PRP Records

Probable Primes Top 10000

(292102 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(2*10^275922+1)/3275922Serge Batalov11/2022
7522^916385-2786383275860Enzo Doria11/2015
7532^915928+82081275722Enzo Doria09/2016
754(4*10^275671+11)/3275672Tyler Busby02/2023
7552^915576-114137275616Enzo Doria01/2015
7562^914828+1876741275391Enzo Doria07/2016
7572^914757-2203275370Yves Minet12/2015
7587*10^275157-27275158Robert Price11/2022
7592^911900+1871245274510Enzo Doria05/2016
760(16*10^274251-91)/3274252Robert Price11/2022
7612^910999+9274239Stefano Morozzi05/2021
762(2^910869-7)/5274199Stefano Morozzi08/2022
7632^910490+283429274085Enzo Doria01/2017
7647*10^273983+39273984Robert Price01/2023
7652^909988-1862249273934Enzo Doria12/2015
7662^909297+1879157273726Enzo Doria08/2016
7672^909257-1864423273714Enzo Doria01/2016
7682^908739-7273558Stefano Morozzi07/2022
7692^908579-1861747273510Enzo Doria12/2015
7702^907635-2791597273226Enzo Doria01/2016
771(53^158341+1)/54273022Paul Bourdelais07/2019
7722^906594-113201272912Enzo Doria08/2014
7732*10^272403-91272404Robert Price02/2023
7742^904773+1872167272364Enzo Doria06/2016
7756^349903+5272278Paul Bourdelais02/2021
7762^904149-1862473272176Enzo Doria12/2015
777(7*10^271757-61)/9271757Erik Branger03/2012
7782^902497+1880117271679Enzo Doria09/2016
7792^901858+77689271487Enzo Doria06/2016
7802^901372+1875301271341Enzo Doria06/2016
7812*10^270802-91270803Robert Price02/2023
78223*10^270799-7270801Robert Price10/2022
7832^899121-115033270663Enzo Doria07/2015
7842^898900+883021270596Enzo Doria12/2016
7852^898762-251511270555Enzo Doria12/2013
7862^898589+47270503Lelio R Paula03/2016
787187322*10^270343-187321270349Danilo Nitsche09/2013
78848358*10^270343-48357270348Danilo Nitsche09/2013
789(10^270343-1)/9270343Maksym Voznyy07/2007
7902^897867-3217270285Yves Minet12/2016
7912^897849-115273270280Enzo Doria07/2015
7922^896616-114179269909Enzo Doria12/2014
7932^894928+583561269401Enzo Doria04/2017
7942^894673-39343269324Enzo Doria08/2015
795F(1285607)268676Henri Lifchitz11/2008
7962^892112+187663268553Enzo Doria08/2016
797(266*10^268407-17)/3268409Robert Price02/2023
798(10^268207+1)/11268206Paul Bourdelais02/2010
7992^890957-69583268205Enzo Doria12/2015
80032841!^2+32840!^2+...+2!^2+1!^2268128Serge Batalov07/2017
8012^890122-351401267954Enzo Doria07/2015
802(19^209359-1)/18267718Paul Bourdelais08/2010
803(85^138647+1)/86267507Paul Bourdelais07/2019
804(485^99523-1)/484267291Michael Stocker05/2020
8052^886324+77791266811Enzo Doria06/2016
8067*10^266731+87266732Robert Price11/2022
8072^884714+1880527266326Enzo Doria10/2016
80811^255426+255426^11265999Serge Batalov05/2014
8092^883462-343421265949Enzo Doria07/2015
8102^883442+1875019265943Enzo Doria06/2016
8112^883333-291583265910Enzo Doria07/2015
812(2*10^265321-17)/3265321Serge Batalov11/2022
813(16*10^265052-91)/3265053Robert Price11/2022
8142^880411+1882673265031Enzo Doria12/2016
815(14*10^264791-11)/3264792Robert Price08/2022
8162^879530-2788031264765Enzo Doria12/2015
817(2*10^264539+61)/9264539Serge Batalov11/2022
8182^878118+2793079264340Enzo Doria02/2016
819(2^878073-7)/5264326Stefano Morozzi08/2022
820(37^168527-1)/36264283Paul Bourdelais08/2019
8212^876202-17263764Stefano Morozzi07/2022
822(14*10^263720-11)/3263721Robert Price08/2022
8232^875748-461129263627Enzo Doria07/2015
8242^875518-15263558Stefano Morozzi07/2022
825(29*10^263523-17)/3263524Robert Price01/2023
8262^875181-2789923263456Enzo Doria12/2015
8272^875101-350083263432Enzo Doria08/2015
8282^874684+1883587263307Enzo Doria01/2017
8292^874616+1872211263286Enzo Doria05/2016
8303^551491+16263129Robert Price04/2020
8312^874073+2792957263123Enzo Doria02/2016
8322^873628+1878751262989Enzo Doria08/2016
8332^873288-269262886Yves Minet01/2015
