PRP Records

Probable Primes Top 10000

(300940 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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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 ?
10012^1078242+1881649324584Enzo Doria11/2016
10022^1077737+1880117324432Enzo Doria10/2016
10033^679017-5*2^679017323974Jon Grantham08/2023
10042^1076006+29539323911Enzo Doria03/2024
10052^1075573+32417323780Enzo Doria05/2024
10062^1075425+1880117323736Enzo Doria10/2016
1007(28^223381+1)/29323267Paul Bourdelais12/2020
100810^322999+187071323000Stefano Morozzi03/2019
100910^322999-143151322999Patrick De Geest05/2020
10102^1072744+32641322929Enzo Doria05/2024
10112^1072146+1886869322749Enzo Doria04/2017
10122^1072118-7321953322740Enzo Doria02/2015
10132025^97561-2024^97561322579Henri Lifchitz01/2025
10142^1071026+1886869322411Enzo Doria04/2017
10152^1070539+1880633322265Enzo Doria10/2016
10162^1069788+26587322039Enzo Doria12/2023
10172^1069293-1147195321890Enzo Doria05/2015
10182^1065968+1880941320889Enzo Doria10/2016
10192^1065897-1147195320867Enzo Doria05/2015
10202^1063427+1882103320124Enzo Doria12/2016
10212^1061095-1061095319422Henri Lifchitz10/2013
10222^1060950+653119319378Enzo Doria12/2016
10232^1060363+782753319202Enzo Doria11/2016
10242^1060028+31771319101Enzo Doria04/2024
1025(71^172259-1)/70318895Paul Bourdelais08/2020
10262^1058425+38507318618Enzo Doria11/2024
1027-30*Bern(85996)/236037521318354Sergey Batalov10/2023
10282^1055665+30407317787Enzo Doria03/2024
10292^1054736+483061317508Enzo Doria12/2016
10302^1053965+1879667317276Enzo Doria10/2016
1031(43^194119-1)/42317086Paul Bourdelais08/2020
10322^1052899+225413316955Enzo Doria08/2024
10332^1052186-458165316740Enzo Doria03/2015
103411^303909+2316489Paul Bourdelais08/2023
10352^1049026+214609315789Enzo Doria11/2023
10362^1048576+69661315653Boyan Hu08/2024
10372^1046613-114685315062Enzo Doria04/2015
10382^1045625-459373314765Enzo Doria06/2015
103910^(2*157363+1)-8*10^157363-1314727Robert Price07/2023
1040(7*10^314564-61)/9314564Erik Branger09/2016
10412^1044771+228023314508Enzo Doria11/2024
10422^1044206+7314338Stefano Morozzi10/2022
1043(7^371669-1)/6314096Paul Bourdelais02/2010
1044(53^181981-1)/52313784Paul Bourdelais08/2020
1045(8^347437-5^347437)/3313767Jon Grantham08/2023
1046(10^313741+1)/11/11294677313733Alfred Reich04/2024
10472^1041944+283051313657Enzo Doria12/2016
1048(1624^97969-1)/(1624^313-1)313533Sergey Batalov11/2023
10492^1041153-114391313419Enzo Doria02/2015
1050(2^1039700+9)/5312981Stefano Morozzi09/2022
1051(74^167311+1)/75312742Paul Bourdelais12/2020
10522^1038871+1866983312732Enzo Doria04/2016
10532^1038545+71657312634Enzo Doria08/2023
1054(55^179573-1)/54312521Paul Bourdelais08/2020
10552^1037647+1881263312363Enzo Doria11/2016
10562^1037226+1879699312237Enzo Doria10/2016
10572^1036867+1865843312129Enzo Doria02/2016
1058(76^165947+1)/77312114Paul Bourdelais01/2021
10592^1036324+39091311965Enzo Doria11/2024
10602^1036020-114539311874Enzo Doria02/2015
1061(90^159463-1)/89311628Paul Bourdelais08/2020
10622^1034546+28819311430Enzo Doria02/2024
10632^1032240+1883431310736Enzo Doria01/2017
