PRP Records

Probable Primes Top 10000

(291910 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(53^158341+1)/54273022Paul Bourdelais07/2019
7522^906594-113201272912Enzo Doria08/2014
7532^904773+1872167272364Enzo Doria06/2016
7546^349903+5272278Paul Bourdelais02/2021
7552^904149-1862473272176Enzo Doria12/2015
756(7*10^271757-61)/9271757Erik Branger03/2012
7572^902497+1880117271679Enzo Doria09/2016
7582^901858+77689271487Enzo Doria06/2016
7592^901372+1875301271341Enzo Doria06/2016
76023*10^270799-7270801Robert Price10/2022
7612^899121-115033270663Enzo Doria07/2015
7622^898900+883021270596Enzo Doria12/2016
7632^898762-251511270555Enzo Doria12/2013
7642^898589+47270503Lelio R Paula03/2016
765187322*10^270343-187321270349Danilo Nitsche09/2013
76648358*10^270343-48357270348Danilo Nitsche09/2013
767(10^270343-1)/9270343Maksym Voznyy07/2007
7682^897867-3217270285Yves Minet12/2016
7692^897849-115273270280Enzo Doria07/2015
7702^896616-114179269909Enzo Doria12/2014
7712^894928+583561269401Enzo Doria04/2017
7722^894673-39343269324Enzo Doria08/2015
773F(1285607)268676Henri Lifchitz11/2008
7742^892112+187663268553Enzo Doria08/2016
775(10^268207+1)/11268206Paul Bourdelais02/2010
7762^890957-69583268205Enzo Doria12/2015
77732841!^2+32840!^2+...+2!^2+1!^2268128Serge Batalov07/2017
7782^890122-351401267954Enzo Doria07/2015
779(19^209359-1)/18267718Paul Bourdelais08/2010
780(85^138647+1)/86267507Paul Bourdelais07/2019
781(485^99523-1)/484267291Michael Stocker05/2020
7822^886324+77791266811Enzo Doria06/2016
7837*10^266731+87266732Robert Price11/2022
7842^884714+1880527266326Enzo Doria10/2016
78511^255426+255426^11265999Serge Batalov05/2014
7862^883462-343421265949Enzo Doria07/2015
7872^883442+1875019265943Enzo Doria06/2016
7882^883333-291583265910Enzo Doria07/2015
789(2*10^265321-17)/3265321Serge Batalov11/2022
790(16*10^265052-91)/3265053Robert Price11/2022
7912^880411+1882673265031Enzo Doria12/2016
792(14*10^264791-11)/3264792Robert Price08/2022
7932^879530-2788031264765Enzo Doria12/2015
794(2*10^264539+61)/9264539Serge Batalov11/2022
7952^878118+2793079264340Enzo Doria02/2016
796(2^878073-7)/5264326Stefano Morozzi08/2022
797(37^168527-1)/36264283Paul Bourdelais08/2019
7982^876202-17263764Stefano Morozzi07/2022
799(14*10^263720-11)/3263721Robert Price08/2022
8002^875748-461129263627Enzo Doria07/2015
8012^875518-15263558Stefano Morozzi07/2022
802(29*10^263523-17)/3263524Robert Price01/2023
8032^875181-2789923263456Enzo Doria12/2015
8042^875101-350083263432Enzo Doria08/2015
8052^874684+1883587263307Enzo Doria01/2017
8062^874616+1872211263286Enzo Doria05/2016
8073^551491+16263129Robert Price04/2020
8082^874073+2792957263123Enzo Doria02/2016
8092^873628+1878751262989Enzo Doria08/2016
8102^873288-269262886Yves Minet01/2015
811(2*10^262874+7)/9262874Rytis Slatkevicius01/2023
812(2*10^262603-11)/9262603Serge Batalov11/2022
8132^871991-4207262496Yves Minet03/2021
8142^871146-3173262242Yves Minet07/2016
8152^869601-163261776Yves Minet01/2015
816(2*10^261704+61)/9261704Serge Batalov11/2022
8172^869326+282859261694Enzo Doria11/2016
8182^869035-114181261606Enzo Doria12/2014
8194*10^261248+91261249Robert Price11/2022
8202^865715+80303260607Enzo Doria07/2016
8212^865048+1882411260406Enzo Doria12/2016
8222^864899-113871260361Enzo Doria10/2014
823(16*10^260256-91)/3260257Robert Price11/2022
824(7*10^260198-61)/9260198Erik Branger11/2011
8252^864298-2788421260180Enzo Doria12/2015
8262^864039-2791357260102Enzo Doria01/2016
8272^863621-113833259976Enzo Doria10/2014
8282^862837+75767259740Enzo Doria05/2016
8292^862637-31259680Jorge Menendez05/2019
8302^862088+1874941259515Enzo Doria06/2016
8312^861987-134557259484Hans Havermann10/2018
8322^861516-1854029259343Enzo Doria09/2015
8332^860975-1853977259180Enzo Doria09/2015
8343^543128+16259138Robert Price04/2020
