PRP Records

Probable Primes Top 10000

(294627 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 ?
751(28^223381+1)/29323267Paul Bourdelais12/2020
75210^322999+187071323000Stefano Morozzi03/2019
75310^322999-143151322999Patrick De Geest05/2020
7542^1072146+1886869322749Enzo Doria04/2017
7552^1072118-7321953322740Enzo Doria02/2015
7562^1071026+1886869322411Enzo Doria04/2017
7572^1070539+1880633322265Enzo Doria10/2016
7582^1069788+26587322039Enzo Doria12/2023
7592^1069293-1147195321890Enzo Doria05/2015
7602^1065968+1880941320889Enzo Doria10/2016
7612^1065897-1147195320867Enzo Doria05/2015
7622^1063427+1882103320124Enzo Doria12/2016
7632^1061095-1061095319422Henri Lifchitz10/2013
7642^1060950+653119319378Enzo Doria12/2016
7652^1060363+782753319202Enzo Doria11/2016
766(71^172259-1)/70318895Paul Bourdelais08/2020
767-30*Bern(85996)/236037521318354Sergey Batalov10/2023
7682^1054736+483061317508Enzo Doria12/2016
7692^1053965+1879667317276Enzo Doria10/2016
770(43^194119-1)/42317086Paul Bourdelais08/2020
7712^1052186-458165316740Enzo Doria03/2015
77211^303909+2316489Paul Bourdelais08/2023
7732^1049026+214609315789Enzo Doria11/2023
7742^1046613-114685315062Enzo Doria04/2015
7752^1045625-459373314765Enzo Doria06/2015
77610^(2*157363+1)-8*10^157363-1314727Robert Price07/2023
777(7*10^314564-61)/9314564Erik Branger09/2016
7782^1044206+7314338Stefano Morozzi10/2022
779(7^371669-1)/6314096Paul Bourdelais02/2010
780(53^181981-1)/52313784Paul Bourdelais08/2020
781(8^347437-5^347437)/3313767Jon Grantham08/2023
7822^1041944+283051313657Enzo Doria12/2016
783(1624^97969-1)/(1624^313-1)313533Sergey Batalov11/2023
7842^1041153-114391313419Enzo Doria02/2015
785(2^1039700+9)/5312981Stefano Morozzi09/2022
786(74^167311+1)/75312742Paul Bourdelais12/2020
7872^1038871+1866983312732Enzo Doria04/2016
7882^1038545+71657312634Enzo Doria08/2023
789(55^179573-1)/54312521Paul Bourdelais08/2020
7902^1037647+1881263312363Enzo Doria11/2016
7912^1037226+1879699312237Enzo Doria10/2016
7922^1036867+1865843312129Enzo Doria02/2016
793(76^165947+1)/77312114Paul Bourdelais01/2021
7942^1036020-114539311874Enzo Doria02/2015
795(90^159463-1)/89311628Paul Bourdelais08/2020
7962^1034546+28819311430Enzo Doria02/2024
7972^1032240+1883431310736Enzo Doria01/2017
79864211^64588+64588^64211310514Norbert Schneider11/2023
7992^1030352+1870021310167Enzo Doria06/2016
8002^1030046+1882843310075Enzo Doria11/2016
8013^648872+16309591Robert Price04/2020
802(16976^73441-1)/(16976^271-1)309498Ryan Propper11/2023
80364221^64366+64366^64221309451Norbert Schneider06/2023
804(11121^76729-1)/(11121^277-1)309336Ryan Propper11/2023
8052^1027478+219259309302Enzo Doria02/2024
8062^1026999+20513309158Enzo Doria07/2023
8075^442281+2309142Paul Bourdelais01/2021
8082^1026204+22741308919Enzo Doria09/2023
8092^1026190+15308914Stefano Morozzi10/2022
8102^1025108+20851308589Enzo Doria08/2023
811A352736(16)306985Kellen Shenton05/2022
8122^1019777+213947306984Enzo Doria10/2023
813(11^293831-1)/10305993Paul Bourdelais03/2010
814(67^167449-1)/66305773Paul Bourdelais08/2020