106464211^64588+64588^64211310514Norbert Schneider11/2023
10652^1031450+29629310498Enzo Doria03/2024
10662^1030352+1870021310167Enzo Doria06/2016
10672^1030046+1882843310075Enzo Doria11/2016
10682^1029120+227971309796Enzo Doria11/2024
10693^648872+16309591Robert Price04/2020
1070(16976^73441-1)/(16976^271-1)309498Ryan Propper11/2023
107164221^64366+64366^64221309451Norbert Schneider06/2023
1072(11121^76729-1)/(11121^277-1)309336Ryan Propper11/2023
10732^1027478+219259309302Enzo Doria02/2024
10742^1026999+20513309158Enzo Doria07/2023
10755^442281+2309142Paul Bourdelais01/2021
10762^1026204+22741308919Enzo Doria09/2023
10772^1026190+15308914Stefano Morozzi10/2022
10782^1025108+20851308589Enzo Doria08/2023
1079A352736(16)306985Kellen Shenton05/2022
10802^1019777+213947306984Enzo Doria10/2023
1081(11^293831-1)/10305993Paul Bourdelais03/2010
1082(67^167449-1)/66305773Paul Bourdelais08/2020
1083(62^170539+1)/63305671Paul Bourdelais12/2020
10842^1015321-1015321305643Henri Lifchitz08/2013
10852^1014775+27113305478Enzo Doria12/2023
10862^1014450+7305380Stefano Morozzi10/2022
10872^1014336+215731305346Enzo Doria12/2023
10882^1014224-2791229305312Enzo Doria01/2016
1089(10^304986+7)/673304984Alfred Reich11/2021
109065473^45250+45250^65473304818Hans Havermann02/2022
109166012^41423+41423^66012304794Hans Havermann03/2022
109265073^48202+48202^65073304742Hans Havermann04/2022
10932^1012054+31669304659Enzo Doria06/2024
1094238176^19+19^238176304569Hans Havermann03/2022
109573122^14615+14615^73122304539Hans Havermann05/2022
109664492^52639+52639^64492304487Hans Havermann03/2022
109765955^41288+41288^65955304437Hans Havermann04/2022
109871729^17530+17530^71729304403Hans Havermann03/2022
109970170^21733+21733^70170304336Hans Havermann03/2022
11002^1010751-107709304267Enzo Doria03/2014
110184473^3994+3994^84473304222Hans Havermann03/2022
1102(2^1010623-1)/12602017578957977304212Tony Prest / Never Odd Or Even02/2014
110374442^12125+12125^74442303998Hans Havermann02/2022
110477842^8039+8039^77842303989Hans Havermann01/2022
110564209^54140+54140^64209303935Hans Havermann02/2022
11062^1009577+1869587303913Enzo Doria06/2016
110767389^32338+32338^67389303906Hans Havermann02/2022
11088^336419-7^336419303817Jean-Louis Charton01/2008
11092^1009168+15303790Stefano Morozzi10/2022
111080766^5771+5771^80766303782Hans Havermann01/2022
111166094^39385+39385^66094303724Hans Havermann01/2022
111269147^24574+24574^69147303589Hans Havermann02/2022
111378390^7459+7459^78390303580Hans Havermann01/2022
11142^1008301+1869377303529Enzo Doria06/2016
111565008^46615+46615^65008303492Hans Havermann02/2022
1116(2^1007838+5)/3303389Serge Batalov08/2015
111765018^46293+46293^65018303343Hans Havermann01/2022
11186^389756+5303290Paul Bourdelais02/2021
111971016^18649+18649^71016303285Hans Havermann01/2022
11202^1007065+29231303157Enzo Doria03/2024
112180160^6047+6047^80160303129Hans Havermann01/2022
112267434^31237+31237^67434303094Hans Havermann03/2022
112365537^42102+42102^65537303063Hans Havermann02/2022
112471790^16553+16553^71790302874Hans Havermann11/2021
112565208^44129+44129^65208302874Hans Havermann11/2021
