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 ?
900123277^12058+12058^2327795000Hans Havermann09/2020
90021*10^94983+2194984Robert Price03/2011
900310^94983-71794983Patrick De Geest08/2013
900417^77187-8294975Lelio R Paula07/2016
90053*10^94964+3794965Robert Price10/2017
9006(2^315481-1017)/2062728594962Lelio R Paula06/2013
90072^315423-11032994952Enzo Doria05/2014
900811^91169-723094943Enzo Doria02/2013
90097*10^94938+6194939Robert Price02/2017
90102^315351+102594931Lelio R Paula03/2016
90112^315350-11225394930Enzo Doria06/2014
9012(2^315343+1766)/294928Stefano Morozzi09/2020
9013(2^315343+3066)/294928Stefano Morozzi09/2020
9016((1001327^(15817)+1)/1001328)94906Faysal YAtim10/2010
90152^315268+794906Lelio R Paula10/2012
901411^91133+6294906Lelio R Paula05/2016
9017(2^315264+1558)/294904Stefano Morozzi09/2020
901830^64244+4194897Lelio R Paula08/2012
9019(151*10^94885-7)/994887Robert Price07/2017
90204^157583+2214794875Mike Oakes01/2011
90212^315098+12394854Lelio R Paula11/2012
90223^198791-3494848Robert Price11/2013
90233*2^315067+794846Lelio R Paula08/2014
9024(9*2^315057+1)/7394841Lelio R Paula09/2013
902522576^15875+15875^2257694836Hans Havermann09/2020
9026(16*10^94822+53)/394823Robert Price12/2016
90278*6^121849-794818Lelio R Paula10/2014
9028(85*10^94802+473)/994803Robert Price03/2017
902921767^21852-21852^2176794790Norbert Schneider06/2020
90302^314870-10876194786Enzo Doria03/2014
90315*2^314841-394778Lelio R Paula08/2014
9032(2^314842+550)/294777Stefano Morozzi09/2020
903311738^23289-23289^1173894777Norbert Schneider05/2022
9034(2^314787+2630)/294761Stefano Morozzi09/2020
90356^121772+11394758Lelio R Paula05/2016
9036(2^314740+3642)/294746Stefano Morozzi09/2020
90376^121756-1625394745Enzo Doria02/2013
90382^314718-11279394740Enzo Doria06/2014
90392^314697-184729394734Enzo Doria07/2015
904022836^14065+14065^2283694727Hans Havermann09/2020
90422^314548-24994689Yves Minet02/2012
90415^135469+4294689Lelio R Paula04/2016
9043gcd(V(1137755),5*F(227551)*(F(227551)-1)+1)94676Serge Batalov04/2015
904425773^4712+4712^2577394670Hans Havermann08/2020
9045(2^314485+3614)/294670Stefano Morozzi09/2020
9046(2*10^94604+547)/994604Robert Price10/2017
9047(2^314164+2562)/294573Stefano Morozzi09/2020
90483*2^314152+594570Lelio R Paula08/2014
90492*6^121530-594570Lelio R Paula10/2014
90507*10^94563+8794564Robert Price11/2016
90512^314114-10967794558Enzo Doria04/2014
9052(218389#+240867)/(3*11*811)94557Makoto Morimoto10/2017
90532^314059+7658394542Enzo Doria05/2016
90542^314041-403594536Lelio R Paula03/2016
9055(2^314028+3102)/294532Stefano Morozzi09/2020
9056(2^314012+618)/294527Stefano Morozzi09/2020
9057(7*2^314003-11)/1594524Renaud Lifchitz03/2011
905811^90760-471094517Enzo Doria01/2013
905921675^21796+21796^2167594507Norbert Schneider04/2020
90602^313942+10028024506594506Paul Bourdelais10/2021
9061(7*2^313926-1)/14882194497Lelio R Paula02/2014
906294*10^94493-394495Robert Price11/2016