815(62^170539+1)/63305671Paul Bourdelais12/2020
8162^1015321-1015321305643Henri Lifchitz08/2013
8172^1014775+27113305478Enzo Doria12/2023
8182^1014450+7305380Stefano Morozzi10/2022
8192^1014336+215731305346Enzo Doria12/2023
8202^1014224-2791229305312Enzo Doria01/2016
821(10^304986+7)/673304984Alfred Reich11/2021
82265473^45250+45250^65473304818Hans Havermann02/2022
82366012^41423+41423^66012304794Hans Havermann03/2022
82465073^48202+48202^65073304742Hans Havermann04/2022
825238176^19+19^238176304569Hans Havermann03/2022
82673122^14615+14615^73122304539Hans Havermann05/2022
82764492^52639+52639^64492304487Hans Havermann03/2022
82865955^41288+41288^65955304437Hans Havermann04/2022
82971729^17530+17530^71729304403Hans Havermann03/2022
83070170^21733+21733^70170304336Hans Havermann03/2022
8312^1010751-107709304267Enzo Doria03/2014
83284473^3994+3994^84473304222Hans Havermann03/2022
833(2^1010623-1)/12602017578957977304212Tony Prest / Never Odd Or Even02/2014
83474442^12125+12125^74442303998Hans Havermann02/2022
83577842^8039+8039^77842303989Hans Havermann01/2022
83664209^54140+54140^64209303935Hans Havermann02/2022
8372^1009577+1869587303913Enzo Doria06/2016
83867389^32338+32338^67389303906Hans Havermann02/2022
8398^336419-7^336419303817Jean-Louis Charton01/2008
8402^1009168+15303790Stefano Morozzi10/2022
84180766^5771+5771^80766303782Hans Havermann01/2022
84266094^39385+39385^66094303724Hans Havermann01/2022
84369147^24574+24574^69147303589Hans Havermann02/2022
84478390^7459+7459^78390303580Hans Havermann01/2022
8452^1008301+1869377303529Enzo Doria06/2016
84665008^46615+46615^65008303492Hans Havermann02/2022
847(2^1007838+5)/3303389Serge Batalov08/2015
84865018^46293+46293^65018303343Hans Havermann01/2022
8496^389756+5303290Paul Bourdelais02/2021
85071016^18649+18649^71016303285Hans Havermann01/2022
8512^1007065+29231303157Enzo Doria03/2024
85280160^6047+6047^80160303129Hans Havermann01/2022
85367434^31237+31237^67434303094Hans Havermann03/2022
85465537^42102+42102^65537303063Hans Havermann02/2022
85571790^16553+16553^71790302874Hans Havermann11/2021
85665208^44129+44129^65208302874Hans Havermann11/2021
85784181^3960+3960^84181302858Hans Havermann11/2021
858(13703^73441-1)/(13703^271-1)302691Ryan Propper11/2023
85971956^16087+16087^71956302682Hans Havermann11/2021
8602^1005326+383059302634Enzo Doria12/2016
8612^1004929+1877567302514Enzo Doria08/2016
86269341^22978+22978^69341302418Hans Havermann12/2021
863111443^516+516^111443302306Hans Havermann12/2021
86467638^29387+29387^67638302218Hans Havermann11/2021
8652^1003494+1874899302082Enzo Doria06/2016
86675189^10400+10400^75189302037Hans Havermann12/2021
86767237^31042+31042^67237302026Hans Havermann12/2021
86864540^47791+47791^64540302005Hans Havermann11/2021
8692^1003046+60529301947Enzo Doria04/2016
87083278^4209+4209^83278301815Hans Havermann09/2021
87164431^48250+48250^64431301763Hans Havermann09/2021
87267237^30714+30714^67237301716Hans Havermann09/2021
87364641^46288+46288^64641301581Hans Havermann09/2021
