 |
7019 | 13129^26072-26072^13129 | 107371 | Norbert Schneider | 09/2022 |
7020 | 2^356654+85 | 107364 | Lelio R Paula | 11/2011 |
7021 | 2^356641-19921 | 107360 | Enzo Doria | 06/2013 |
7022 | 5*10^107355+11 | 107356 | Robert Price | 08/2019 |
7023 | 2^356623-465 | 107355 | Lelio R Paula | 03/2017 |
7024 | 19^83945-92 | 107345 | Lelio R Paula | 02/2017 |
7025 | 25491^16246+16246^25491 | 107337 | Hans Havermann | 11/2020 |
7026 | 10^107334+28149 | 107335 | Patrick De Geest | 03/2017 |
7027 | 10^107334-83 | 107334 | Lelio R Paula | 02/2017 |
7028 | 2^356518+885 | 107323 | Lelio R Paula | 03/2017 |
7029 | (59*10^107322+391)/9 | 107323 | Robert Price | 03/2021 |
7030 | (3*2^356506-1)/467 | 107317 | Lelio R Paula | 03/2014 |
7031 | (2^356468+1162)/2 | 107308 | Stefano Morozzi | 09/2020 |
7032 | 2^356442-114713 | 107300 | Enzo Doria | 04/2015 |
7033 | 2^356425+72257 | 107295 | Enzo Doria | 04/2016 |
7034 | 2^356351-112237 | 107273 | Enzo Doria | 06/2014 |
7036 | (6^137845-11)/5 | 107264 | Paul Bourdelais | 11/2011 |
7035 | 2^356322+74539 | 107264 | Enzo Doria | 04/2016 |
7037 | 2^356274+1874479 | 107250 | Enzo Doria | 06/2016 |
7038 | 24606^22819+22819^24606 | 107241 | Hans Havermann | 10/2020 |
7039 | (2^356243+3686)/2 | 107240 | Stefano Morozzi | 09/2020 |
7040 | 20^82422-93 | 107234 | Lelio R Paula | 02/2017 |
7041 | 2^356157-20365 | 107214 | Enzo Doria | 06/2013 |
7042 | 8*10^107209+99 | 107210 | Robert Price | 03/2021 |
7043 | 2^356129-18949 | 107206 | Enzo Doria | 05/2013 |
7044 | 2^356100-109587 | 107197 | Enzo Doria | 04/2014 |
7045 | 2*10^107173-37 | 107174 | Robert Price | 11/2021 |
7046 | (2^355978+3262)/2 | 107160 | Stefano Morozzi | 02/2021 |
7047 | (31*2^355970+1)/5 | 107159 | Lelio R Paula | 03/2014 |
7048 | 2^355968-64875 | 107158 | Lelio R Paula | 01/2017 |
7049 | 2^355952+1870321 | 107153 | Enzo Doria | 05/2016 |
7050 | 27069^9088+9088^27069 | 107152 | Hans Havermann | 11/2020 |
7051 | 2^355915-117 | 107142 | Lelio R Paula | 11/2011 |
7052 | (16*10^107140+77)/3 | 107141 | Robert Price | 03/2019 |
7053 | 24628^22369+22369^24628 | 107124 | Hans Havermann | 11/2020 |
7054 | (19*2^355838-1)/15 | 107119 | Lelio R Paula | 03/2014 |
7055 | 3^224495-8 | 107112 | Lelio R Paula | 12/2013 |
7056 | 3*10^107096+23 | 107097 | Robert Price | 03/2022 |
7057 | 25077^18632+18632^25077 | 107086 | Hans Havermann | 10/2020 |
7058 | 7^126691-44 | 107067 | Lelio R Paula | 03/2017 |
7059 | 4^177830-8243 | 107065 | Mike Oakes | 02/2011 |
7060 | (509*10^107057+13)/9 | 107059 | Robert Price | 05/2022 |
7061 | 2^355604+214051 | 107048 | Enzo Doria | 10/2023 |
7062 | (2^355562+1702)/2 | 107035 | Stefano Morozzi | 09/2020 |
7063 | 10^107028+3593037 | 107029 | Paul Bourdelais | 10/2021 |
7064 | 10^107028-43301 | 107028 | Alfred Reich | 08/2024 |
7065 | 2^355524-21237 | 107024 | Enzo Doria | 06/2013 |