9063(1000547^15749+1)/100054894492Faysal YAtim12/2008
9064(2^313859+2706)/294481Stefano Morozzi09/2020
9065(F(3*75345)^2+L(3*75345)^2)/494477Henri Lifchitz10/2017
90667^111792-3294476Lelio R Paula04/2016
9067(2^313800+822)/294463Stefano Morozzi01/2021
90689*10^94462-4794463Robert Price11/2021
906911*10^94460+394462Robert Price07/2021
9070(202*10^94441-1)/394443Robert Price05/2020
907111^90680-585094434Enzo Doria01/2013
9072(752^32833-1)/75194432Michael Stocker05/2020
90732^313675-11012594426Enzo Doria04/2014
9074(2999*29^64556-2427)/494410Curtis Bright05/2015
90752^313609-11222594406Enzo Doria06/2014
90762^313584+7290194399Enzo Doria04/2016
9077(2^313567+1310)/294393Stefano Morozzi02/2021
9078(2^313562+730)/294392Stefano Morozzi09/2020
90792^313510-11286594376Enzo Doria06/2014
90807*10^94373+8794374Robert Price11/2016
9081(9^98897+8^98897)/1794371Robert Price12/2012
90822^313453-11470394359Enzo Doria04/2015
90838*10^94357-5194358Robert Price10/2017
908425903^4392+4392^2590394356Hans Havermann09/2020
908531706^945+945^3170694340Hans Havermann09/2020
9086(379*10^94337-1)/994339Robert Price08/2017
90872^313344-313344+194326Robert Price10/2014
9088(2^313313+3662)/294317Stefano Morozzi09/2020
908920^72481-4994300Lelio R Paula05/2016
9090(34*10^94293-259)/994294Robert Price12/2021
909144725!2+12894289Robert Price03/2015
90924*10^94286+994287Robert Price05/2015
909317^76621+2494279Lelio R Paula07/2016
909426274^3875+3875^2627494279Hans Havermann09/2020
90954*10^94270-3394271Robert Price04/2021
90962^313156-11285994270Enzo Doria06/2014
9097(49*10^94262-211)/994263Robert Price06/2022
90986^121130-5994258Lelio R Paula05/2016
90993^197542+2894252Robert Price11/2013
9100(2^313076+3550)/294245Stefano Morozzi09/2020
9101(3^197521+2)/5165594237Lelio R Paula04/2013
91022^313045-595594236Lelio R Paula03/2016
910322099^18358+18358^2209994227Hans Havermann08/2020
9104(67*10^94212+23)/994213Ray Chandler02/2011
91052^312909-186520394195Enzo Doria03/2016
910625013^5830+5830^2501394191Hans Havermann09/2020
91072^312848-14994177Lelio R Paula11/2012
9108(2^312819+3278)/294168Stefano Morozzi02/2021
91094^156403-7759794164Mike Oakes04/2011
911018^75004-8594151Lelio R Paula06/2016
911119^73622-4894145Lelio R Paula06/2016
9112(11^90397-3^90397)/894138Robert Price04/2011
9113(3^197287+5)/1694129Lelio R Paula04/2013
9114(23*10^94123-29)/394124Robert Price03/2022
911524220^7691+7691^2422094119Hans Havermann09/2020
911612^87212-3794118Lelio R Paula06/2016
911711^90376+7694117Lelio R Paula05/2016
9118(6^120946-11)/594114Paul Bourdelais11/2011
9119(2^312622+534)/294109Stefano Morozzi09/2020
9120(10^94096+191)/394096Robert Price11/2017
912123794^9005+9005^2379494093Hans Havermann09/2020
91222^312562-11268594091Enzo Doria06/2014
9123137^44026-294072Lelio R Paula10/2017
9124s(164441)94052Robert Price05/2020
91252^312404-86968810594043Lelio R Paula09/2016
91262^312387+279353394038Enzo Doria03/2016
912810^94016+9194017Robert Price04/2011