8352^860625-1858843259074Enzo Doria10/2015
8362^860110+77689258919Enzo Doria05/2016
8372^859600+1880371258766Enzo Doria10/2016
8382^859433+494711258716Makoto Morimoto10/2013
839(2^859433-44)/(2^2*3)258715Makoto Morimoto08/2019
840(2^859431-11)/3258715Stefano Morozzi08/2022
841(2^859433+39899)/(73*3907*46301)258705Makoto Morimoto10/2016
8422^859240+1875271258658Enzo Doria06/2016
843Tau(971^15738)258571Nik Lygeros / Olivier Rozier05/2015
844(144^119671+1)/145258292Paul Bourdelais08/2019
8452^857608+105258166Stefano Morozzi05/2021
846(11*2^857159-13)/15258031Renaud Lifchitz08/2011
8472^857016-633113257988Enzo Doria12/2013
8482^855732-113969257602Enzo Doria10/2014
8492^853682-3911256984Enzo Doria05/2014
85011^246668-90256879Enzo Doria12/2012
8512^851904-113939256449Enzo Doria10/2014
8522^851725-851725^2256395Henri Lifchitz03/2019
85311^246167-90256357Enzo Doria12/2012
854(85*10^256301-1)/3256303Robert Price12/2022
855(10^256187+7)/63443/148782853256175Alfred Reich10/2021
8562^850700-569049256087Enzo Doria11/2013
8572^850675+153256079Stefano Morozzi05/2021
85821^193601-20^193601255983Jean-Louis Charton02/2015
859(37^163193+1)/38255918Paul Bourdelais07/2019
860(14*10^255805-83)/3255806Robert Price11/2022
8612^849177-114025255628Enzo Doria12/2014
8622^848502-3173255425Yves Minet07/2016
8632^848178-140291255328Enzo Doria01/2014
8647*10^255167+87255168Robert Price11/2022
8652^847622-2441255160Yves Minet02/2016
8662^847291+182843255061Enzo Doria11/2016
8672^847174+1879429255025Enzo Doria09/2016
86824*29^174239+13361254809Curtis Bright04/2015
86922*10^254639+7254641Robert Price10/2022
8702^845633-933075254561Paul Bourdelais11/2021
8712^845610-1868591254554Enzo Doria04/2016
8722^845484+81931254517Enzo Doria08/2016
8732^845402-114761254492Enzo Doria05/2015
8742^844334-2792441254170Enzo Doria02/2016
87511^243796-90253888Enzo Doria12/2012
876(10^253891+7)/44777/79843/16940711253875Alfred Reich10/2021
87730^171733-29^171733253671Jean-Louis Charton10/2018
8782^842209+1876037253531Enzo Doria07/2016
8792^842123-59197253505Enzo Doria10/2015
880(8*10^253313-53)/9253313Serge Batalov11/2022
8812^840797-3253106Paul Bourdelais06/2019
8822^840716-2969253081Yves Minet05/2016
8832^840358-462491252973Enzo Doria08/2015
8842^840310+1878379252959Enzo Doria08/2016
8852^840203-21252927Stefano Morozzi07/2022
88611^242579-60252620Enzo Doria10/2012
88745^152659+2252378Robert Price09/2015
888(95^127583+1)/96252322Paul Bourdelais07/2019
8897*10^252209-17252210Robert Price12/2022
8902^837725+1869377252181Enzo Doria05/2016
8912^837536-311039252124Enzo Doria06/2015
89221^190632-2252058Robert Price07/2015
8932^837242+1873297252035Enzo Doria06/2016
8942^836656-2787929251859Enzo Doria11/2015
8952^836380+1875541251776Enzo Doria07/2016
896(359^98327-1)/358251233Alexander Zhirkov11/2017
897tau(41^28288)250924Nik Lygeros / Olivier Rozier10/2013
8982^832511-461197250611Enzo Doria07/2015
8992^832505+1881137250609Enzo Doria11/2016
9002^832363+583295250567Enzo Doria12/2016
9012^832244-403635250531Enzo Doria01/2014
902(14*10^250336-41)/9250337Serge Batalov01/2023
9032^831157+1880657250204Enzo Doria11/2016
9042^831088-7200899250183Enzo Doria01/2015
9052^830956-1349250143Yves Minet07/2015
9062^830037+282317249867Enzo Doria09/2016
9072^829589-113653249732Enzo Doria09/2014
908(4*10^249550-7)/3249551Serge Batalov01/2023
9092^828281-3193249338Yves Minet08/2016
910(2^828140-19)/3249295Stefano Morozzi08/2022
9112^828064-2785619249273Enzo Doria10/2015
9122^827602+60409249134Enzo Doria03/2016
91310^249010+348861249011Patrick De Geest04/2016
91410^249010-21249010Serge Batalov12/2014
9152^826733+1882907248872Enzo Doria12/2016
9162^825682+1876549248556Enzo Doria07/2016
9172^824991-114121248348Enzo Doria12/2014
9182^824642-362727248242Enzo Doria12/2013