112684181^3960+3960^84181302858Hans Havermann11/2021
1127(13703^73441-1)/(13703^271-1)302691Ryan Propper11/2023
112871956^16087+16087^71956302682Hans Havermann11/2021
11292^1005326+383059302634Enzo Doria12/2016
11302^1004929+1877567302514Enzo Doria08/2016
113169341^22978+22978^69341302418Hans Havermann12/2021
1132111443^516+516^111443302306Hans Havermann12/2021
113367638^29387+29387^67638302218Hans Havermann11/2021
11342^1003494+1874899302082Enzo Doria06/2016
113575189^10400+10400^75189302037Hans Havermann12/2021
113667237^31042+31042^67237302026Hans Havermann12/2021
113764540^47791+47791^64540302005Hans Havermann11/2021
11382^1003046+60529301947Enzo Doria04/2016
113983278^4209+4209^83278301815Hans Havermann09/2021
114064431^48250+48250^64431301763Hans Havermann09/2021
114167237^30714+30714^67237301716Hans Havermann09/2021
114264641^46288+46288^64641301581Hans Havermann09/2021
114371513^16482+16482^71513301572Hans Havermann10/2021
114472017^15396+15396^72017301565Hans Havermann09/2021
114565534^39927+39927^65534301540Hans Havermann10/2021
1146(23^221411-1)/22301501Paul Bourdelais08/2020
114763169^59152+59152^63169301441Hans Havermann09/2021
114875055^10348+10348^75055301336Hans Havermann09/2021
11492^1000647+1881353301225Enzo Doria11/2016
115083686^3961+3961^83686301086Hans Havermann10/2021
115168529^24742+24742^68529301078Hans Havermann09/2021
115265207^41416+41416^65207301072Hans Havermann10/2021
11542^1000000+821751301030Tony Prest / Never Odd Or Even10/2015
11532^999999+77151301030Norman Luhn09/2023
115590762^2071+2071^90762300984Hans Havermann06/2021
115663909^51142+51142^63909300934Hans Havermann08/2021
11572^999646+1874029300924Enzo Doria06/2016
115866280^34607+34607^66280300856Hans Havermann06/2021
115965534^38925+38925^65534300817Hans Havermann07/2021
116063296^56517+56517^63296300794Hans Havermann06/2021
1161110610^523+523^110610300694Hans Havermann06/2021
116266428^33609+33609^66428300684Hans Havermann06/2021
116374247^11210+11210^74247300672Hans Havermann06/2021
1164(59^169777-1)/58300649Paul Bourdelais08/2020
116510^300476+3300477Ed Trice10/2012
116610^300476-530913300476Patrick De Geest03/2016
116766703^31960+31960^66703300471Hans Havermann06/2021
116863722^51915+51915^63722300468Hans Havermann06/2021
11692^998053+1879667300444Enzo Doria09/2016
117077018^7959+7959^77018300437Hans Havermann07/2021
1171314738^9+9^314738300337Anatoly F. Selevich02/2011
11722^997689+217787300335Enzo Doria01/2024
117369478^20987+20987^69478300281Hans Havermann07/2021
117464088^48393+48393^64088300239Hans Havermann07/2021
117564605^44146+44146^64605300084Hans Havermann08/2021
11762^996845+29027300081Enzo Doria02/2024
11777^355039-6^355039300043Jean-Louis Charton05/2011
117867594^27465+27465^67594300035Hans Havermann06/2021
117910^300000+287389300001Patrick De Geest10/2019
118010^300000-83657300000Patrick De Geest10/2019
118170599^17756+17756^70599300000Hans Havermann06/2021
1182numbpart(72526161452)299999Serge Batalov04/2017
11832^996182-114431299881Enzo Doria02/2015
11843*2^996126+5299865Jon Grantham07/2023
11852^996034-17299837Stefano Morozzi07/2022
