PRP Records

Probable Primes Top 10000

(271000 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 ?
600110^90358+10464190359Patrick De Geest07/2019
60042*6^116118+790358Lelio R Paula10/2014
600310^90358-497990358Patrick De Geest11/2018
600210^90357+11283790358Patrick De Geest07/2019
600510^90357-18959390357Patrick De Geest07/2019
600610^90356+5311390357Patrick De Geest07/2019
600710^90356-719790356Patrick De Geest11/2018
600810^90353+60321190354Patrick De Geest07/2019
600910^90353-108990353Patrick De Geest11/2018
6010(24737*2^300101+1)/2590343Lelio R Paula06/2014
60114*10^90334-2190335Robert Price04/2016
6012(4546^24697-1)/454590329Serge Batalov08/2020
601310^90322+13769190323Patrick De Geest07/2019
601410^90322-955190322Patrick De Geest11/2018
601510^90316+999190317Patrick De Geest11/2018
6016(4550^24691-1)/454990317Serge Batalov08/2020
601710^90316-4562790316Patrick De Geest07/2019
601810^90315+3288990316Patrick De Geest07/2019
60202^300019-11033590315Enzo Doria05/2014
601910^90315-856190315Patrick De Geest11/2018
6021FAB2(300001,5032)90310Robert Price05/2019
6022FAB2(300001,29405)90310Robert Price05/2019
6023(2^299965+2774)/290299Stefano Morozzi01/2020
602423679^6506+6506^2367990296Hans Havermann08/2020
60252^299949-100590294Lelio R Paula11/2013
6026(2^299947+2054)/290293Stefano Morozzi01/2020
602721740^14229+14229^2174090291Hans Havermann08/2020
602810^90279+6245790280Patrick De Geest07/2019
602910^90279-155190279Patrick De Geest09/2018
6030(2^299892+1986)/290277Stefano Morozzi01/2020
6031(2^299893+3866)/290277Stefano Morozzi01/2020
60322^299868-10961390270Enzo Doria04/2014
603310^90259+35929990260Patrick De Geest07/2019
603410^90259-944390259Patrick De Geest09/2018
6035(2^299831+3786)/290258Stefano Morozzi01/2020
603610^90252+10287390253Patrick De Geest07/2019
603710^90252-810390252Patrick De Geest09/2018
60395*2^299799-390250Lelio R Paula08/2014
6038(2^299803+3326)/290250Stefano Morozzi01/2020
604013^81008-290239Lelio R Paula09/2013
604180697!4-25690234Robert Price11/2019
604364^49957-63^4995790232Robert Price07/2013
6042(2^299745+2994)/290232Stefano Morozzi01/2020
604410^90227+5628190228Patrick De Geest06/2016
60472^299725+31590227Lelio R Paula11/2013
604510^90227-100000000190227Robert Price05/2016
604610^90227-6876390227Patrick De Geest06/2016
60485^129082+4890225Lelio R Paula03/2016
60492^299699+19590219Lelio R Paula10/2012
6050(55*10^90211-1)/990212Ray Chandler02/2012
605122131^11918+11918^2213190211Hans Havermann08/2020
605210^90209+897190210Patrick De Geest09/2018
605310^90209-72479790209Patrick De Geest07/2019
605410^90208+18953190209Patrick De Geest07/2019
605510^90208-224790208Patrick De Geest09/2018
6056(629^32233-1)/62890207Michael Stocker05/2020
6057116^43693-11590203Norbert Schneider08/2018
605810^90202+355390203Patrick De Geest09/2018
60603^189053+28090202Lelio R Paula04/2016
605910^90202-6779390202Patrick De Geest07/2019
60612^299639-18790201Lelio R Paula10/2012
606210^90199+25403190200Patrick De Geest07/2019
606310^90199-289190199Patrick De Geest09/2018
60652^299631+18390198Lelio R Paula10/2012
606421567^15212+15212^2156790198Hans Havermann08/2020
606610^90196+18753990197Patrick De Geest07/2019
606810^90196-968390196Patrick De Geest09/2018
606721708^14287+14287^2170890196Hans Havermann08/2020
606910^90193+10497390194Patrick De Geest07/2019
607010^90193-980990193Patrick De Geest09/2018
6071(21*2^299611-1)/2990192Lelio R Paula02/2014
6072(2277^26863-1)/227690186Serge Batalov08/2020
60732^299567+11390179Lelio R Paula10/2012
60742^299550+18990174Lelio R Paula10/2012
607510^90170+37606390171Patrick De Geest07/2019