834(2*10^262874+7)/9262874Rytis Slatkevicius01/2023
835(2*10^262603-11)/9262603Serge Batalov11/2022
8362^871991-4207262496Yves Minet03/2021
8372^871146-3173262242Yves Minet07/2016
8382^869601-163261776Yves Minet01/2015
839(2*10^261704+61)/9261704Serge Batalov11/2022
8402^869326+282859261694Enzo Doria11/2016
8412^869035-114181261606Enzo Doria12/2014
8424*10^261248+91261249Robert Price11/2022
8432^865715+80303260607Enzo Doria07/2016
8442^865048+1882411260406Enzo Doria12/2016
8452^864899-113871260361Enzo Doria10/2014
846(16*10^260256-91)/3260257Robert Price11/2022
847(7*10^260198-61)/9260198Erik Branger11/2011
8482^864298-2788421260180Enzo Doria12/2015
8492^864039-2791357260102Enzo Doria01/2016
8502^863621-113833259976Enzo Doria10/2014
8512^862837+75767259740Enzo Doria05/2016
8522^862637-31259680Jorge Menendez05/2019
8532^862088+1874941259515Enzo Doria06/2016
8542^861987-134557259484Hans Havermann10/2018
8552^861516-1854029259343Enzo Doria09/2015
8562^860975-1853977259180Enzo Doria09/2015
8573^543128+16259138Robert Price04/2020
8582^860625-1858843259074Enzo Doria10/2015
8592^860110+77689258919Enzo Doria05/2016
8602^859600+1880371258766Enzo Doria10/2016
8612^859433+494711258716Makoto Morimoto10/2013
862(2^859433-44)/(2^2*3)258715Makoto Morimoto08/2019
863(2^859431-11)/3258715Stefano Morozzi08/2022
864(2^859433+39899)/(73*3907*46301)258705Makoto Morimoto10/2016
8652^859240+1875271258658Enzo Doria06/2016
866Tau(971^15738)258571Nik Lygeros / Olivier Rozier05/2015
867(144^119671+1)/145258292Paul Bourdelais08/2019
8682^857608+105258166Stefano Morozzi05/2021
869(11*2^857159-13)/15258031Renaud Lifchitz08/2011
8702^857016-633113257988Enzo Doria12/2013
8712^855732-113969257602Enzo Doria10/2014
8722^853682-3911256984Enzo Doria05/2014
87311^246668-90256879Enzo Doria12/2012
8742^851904-113939256449Enzo Doria10/2014
8752^851725-851725^2256395Henri Lifchitz03/2019
87611^246167-90256357Enzo Doria12/2012
877(85*10^256301-1)/3256303Robert Price12/2022
878(10^256187+7)/63443/148782853256175Alfred Reich10/2021
8792^850700-569049256087Enzo Doria11/2013
8802^850675+153256079Stefano Morozzi05/2021
88121^193601-20^193601255983Jean-Louis Charton02/2015
882(37^163193+1)/38255918Paul Bourdelais07/2019
883(14*10^255805-83)/3255806Robert Price11/2022
8842^849177-114025255628Enzo Doria12/2014
8852^848502-3173255425Yves Minet07/2016
8862^848178-140291255328Enzo Doria01/2014
8877*10^255167+87255168Robert Price11/2022
8882^847622-2441255160Yves Minet02/2016
8892^847291+182843255061Enzo Doria11/2016
8902^847174+1879429255025Enzo Doria09/2016
89124*29^174239+13361254809Curtis Bright04/2015
89222*10^254639+7254641Robert Price10/2022
8932^845633-933075254561Paul Bourdelais11/2021
8942^845610-1868591254554Enzo Doria04/2016
8952^845484+81931254517Enzo Doria08/2016
8962^845402-114761254492Enzo Doria05/2015
8972^844334-2792441254170Enzo Doria02/2016
898(4*10^254107+11)/3254108Tyler Busby02/2023
89911^243796-90253888Enzo Doria12/2012
900(10^253891+7)/44777/79843/16940711253875Alfred Reich10/2021
90130^171733-29^171733253671Jean-Louis Charton10/2018
9022^842209+1876037253531Enzo Doria07/2016
9032^842123-59197253505Enzo Doria10/2015
904(8*10^253313-53)/9253313Serge Batalov11/2022
9052^840797-3253106Paul Bourdelais06/2019
9062^840716-2969253081Yves Minet05/2016
9072^840358-462491252973Enzo Doria08/2015
9082^840310+1878379252959Enzo Doria08/2016
9092^840203-21252927Stefano Morozzi07/2022
91011^242579-60252620Enzo Doria10/2012
91145^152659+2252378Robert Price09/2015
912(95^127583+1)/96252322Paul Bourdelais07/2019
9137*10^252209-17252210Robert Price12/2022
9142^837725+1869377252181Enzo Doria05/2016
9152^837536-311039252124Enzo Doria06/2015
91621^190632-2252058Robert Price07/2015
9172^837242+1873297252035Enzo Doria06/2016
9182^836656-2787929251859Enzo Doria11/2015