11862^995793+36587299764Enzo Doria09/2024
1187(19*10^299640+77)/3299641Robert Price03/2023
11882^995214-2788361299590Enzo Doria12/2015
11892^994791-114319299462Enzo Doria01/2015
11902^994490-1863791299372Enzo Doria01/2016
11912^993322+1885729299020Enzo Doria03/2017
11922^993227+230033298992Enzo Doria12/2024
1193(36395^65536+36393^65536)/2298913Kellen Shenton04/2022
11942^992711-2788807298836Enzo Doria12/2015
11952^992525-114199298780Enzo Doria12/2014
1196(7^353501-3^353501)/4298743Jon Grantham08/2023
11972^992329+1884707298721Enzo Doria02/2017
11982^992292+229801298710Enzo Doria12/2024
11992^992052+215491298638Enzo Doria11/2023
12002^991968-23298613Stefano Morozzi07/2022
12012^991715-19298536Stefano Morozzi07/2022
1202(10^298414+7)/191/823/56921/1334467298398Alfred Reich10/2021
12032^989562+25297888Stefano Morozzi05/2021
12042^988580+214051297593Enzo Doria10/2023
12052^988537+218837297580Enzo Doria03/2024
1206(19*10^297497+77)/3297498Robert Price03/2023
1207(2*10^297488-23)/3297488Robert Price10/2022
1208(2^986191+1)/3296873Vincent Diepeveen06/2008
12092^985217-114553296580Enzo Doria03/2015
1210(76^157649-1)/75296507Paul Bourdelais07/2019
12112^984650+21529296410Enzo Doria08/2023
12122^984131-1828009296253Enzo Doria01/2015
12132^983620+60451296100Phil Moore03/2008
12142^982721-2683295829Yves Minet02/2016
1215(23*10^295581+7)/3295582Robert Price05/2023
12162^981298-2788421295401Enzo Doria12/2015
12172^981163-2790967295360Enzo Doria12/2015
12182^981016-15295316Stefano Morozzi07/2022
12198*10^295160-13295161Robert Price08/2023
12202^979594+1865839294888Enzo Doria02/2016
12212^979502+221029294860Enzo Doria03/2024
12222*10^294527-91294528Robert Price02/2023
1223(49363^63001-1)/(49363^251-1)294511Ryan Propper11/2023
122410^294475+49294476Robert Price02/2023
1225(11*10^294308+91)/3294309Robert Price03/2023
12262^976760+1885021294035Enzo Doria02/2017
12273*2^976518+5293962Jon Grantham07/2023
12282^975798+218599293745Enzo Doria01/2024
12292^974441+1878407293336Enzo Doria08/2016
12302^974180+1876831293258Enzo Doria07/2016
12312^974170+453319293255Enzo Doria01/2017
1232(211^126023-1)/210292911Anonymous05/2024
12332^972744-114419292826Enzo Doria03/2015
123411^281143+6292781Paul Bourdelais03/2021
1235(4*10^292619-91)/3292620Robert Price12/2022
1236E(69468)/13247122135292549Sergey Batalov10/2023
1237CopelandErdos(292447)292447Mark Rodenkirch12/2015
12383*10^292344-97292345Robert Price01/2023
12392^970911+1873373292274Enzo Doria07/2016
12402^970670+383059292201Enzo Doria12/2016
12412^970141-100363292042Enzo Doria02/2014
12422^969945+1874717291983Enzo Doria06/2016
12432^969384+1880701291814Enzo Doria10/2016
1244(13*10^291721-43)/3291722Robert Price08/2023
1245(3^611333-2^611333)/(99035947*87109884549431)291659Mike Oakes02/2017
12463*2^963892+5290161Jon Grantham07/2023
1247(151*10^289877-1)/3289879Robert Price07/2023
12482^962194+60139289650Enzo Doria02/2016
12492^959307-1861507288781Enzo Doria11/2015
1250(17*10^288692+31)/3288693Robert Price04/2023


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 10 2025 11:16 (Time in France)

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