9127(15*2^312325-1)/720194017Lelio R Paula02/2014
912910^94016-18896394016Patrick De Geest08/2013
9130(17*2^312315-1)/4594016Lelio R Paula02/2014
9131(401*10^94010+13)/994012Robert Price09/2021
913223866^8691+8691^2386694010Hans Havermann08/2020
91336^120802+766194003Mike Oakes04/2011
9134(67607*2^312254+1)/17794001Lelio R Paula06/2014
9135(2^312245+702)/293995Stefano Morozzi09/2020
9136(56*10^93993+493)/993994Robert Price10/2021
9137(11*2^312207+1)/1993984Lelio R Paula09/2013
91382^312201+5193982Lelio R Paula11/2012
9139(4*6^120749+1)/593961Serge Batalov10/2014
9140(781*10^93942-7)/993944Robert Price12/2021
91413^196892+5893942Lelio R Paula05/2016
91422^312060+1891593940Lelio R Paula03/2016
914342^57867-4193933Norbert Schneider08/2018
91448*10^93921+8393922Robert Price11/2021
91452^311992-1620993919Enzo Doria04/2013
9146(85^48677+1)/8693917Paul Bourdelais08/2017
91472^311965-3993911Lelio R Paula11/2012
91482^311920-11168993898Enzo Doria05/2014
9149130^44414+12993889Norbert Schneider01/2019
9150(2^311892+2730)/293889Stefano Morozzi09/2020
91517*10^93887-4793888Robert Price02/2017
91529*10^93878-3793879Robert Price06/2021
9153(28*10^93874+323)/993875Robert Price10/2021
9154(2^311778+1530)/293855Stefano Morozzi09/2020
915512^86965-1393851Lelio R Paula06/2016
915624862^5953+5953^2486293848Hans Havermann09/2020
915722299^16148+16148^2229993837Hans Havermann08/2020
91582^311705+1609593833Lelio R Paula03/2016
9159(2^311701+3002)/293832Stefano Morozzi09/2020
9160norm(Mod(x,x^3-x-1)^768329-1)93831Paul Vanderveen09/2022
91622^311665-8193821Lelio R Paula11/2012
9161(2^311665+2654)/293821Stefano Morozzi09/2020
9163(2^311648+3058)/293816Stefano Morozzi09/2020
9164(2^311639+2738)/293813Stefano Morozzi01/2021
9165730^32761+32761^73093806Norbert Schneider09/2017
916611^90073+9293802Lelio R Paula05/2016
91676*10^93792+4193793Robert Price01/2017
916810^93790+6461193791Patrick De Geest04/2020
9171(2^311580+7)/59132993790Lelio R Paula06/2013
916910^93790-12345678993790Robert Price02/2020
917010^93790-15751793790Patrick De Geest04/2020
9172(49*10^93782+293)/993783Robert Price03/2021
917312^86900-7793781Lelio R Paula06/2016
91742^311508-10976993774Enzo Doria04/2014
91752^311486-185962193767Enzo Doria03/2016
9176Phi(93811,10)/968129521/2109997013/3280113810431/63963778254583193765Kurt Beschorner04/2015
9177(10^93811-1)/(9*968129521*2109997013*3280113810431*639637782545831)93765Gord Palameta10/2018
91782^311471+31146993763Renaud Lifchitz01/2003
9179(88*10^93760-1)/393762Robert Price10/2017
91802^311426+7945993749Enzo Doria06/2016
918121537^21634+21634^2153793745Norbert Schneider04/2020
91822^311409+11154643593744Paul Bourdelais10/2021
9183(2^311360+3078)/293729Stefano Morozzi09/2020
9184(2^311341+2186)/293723Stefano Morozzi09/2020
9185(2^311313+774)/293715Stefano Morozzi09/2020
91872^311294+577593709Lelio R Paula03/2016
918625155^5312+5312^2515593709Hans Havermann09/2020
91882^311252-101793697Lelio R Paula03/2016