7067 | (10223*2^355515+1)/4855 | 107022 | Lelio R Paula | 07/2014 |
7066 | 24843^20320+20320^24843 | 107022 | Hans Havermann | 10/2020 |
7068 | 2^355494-19901 | 107015 | Enzo Doria | 06/2013 |
7069 | 2^355454-869688105 | 107003 | Lelio R Paula | 01/2017 |
7070 | 4*10^106997+13 | 106998 | Robert Price | 02/2021 |
7071 | (8*10^106985-629)/9 | 106985 | Robert Price | 01/2022 |
7072 | 2^355366+54615 | 106976 | Lelio R Paula | 01/2017 |
7073 | (31*2^355346-1)/1563 | 106969 | Lelio R Paula | 03/2014 |
7074 | 2^355275-19861 | 106949 | Enzo Doria | 06/2013 |
7075 | 27503^7738+7738^27503 | 106949 | Hans Havermann | 11/2020 |
7076 | (85*10^106943+77)/9 | 106944 | Robert Price | 07/2022 |
7077 | (9179*2^355234-1)/1915 | 106937 | Lelio R Paula | 05/2015 |
7078 | 4*10^106914-93 | 106915 | Robert Price | 07/2020 |
7079 | 4*10^106892-3 | 106893 | Robert Price | 10/2015 |
7080 | (66^58741+1)/67 | 106881 | Paul Bourdelais | 08/2017 |
7081 | 2^355001+335931 | 106866 | Enzo Doria | 08/2024 |
7082 | 2^354946-3 | 106850 | M. Frind & P. Underwood | 08/2002 |
7083 | (2^354945+3134)/2 | 106849 | Stefano Morozzi | 09/2020 |
7084 | (46^64384+1)/(46^128+1) | 106843 | Martin Hopf | 12/2023 |
7085 | 2^354873-18693 | 106828 | Enzo Doria | 05/2013 |
7086 | (2^354831+3186)/2 | 106815 | Stefano Morozzi | 09/2020 |
7088 | 2^354828+4257 | 106814 | Lelio R Paula | 01/2017 |
7087 | 25216^17217+17217^25216 | 106814 | Hans Havermann | 10/2020 |
7089 | (2^354799+1218)/2 | 106805 | Stefano Morozzi | 09/2020 |
7090 | 436^40459+40459^436 | 106791 | Norbert Schneider | 03/2019 |
7091 | (21^80761+1)/22 | 106783 | Paul Bourdelais | 03/2010 |
7092 | (115*10^106772-7)/9 | 106774 | Robert Price | 02/2020 |
7093 | 2^354640-354640+1 | 106758 | Robert Price | 10/2014 |
7094 | (2^354603+2606)/2 | 106746 | Stefano Morozzi | 09/2020 |
7095 | 2^354585+95 | 106741 | Lelio R Paula | 10/2011 |
7096 | (206*10^106737+1)/9 | 106739 | Robert Price | 04/2022 |
7097 | 2^354553+189 | 106732 | Lelio R Paula | 10/2011 |
7099 | (2^354546+1338)/2 | 106729 | Stefano Morozzi | 02/2021 |
7098 | (8*10^106729-71)/9 | 106729 | Serge Batalov | 11/2022 |
7100 | 2^354514-109031 | 106720 | Enzo Doria | 04/2014 |
7101 | 2^354509-109465 | 106718 | Enzo Doria | 04/2014 |
7102 | fibonacci(510628)+2 | 106715 | Jon Grantham | 08/2023 |
7103 | (15*2^354478-1)/26983 | 106706 | Lelio R Paula | 03/2014 |
7104 | Phi(217618,10)/899798636917 | 106693 | Makoto Kamada | 06/2019 |
7105 | 15^90710+28 | 106684 | Lelio R Paula | 04/2017 |
7106 | 7^126237+34 | 106683 | Lelio R Paula | 03/2017 |
7107 | 2^354385-115315 | 106681 | Enzo Doria | 06/2015 |
7108 | 2^354327-19305 | 106664 | Enzo Doria | 06/2013 |
7109 | (35*10^106649+1)/9 | 106650 | Serge Batalov | 11/2010 |
7110 | 10^106636+97 | 106637 | Lelio R Paula | 02/2017 |
7111 | 10^106636-22923 | 106636 | Patrick De Geest | 03/2017 |