9192^836380+1875541251776Enzo Doria07/2016
920(359^98327-1)/358251233Alexander Zhirkov11/2017
921tau(41^28288)250924Nik Lygeros / Olivier Rozier10/2013
9222^832511-461197250611Enzo Doria07/2015
9232^832505+1881137250609Enzo Doria11/2016
9242^832363+583295250567Enzo Doria12/2016
9252^832244-403635250531Enzo Doria01/2014
926(14*10^250336-41)/9250337Serge Batalov01/2023
9272^831157+1880657250204Enzo Doria11/2016
9282^831088-7200899250183Enzo Doria01/2015
9292^830956-1349250143Yves Minet07/2015
9302^830037+282317249867Enzo Doria09/2016
9312^829589-113653249732Enzo Doria09/2014
932(4*10^249550-7)/3249551Serge Batalov01/2023
9332^828281-3193249338Yves Minet08/2016
934(2^828140-19)/3249295Stefano Morozzi08/2022
9352^828064-2785619249273Enzo Doria10/2015
9362^827602+60409249134Enzo Doria03/2016
93710^249010+348861249011Patrick De Geest04/2016
93810^249010-21249010Serge Batalov12/2014
9392^826733+1882907248872Enzo Doria12/2016
9402^825682+1876549248556Enzo Doria07/2016
9412^824991-114121248348Enzo Doria12/2014
9422^824642-362727248242Enzo Doria12/2013
9432^824565-114265248219Enzo Doria01/2015
944(73*10^248145-1)/9248146Robert Price01/2015
945(2^823337+1)/(3*362268281)247841Gord Palameta08/2018
946(2^822971-1)/6583769/28211445881/21255852651726486149207247700Robert Kinser09/2016
9472^822296+76501247536Enzo Doria05/2016
9482^821590-114167247324Enzo Doria12/2014
9492^821512-2790659247300Enzo Doria12/2015
9502^820077+382847246868Enzo Doria11/2016
9512^820001+81269246845Enzo Doria07/2016
9522^819463-59197246683Enzo Doria10/2015
9532^819296+80581246633Enzo Doria07/2016
9542^817160-350369245990Enzo Doria06/2015
9552^816039-19245653Stefano Morozzi07/2022
956(71*10^245558-17)/9245559Serge Batalov01/2023
95788093#+(653879#)/(88093#)245374Makoto Morimoto11/2017
9582^815111-113857245373Enzo Doria10/2014
9592^814914-4001245314Yves Minet05/2017
960846^83761-845^83761245200Jean-Louis Charton12/2012
9612^814356-2790449245146Enzo Doria12/2015
9622^814276-459029245122Enzo Doria04/2015
9632^814023+180923245046Enzo Doria07/2016
964(3^513059-2^513059)/(1026119*5430216457)244776Mike Oakes03/2017
9653^513007+16244767Robert Price04/2020
9662^811842-113675244389Enzo Doria09/2014
9672^811132-2787929244176Enzo Doria11/2015
9682^809746-2790971243758Enzo Doria01/2016
9692^808767-3295243464Yves Minet12/2016
9702^808621-113809243420Enzo Doria09/2014
9712^807724+1879621243150Enzo Doria09/2016
9722*10^242822-91242823Robert Price02/2023
97320^186554-3242713Paul Bourdelais12/2020
9742^805843-113611242583Enzo Doria08/2014
9752^805745-459763242554Enzo Doria05/2015
9762^805353+782687242436Enzo Doria11/2016
9776^311257+5242206Paul Bourdelais02/2021
9782^804277-417933242112Enzo Doria01/2014
9792^803468-269039241868Enzo Doria10/2013
9802^803172+80851241779Enzo Doria07/2016
9813^506233-2241535Robert Price11/2013
9822^802025-25999241434Enzo Doria10/2013
983(3^505823+3^252912+1)/7241339Serge Batalov03/2014
9842^801303+1872923241217Enzo Doria05/2016
9852^800579-1862947240999Enzo Doria12/2015
9863^504206+2240568Luke W. Richards03/2018
9872^798973-26283240515Enzo Doria10/2013
9882^798671-69487240424Enzo Doria12/2015
9892^797220+79831239988Enzo Doria06/2016
9902^796910-26001239894Enzo Doria10/2013
9912^796598+653119239800Enzo Doria12/2016
9922^796432-1859729239750Enzo Doria11/2015
9932^796002-1852211239621Enzo Doria08/2015
9942^795709+75767239533Enzo Doria04/2016
9952^795708+81721239532Enzo Doria08/2016
9962^795468-2786249239460Enzo Doria10/2015
9972^795442+80779239452Enzo Doria07/2016
9982^795075-1852057239342Enzo Doria08/2015
999(86^123677+1)/87239252Paul Bourdelais01/2019
10002^794043+1875023239031Enzo Doria06/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 20 2023 09:01 (Time in France)

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