87471513^16482+16482^71513301572Hans Havermann10/2021
87572017^15396+15396^72017301565Hans Havermann09/2021
87665534^39927+39927^65534301540Hans Havermann10/2021
877(23^221411-1)/22301501Paul Bourdelais08/2020
87863169^59152+59152^63169301441Hans Havermann09/2021
87975055^10348+10348^75055301336Hans Havermann09/2021
8802^1000647+1881353301225Enzo Doria11/2016
88183686^3961+3961^83686301086Hans Havermann10/2021
88268529^24742+24742^68529301078Hans Havermann09/2021
88365207^41416+41416^65207301072Hans Havermann10/2021
8852^1000000+821751301030Tony Prest / Never Odd Or Even10/2015
8842^999999+77151301030Norman Luhn09/2023
88690762^2071+2071^90762300984Hans Havermann06/2021
88763909^51142+51142^63909300934Hans Havermann08/2021
8882^999646+1874029300924Enzo Doria06/2016
88966280^34607+34607^66280300856Hans Havermann06/2021
89065534^38925+38925^65534300817Hans Havermann07/2021
89163296^56517+56517^63296300794Hans Havermann06/2021
892110610^523+523^110610300694Hans Havermann06/2021
89366428^33609+33609^66428300684Hans Havermann06/2021
89474247^11210+11210^74247300672Hans Havermann06/2021
895(59^169777-1)/58300649Paul Bourdelais08/2020
89610^300476+3300477Ed Trice10/2012
89710^300476-530913300476Patrick De Geest03/2016
89866703^31960+31960^66703300471Hans Havermann06/2021
89963722^51915+51915^63722300468Hans Havermann06/2021
9002^998053+1879667300444Enzo Doria09/2016
90177018^7959+7959^77018300437Hans Havermann07/2021
902314738^9+9^314738300337Anatoly F. Selevich02/2011
9032^997689+217787300335Enzo Doria01/2024
90469478^20987+20987^69478300281Hans Havermann07/2021
90564088^48393+48393^64088300239Hans Havermann07/2021
90664605^44146+44146^64605300084Hans Havermann08/2021
9072^996845+29027300081Enzo Doria02/2024
9087^355039-6^355039300043Jean-Louis Charton05/2011
90967594^27465+27465^67594300035Hans Havermann06/2021
91010^300000+287389300001Patrick De Geest10/2019
91110^300000-83657300000Patrick De Geest10/2019
91270599^17756+17756^70599300000Hans Havermann06/2021
913numbpart(72526161452)299999Serge Batalov04/2017
9142^996182-114431299881Enzo Doria02/2015
9153*2^996126+5299865Jon Grantham07/2023
9162^996034-17299837Stefano Morozzi07/2022
917(19*10^299640+77)/3299641Robert Price03/2023
9182^995214-2788361299590Enzo Doria12/2015
9192^994791-114319299462Enzo Doria01/2015
9202^994490-1863791299372Enzo Doria01/2016
9212^993322+1885729299020Enzo Doria03/2017
922(36395^65536+36393^65536)/2298913Kellen Shenton04/2022
9232^992711-2788807298836Enzo Doria12/2015
9242^992525-114199298780Enzo Doria12/2014
925(7^353501-3^353501)/4298743Jon Grantham08/2023
9262^992329+1884707298721Enzo Doria02/2017
9272^992052+215491298638Enzo Doria11/2023
9282^991968-23298613Stefano Morozzi07/2022
9292^991715-19298536Stefano Morozzi07/2022
930(10^298414+7)/191/823/56921/1334467298398Alfred Reich10/2021
9312^989562+25297888Stefano Morozzi05/2021
9322^988580+214051297593Enzo Doria10/2023
9332^988537+218837297580Enzo Doria03/2024
934(19*10^297497+77)/3297498Robert Price03/2023
935(2*10^297488-23)/3297488Robert Price10/2022
936(2^986191+1)/3296873Vincent Diepeveen06/2008