7112 | 2^354220-57 | 106631 | Lelio R Paula | 10/2011 |
7113 | (68*10^106628-329)/9 | 106629 | Robert Price | 03/2021 |
7114 | (29*10^106620-77)/3 | 106621 | Robert Price | 02/2020 |
7115 | (746*10^106618+1)/9 | 106620 | Robert Price | 03/2020 |
7116 | 2*10^106613+29 | 106614 | Robert Price | 02/2021 |
7117 | 2^354157-17041 | 106612 | Enzo Doria | 05/2013 |
7118 | 12^98778+73 | 106600 | Lelio R Paula | 02/2017 |
7119 | 33333^1576+1576^33333 | 106585 | Hans Havermann | 11/2020 |
7120 | 2^354064+1870651 | 106584 | Enzo Doria | 05/2016 |
7121 | 24568^21779+21779^24568 | 106577 | Hans Havermann | 11/2020 |
7122 | 2^353992-57 | 106563 | Lelio R Paula | 10/2011 |
7123 | 9*10^106559+59 | 106560 | Robert Price | 01/2020 |
7124 | 7*10^106553+27 | 106554 | Robert Price | 11/2020 |
7125 | 28847^4938+4938^28847 | 106548 | Hans Havermann | 10/2020 |
7126 | NSW(139160) | 106535 | Robert Price | 12/2018 |
7127 | f(278321) | 106535 | Robert Price | 07/2023 |
7128 | (7*10^106516+113)/3 | 106517 | Robert Price | 02/2018 |
7129 | 2^353832-1853849 | 106515 | Enzo Doria | 09/2015 |
7130 | (7^126037-1)/6 | 106513 | Paul Bourdelais | 09/2008 |
7131 | 2^353794-18453 | 106503 | Enzo Doria | 05/2013 |
7132 | (2^353761+2094)/2 | 106493 | Stefano Morozzi | 09/2020 |
7133 | 2^353728+7695 | 106483 | Lelio R Paula | 01/2017 |
7134 | 26476^10509+10509^26476 | 106475 | Hans Havermann | 10/2020 |
7135 | 2^353672-303 | 106466 | Yves Minet | 02/2012 |
7136 | 6^136811+101 | 106460 | Lelio R Paula | 02/2017 |
7137 | 2^353641+1871981 | 106457 | Enzo Doria | 05/2016 |
7138 | (8*10^106454-29)/3 | 106455 | Robert Price | 07/2018 |
7139 | 27845^6654+6654^27845 | 106454 | Hans Havermann | 11/2020 |
7140 | 10^106449-700001 | 106449 | Robert Price | 08/2021 |
7141 | 25316^16017+16017^25316 | 106444 | Hans Havermann | 11/2020 |
7142 | 2^353553+54615 | 106431 | Lelio R Paula | 01/2017 |
7143 | 2^353544-18897 | 106428 | Enzo Doria | 05/2013 |
7144 | 28894^4823+4823^28894 | 106426 | Hans Havermann | 11/2020 |
7145 | (19*10^106422+29)/3 | 106423 | Robert Price | 12/2021 |
7146 | (694*10^106418+53)/9 | 106420 | Robert Price | 02/2022 |
7147 | 6*10^106412-13 | 106413 | Robert Price | 07/2022 |
7148 | 25696^13829+13829^25696 | 106402 | Hans Havermann | 11/2020 |
7149 | 6^136729-133 | 106396 | Lelio R Paula | 02/2017 |
7150 | 2^353418+1605 | 106390 | Lelio R Paula | 01/2017 |
7151 | 2^353387+65 | 106381 | Lelio R Paula | 10/2011 |
7152 | 2^353372+74311 | 106376 | Enzo Doria | 04/2016 |
7153 | 2^353344-3693 | 106368 | Yves Minet | 03/2017 |
7154 | (772*10^106365-7)/9 | 106367 | Robert Price | 06/2022 |
7155 | (56*10^106351+619)/9 | 106352 | Robert Price | 05/2021 |
7156 | 2^353277-20089 | 106347 | Enzo Doria | 06/2013 |
7157 | 2^353275+72173 | 106347 | Enzo Doria | 04/2016 |
7158 | 2^353268-17705 | 106345 | Enzo Doria | 05/2013 |