9192^824565-114265248219Enzo Doria01/2015
920(73*10^248145-1)/9248146Robert Price01/2015
921(2^823337+1)/(3*362268281)247841Gord Palameta08/2018
922(2^822971-1)/6583769/28211445881/21255852651726486149207247700Robert Kinser09/2016
9232^822296+76501247536Enzo Doria05/2016
9242^821590-114167247324Enzo Doria12/2014
9252^821512-2790659247300Enzo Doria12/2015
9262^820077+382847246868Enzo Doria11/2016
9272^820001+81269246845Enzo Doria07/2016
9282^819463-59197246683Enzo Doria10/2015
9292^819296+80581246633Enzo Doria07/2016
9302^817160-350369245990Enzo Doria06/2015
9312^816039-19245653Stefano Morozzi07/2022
932(71*10^245558-17)/9245559Serge Batalov01/2023
93388093#+(653879#)/(88093#)245374Makoto Morimoto11/2017
9342^815111-113857245373Enzo Doria10/2014
9352^814914-4001245314Yves Minet05/2017
936846^83761-845^83761245200Jean-Louis Charton12/2012
9372^814356-2790449245146Enzo Doria12/2015
9382^814276-459029245122Enzo Doria04/2015
9392^814023+180923245046Enzo Doria07/2016
940(3^513059-2^513059)/(1026119*5430216457)244776Mike Oakes03/2017
9413^513007+16244767Robert Price04/2020
9422^811842-113675244389Enzo Doria09/2014
9432^811132-2787929244176Enzo Doria11/2015
9442^809746-2790971243758Enzo Doria01/2016
9452^808767-3295243464Yves Minet12/2016
9462^808621-113809243420Enzo Doria09/2014
9472^807724+1879621243150Enzo Doria09/2016
94820^186554-3242713Paul Bourdelais12/2020
9492^805843-113611242583Enzo Doria08/2014
9502^805745-459763242554Enzo Doria05/2015
9512^805353+782687242436Enzo Doria11/2016
9526^311257+5242206Paul Bourdelais02/2021
9532^804277-417933242112Enzo Doria01/2014
9542^803468-269039241868Enzo Doria10/2013
9552^803172+80851241779Enzo Doria07/2016
9563^506233-2241535Robert Price11/2013
9572^802025-25999241434Enzo Doria10/2013
958(3^505823+3^252912+1)/7241339Serge Batalov03/2014
9592^801303+1872923241217Enzo Doria05/2016
9602^800579-1862947240999Enzo Doria12/2015
9613^504206+2240568Luke W. Richards03/2018
9622^798973-26283240515Enzo Doria10/2013
9632^798671-69487240424Enzo Doria12/2015
9642^797220+79831239988Enzo Doria06/2016
9652^796910-26001239894Enzo Doria10/2013
9662^796598+653119239800Enzo Doria12/2016
9672^796432-1859729239750Enzo Doria11/2015
9682^796002-1852211239621Enzo Doria08/2015
9692^795709+75767239533Enzo Doria04/2016
9702^795708+81721239532Enzo Doria08/2016
9712^795468-2786249239460Enzo Doria10/2015
9722^795442+80779239452Enzo Doria07/2016
9732^795075-1852057239342Enzo Doria08/2015
974(86^123677+1)/87239252Paul Bourdelais01/2019
9752^794043+1875023239031Enzo Doria06/2016
9762^793347-69577238822Enzo Doria01/2016
9772^792988-344429238714Enzo Doria08/2015
9782^792700-2786369238627Enzo Doria11/2015
9792^792663-1844797238616Enzo Doria06/2015
9802^792605-291943238598Enzo Doria07/2015
981(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
9824*10^238163+21238164Robert Price12/2022
9832^789373+1869377237625Enzo Doria05/2016
984((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961237544Serge Batalov04/2015
9852^788942+1866409237496Enzo Doria02/2016
9862^788844-114329237466Enzo Doria01/2015
9872^788705-1859713237424Enzo Doria11/2015
9882^786180+1871971236664Enzo Doria05/2016
98911^227092-90236492Enzo Doria11/2012
9902^785260+1866361236387Enzo Doria02/2016
9912^785220+1880611236375Enzo Doria10/2016
992(2^784689-15)/7236215Stefano Morozzi08/2022
99319^184650-2236122Robert Price10/2014
99410^236059+216513236060Patrick De Geest04/2016
99510^236059-20909236059Robert Price09/2015
9962^783893-21235976Stefano Morozzi07/2022
997(87^121487-1)/86235625Paul Bourdelais12/2018
9982^782634-113981235597Enzo Doria11/2014
9992^782423+1879733235533Enzo Doria09/2016
10002^781682-2789543235310Enzo Doria12/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 02 2023 13:22 (Time in France)

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