9372^985217-114553296580Enzo Doria03/2015
938(76^157649-1)/75296507Paul Bourdelais07/2019
9392^984650+21529296410Enzo Doria08/2023
9402^984131-1828009296253Enzo Doria01/2015
9412^983620+60451296100Phil Moore03/2008
9422^982721-2683295829Yves Minet02/2016
943(23*10^295581+7)/3295582Robert Price05/2023
9442^981298-2788421295401Enzo Doria12/2015
9452^981163-2790967295360Enzo Doria12/2015
9462^981016-15295316Stefano Morozzi07/2022
9478*10^295160-13295161Robert Price08/2023
9482^979594+1865839294888Enzo Doria02/2016
9492*10^294527-91294528Robert Price02/2023
950(49363^63001-1)/(49363^251-1)294511Ryan Propper11/2023
95110^294475+49294476Robert Price02/2023
952(11*10^294308+91)/3294309Robert Price03/2023
9532^976760+1885021294035Enzo Doria02/2017
9543*2^976518+5293962Jon Grantham07/2023
9552^975798+218599293745Enzo Doria01/2024
9562^974441+1878407293336Enzo Doria08/2016
9572^974180+1876831293258Enzo Doria07/2016
9582^974170+453319293255Enzo Doria01/2017
9592^972744-114419292826Enzo Doria03/2015
96011^281143+6292781Paul Bourdelais03/2021
961(4*10^292619-91)/3292620Robert Price12/2022
962E(69468)/13247122135292549Sergey Batalov10/2023
963CopelandErdos(292447)292447Mark Rodenkirch12/2015
9643*10^292344-97292345Robert Price01/2023
9652^970911+1873373292274Enzo Doria07/2016
9662^970670+383059292201Enzo Doria12/2016
9672^970141-100363292042Enzo Doria02/2014
9682^969945+1874717291983Enzo Doria06/2016
9692^969384+1880701291814Enzo Doria10/2016
970(13*10^291721-43)/3291722Robert Price08/2023
971(3^611333-2^611333)/(99035947*87109884549431)291659Mike Oakes02/2017
9723*2^963892+5290161Jon Grantham07/2023
973(151*10^289877-1)/3289879Robert Price07/2023
9742^962194+60139289650Enzo Doria02/2016
9752^959307-1861507288781Enzo Doria11/2015
976(17*10^288692+31)/3288693Robert Price04/2023
97714^251797-3288592Paul Bourdelais12/2020
978(8745^73441-1)/(8745^271-1)288419Ryan Propper11/2023
979(2*10^288371-23)/3288371Robert Price10/2022
980(31*10^288238-1)/3288240Robert Price02/2023
981(7^341063-2^341063)/5288231Jon Grantham08/2023
9822^957372+283531288198Enzo Doria02/2017
9832^957192-1864049288144Enzo Doria01/2016
984(95774^58081-1)/(95774^241-1)288116Ryan Propper11/2023
9852^956446+1875199287919Enzo Doria06/2016
9862^956283+219143287870Enzo Doria02/2024
9877*10^287854+39287855Robert Price01/2023
9882^956082+28309287810Enzo Doria02/2024
989(17^233689+1)/18287542Paul Bourdelais09/2013
9902^955178+1883587287538Enzo Doria12/2016
9912^954127-954127^2287221Henri Lifchitz01/2021
9922^954001+1875257287183Enzo Doria07/2016
9932*10^287175-49287176Robert Price05/2023
994(22*10^287085-19)/3287086Robert Price07/2023
9952^953488+22411287029Enzo Doria09/2023
996(23891^65536+1)/2286932Serge Batalov03/2018
9975*3^601336-2^601336286911Jon Grantham08/2023
9982^952268+1878601286662Enzo Doria09/2016
9992^950801+81557286220Enzo Doria08/2016
10002^949403+217523285799Enzo Doria01/2024


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 12 2024 13:37 (Time in France)

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