7159 | 2^353267-19857 | 106344 | Enzo Doria | 06/2013 |
7160 | (46*10^106343+143)/9 | 106344 | Robert Price | 01/2019 |
7161 | (2^353189+3054)/2 | 106321 | Stefano Morozzi | 09/2020 |
7162 | 35087^1072+1072^35087 | 106321 | Hans Havermann | 10/2020 |
7163 | (2^353184+1290)/2 | 106319 | Stefano Morozzi | 01/2021 |
7164 | F(508799)/24738824977/1990778864897 | 106310 | Serge Batalov | 07/2024 |
7165 | 26985^8684+8684^26985 | 106287 | Hans Havermann | 10/2020 |
7166 | (2^353051+606)/2 | 106279 | Stefano Morozzi | 09/2020 |
7168 | 222748^3+3^222748 | 106278 | Anatoly F. Selevich | 12/2010 |
7167 | (46*10^106277+107)/9 | 106278 | Robert Price | 06/2022 |
7169 | (9179*2^353019-1)/9 | 106273 | Lelio R Paula | 05/2015 |
7170 | 2^353025+72257 | 106272 | Enzo Doria | 04/2016 |
7173 | 2^352932-20345 | 106244 | Enzo Doria | 06/2013 |
7171 | (2^353011-3)/745325861246794515484535 | 106244 | Lelio R Paula | 12/2013 |
7172 | 25628^13983+13983^25628 | 106244 | Hans Havermann | 10/2020 |
7174 | 2^352883-187 | 106229 | Lelio R Paula | 10/2011 |
7175 | 20^81649-19^81649 | 106228 | Jean-Louis Charton | 03/2011 |
7176 | (55*10^106222+377)/9 | 106223 | Robert Price | 02/2019 |
7177 | 2^352814-131 | 106208 | Lelio R Paula | 10/2011 |
7178 | 2^352752+73951 | 106189 | Enzo Doria | 04/2016 |
7179 | 11876*25^75945+357 | 106171 | Eric Chen | 10/2023 |
7180 | 6^136434+5 | 106167 | Lelio R Paula | 11/2014 |
7181 | 25296^15737+15737^25296 | 106166 | Hans Havermann | 09/2020 |
7182 | 8*10^106157-13 | 106158 | Robert Price | 08/2019 |
7183 | 2^352641+225677 | 106156 | Enzo Doria | 08/2024 |
7184 | 7*5^151872-8 | 106155 | Lelio R Paula | 11/2014 |
7185 | 105^52520-2 | 106153 | Lelio R Paula | 10/2017 |
7186 | (23*10^106152-29)/3 | 106153 | Robert Price | 03/2022 |
7187 | 2^352601-1604809 | 106144 | Enzo Doria | 05/2015 |
7188 | 12^98353-43 | 106141 | Lelio R Paula | 02/2017 |
7189 | 2^352585-18901 | 106139 | Enzo Doria | 05/2013 |
7190 | 26363^10614+10614^26363 | 106135 | Hans Havermann | 09/2020 |
7191 | (2^352554-3)/193 | 106128 | Lelio R Paula | 12/2013 |
7192 | 2^352540+15015 | 106126 | Lelio R Paula | 01/2017 |
7193 | 25068^17119+17119^25068 | 106125 | Hans Havermann | 09/2020 |
7194 | 2^352524-3149 | 106121 | Yves Minet | 10/2014 |
7195 | (7*10^106119-67)/3 | 106120 | Robert Price | 10/2021 |
7196 | 2^352486-1858781 | 106109 | Enzo Doria | 04/2016 |
7197 | 2^352444+12705 | 106097 | Lelio R Paula | 01/2017 |
7198 | 28561^5182+5182^28561 | 106090 | Hans Havermann | 10/2020 |
7199 | (182*10^106083+43)/9 | 106085 | Robert Price | 02/2020 |
7200 | (266*10^106066+1)/3 | 106068 | Robert Price | 04/2020 |
7201 | (7*10^106066-187)/9 | 106066 | Tyler Busby | 01/2023 |
7202 | 2^352228-18953 | 106032 | Enzo Doria | 05/2013 |
7203 | (2^352223+1118)/2 | 106030 | Stefano Morozzi | 09/2020 |