91892^311247-11204193695Enzo Doria06/2014
91907*10^93692-8393693Robert Price09/2017
91912^311205-10964593683Enzo Doria04/2014
91925^134027-8493681Lelio R Paula04/2016
9193(2^311148-1017)/55793663Lelio R Paula06/2013
9194(2^311027-2^155514+1)/59362811/2006
919526748^3161+3161^2674893614Hans Havermann08/2020
91963^196192-2893608Robert Price12/2013
9197216091#+26143393606Makoto Morimoto12/2015
91985^133917+6893604Lelio R Paula04/2016
91992^310924-170993598Yves Minet03/2013
920024555^6476+6476^2455593587Hans Havermann08/2020
9201(2^310867+734)/293580Stefano Morozzi09/2020
9202(266*10^93577-11)/393579Robert Price09/2016
9203(16*10^93577+161)/393578Robert Price05/2016
92043^196113-5693570Lelio R Paula04/2016
92052^310806-11034593562Enzo Doria05/2014
92063^196093+8693561Lelio R Paula04/2016
92072^310780-232793555Yves Minet10/2013
920830^63332+4193550Lelio R Paula08/2012
9209(21181*2^310707+1)/2193536Lelio R Paula06/2014
92108*5^133807+793528Lelio R Paula10/2014
92112^310686+819393526Lelio R Paula03/2016
921222681^13282+13282^2268193520Hans Havermann09/2020
92132^310646+6393514Lelio R Paula11/2012
9214(77*10^93508+31)/993509Robert Price10/2015
9215(1000907^15583+1)/100090893499Faysal YAtim04/2009
9216(2*10^93497+7)/993497Erik Branger03/2011
92173^195958-11285293496Enzo Doria07/2014
92182^310583+1638593495Lelio R Paula03/2016
9219(9913*2^310557-1)/3593490Lelio R Paula04/2015
92209*7^110614+293481Lelio R Paula11/2014
9221(19*10^93467+83)/393468Robert Price08/2020
92222^310469-829593461Lelio R Paula03/2016
92232^310459-115993458Yves Minet11/2012
92246^120075-9593437Lelio R Paula05/2016
9225(2^310362+1758)/293428Stefano Morozzi09/2020
9226256*19^73047+993412Eric Chen12/2022
9227148^43041-14793411Norbert Schneider05/2019
92282^310289+9832793407Yves Minet11/2010
922921769^19510+19510^2176993395Hans Havermann08/2020
92302^310217-11314393385Enzo Doria07/2014
92317^110494-6893379Lelio R Paula04/2016
92322^310184-11309393375Enzo Doria07/2014
92332^310180-11041793374Enzo Doria05/2014
9234gcd(V(1124905),5*F(224981)*(F(224981)-1)+1)93372Serge Batalov04/2015
9235(2^310173+3150)/293372Stefano Morozzi09/2020
92363^195669+6893358Lelio R Paula04/2016
923710^93356+9193357Robert Price04/2011
923810^93356-2831393356Patrick De Geest08/2013
9239(85*10^93346+23)/993347Robert Price11/2015
9240(3^195648-5)/315827693342Lelio R Paula04/2013
924110^93333+19106193334Patrick De Geest09/2022
924310^93333-400000193333Robert Price07/2021
924210^93333-4480793333Patrick De Geest09/2022
92443^195556+868093304Lelio R Paula04/2016
92452^309942-10999193302Enzo Doria04/2014
92462^309926-186730193298Enzo Doria03/2016
92472^309924+8595193297Yves Minet03/2011
92482^309896-422993288Yves Minet08/2018
9249(86*10^93263-77)/993264Robert Price05/2016
92506^119836-12593251Lelio R Paula05/2016


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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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