7204 | (2^352212+2250)/2 | 106027 | Stefano Morozzi | 01/2021 |
7205 | (2^352136+2638)/2 | 106004 | Stefano Morozzi | 09/2020 |
7206 | 2^352107+1872533 | 105995 | Enzo Doria | 05/2016 |
7207 | (2^352096+2086)/2 | 105992 | Stefano Morozzi | 09/2020 |
7208 | 2^352066-2591 | 105983 | Yves Minet | 07/2014 |
7209 | 2^352030+715 | 105972 | Lelio R Paula | 10/2011 |
7210 | 9*6^136176-5 | 105967 | Lelio R Paula | 11/2014 |
7211 | 17099*2^351991+58329 | 105965 | Paul Vanderveen | 12/2017 |
7212 | 122^50789-50789^122 | 105965 | Norman Luhn | 09/2024 |
7213 | 28582^5097+5097^28582 | 105963 | Hans Havermann | 09/2020 |
7214 | 155^48377+2 | 105962 | Lelio R Paula | 08/2013 |
7215 | (23*10^105944-119)/3 | 105945 | Robert Price | 07/2021 |
7216 | 2^351865+1869707 | 105922 | Enzo Doria | 05/2016 |
7217 | 24974^17427+17427^24974 | 105921 | Hans Havermann | 09/2020 |
7218 | 25163^16194+16194^25163 | 105920 | Hans Havermann | 09/2020 |
7219 | 2^351831+23 | 105912 | Lelio R Paula | 10/2011 |
7220 | (2^351818+3798)/2 | 105908 | Stefano Morozzi | 02/2021 |
7221 | 9*2^351784-5 | 105899 | Lelio R Paula | 09/2014 |
7222 | (2^351776+2766)/2 | 105895 | Stefano Morozzi | 01/2021 |
7223 | (85*10^105881+203)/9 | 105882 | Robert Price | 09/2020 |
7224 | 2^351671-112387 | 105864 | Enzo Doria | 06/2014 |
7225 | 2^351669-109501 | 105863 | Enzo Doria | 04/2014 |
7226 | 2^351644+74731 | 105856 | Enzo Doria | 04/2016 |
7227 | 13^95025-42 | 105853 | Lelio R Paula | 12/2016 |
7228 | 2^351599+15015 | 105842 | Lelio R Paula | 01/2017 |
7229 | 19^82763+90 | 105834 | Lelio R Paula | 01/2017 |
7230 | (205*10^105831-1)/3 | 105833 | Robert Price | 11/2021 |
7231 | 26050^11551+11551^26050 | 105832 | Hans Havermann | 09/2020 |
7232 | (9179*2^351540-1)/221 | 105826 | Lelio R Paula | 05/2015 |
7233 | 20^81329-51 | 105812 | Lelio R Paula | 01/2017 |
7234 | (5*10^105811+211)/9 | 105811 | Robert Price | 02/2018 |
7235 | 2^351483+28425 | 105807 | Lelio R Paula | 01/2017 |
7236 | 25231^15610+15610^25231 | 105804 | Hans Havermann | 09/2020 |
7237 | 15^89960+86 | 105802 | Lelio R Paula | 02/2017 |
7238 | 2^351460-17289 | 105801 | Enzo Doria | 05/2013 |
7239 | 19^82735+22 | 105798 | Lelio R Paula | 01/2017 |
7240 | 2^351435-109077 | 105793 | Enzo Doria | 04/2014 |
7241 | 2^351393+1089 | 105780 | Lelio R Paula | 01/2017 |
7242 | 2^351364+72631 | 105772 | Enzo Doria | 04/2016 |
7243 | (2^351333+3626)/2 | 105762 | Stefano Morozzi | 09/2020 |
7244 | 26818^8783+8783^26818 | 105761 | Hans Havermann | 09/2020 |
7247 | 2^351305+1872467 | 105754 | Enzo Doria | 05/2016 |
7246 | 3^221649+16 | 105754 | Lelio R Paula | 11/2016 |
7245 | 32511^1790+1790^32511 | 105754 | Hans Havermann | 09/2020 |
7248 | 8*3^221637-5 | 105749 | Lelio R Paula | 09/2014 |
7249 | 2^351279-2780449 | 105746 | Enzo Doria | 03/2016 |
7250 | (2^351263+3198)/2 | 105741 | Stefano Morozzi | 09/2020 |