607610^90170-674990170Patrick De Geest09/2018
6077(2^299535+3)/2990168Lelio R Paula01/2013
6078(2^299521+13)/1590164Stefano Morozzi03/2020
607922316^10971+10971^2231690163Hans Havermann08/2020
608010^90160+27194790161Patrick De Geest07/2019
608110^90160-561390160Patrick De Geest09/2018
6082(97*10^90155-1)/390157Serge Batalov12/2014
60843^188938+868090147Lelio R Paula04/2016
608310^90146+16020990147Patrick De Geest07/2019
608510^90146-202790146Patrick De Geest09/2018
60866^115840-5590142Lelio R Paula05/2016
6087(5*10^90142-473)/990142Robert Price12/2017
60888*7^106659+590139Lelio R Paula10/2014
60912^299406-1665390131Enzo Doria05/2013
6089(317057^16384+1)/290131Richard Fischer10/2019
6090(2^299409+834)/290131Stefano Morozzi01/2020
609210^90128+28867390129Patrick De Geest07/2019
6094208049#+(216091#)/(208049#)90128Makoto Morimoto04/2016
609310^90128-838790128Patrick De Geest09/2018
6095(F(5)^128941-F(4)^128941)/F(3)90126Wayne Halsdorf03/2012
60966^115819-5390125Lelio R Paula05/2016
609710^90123+631390124Patrick De Geest09/2018
60996^115816-1685390123Enzo Doria02/2013
609810^90123-2261790123Patrick De Geest07/2019
61006^115813-2390121Lelio R Paula05/2016
6101(22*10^90110+161)/390111Robert Price02/2017
6103(2^299330-509203)/6990106Lelio R Paula01/2013
610210^90105+91575990106Patrick De Geest07/2019
610510^90105-76790105Patrick De Geest09/2018
610410^90104+4818990105Patrick De Geest07/2019
6106(6050^23827-1)/604990105Serge Batalov08/2020
610710^90104-770390104Patrick De Geest09/2018
610810^90103+915990104Patrick De Geest09/2018
610910^90103-20845790103Patrick De Geest07/2019
611010^90102+7301190103Patrick De Geest07/2019
611110^90102-60243390102Patrick De Geest07/2019
611210^90101+122553790102Patrick De Geest07/2019
611310^90101-320790101Patrick De Geest09/2018
611421730^14007+14007^2173090101Hans Havermann08/2020
6115(29*10^90096-17)/390097Erik Branger09/2014
611610^90089+14318190090Patrick De Geest07/2019
611710^90089-357390089Patrick De Geest09/2018
61182^299247+187052990083Enzo Doria05/2016
611910^90079+160990080Patrick De Geest09/2018
612010^90079-23004390079Patrick De Geest07/2019
61212^299229-279778390077Enzo Doria04/2016
61222^299220-1631790075Enzo Doria04/2013
612311^86491-135090072Enzo Doria12/2012
612410^90071+5233390072Patrick De Geest07/2019
612610^90071-123390071Patrick De Geest09/2018
6125(314401^16384+1)/290071Richard Fischer10/2019
612710^90069+15852790070Patrick De Geest07/2019
612810^90069-784190069Patrick De Geest09/2018
6129(31*10^90064-1)/390066Robert Price03/2017
613010^90060+14943190061Patrick De Geest07/2019
613110^90060-83990060Patrick De Geest09/2018
613210^90052+236190053Patrick De Geest09/2018
613310^90052-9092990052Patrick De Geest07/2019
613410^90047+61990048Patrick De Geest09/2018
613510^90047-15107190047Patrick De Geest07/2019
6136L(430949)/861899/144038756153990045Serge Batalov07/2017
613722996^8233+8233^2299690043Hans Havermann08/2020
61382^299112+7395190042Enzo Doria04/2016
61398^99702+7^(99702-1)90040Robert Price02/2016
614010^90038+15780390039Patrick De Geest07/2019
614110^90038-968790038Patrick De Geest09/2018
61435*10^90033+390034Dmitry Domanov11/2010
6142(17574^21211-1)/1757390034Serge Batalov08/2020
614410^90030+22581390031Patrick De Geest07/2019
614510^90030-146190030Patrick De Geest09/2018
6146243^37738+37738^24390029Norbert Schneider01/2015
614710^90025+7056990026Patrick De Geest07/2019
614810^90025-870390025Patrick De Geest09/2018
61492^299048-11329790023Enzo Doria07/2014
615010^90015+84990016Patrick De Geest09/2018
615110^90015-22838790015Patrick De Geest07/2019
615210^90010+681190011Patrick De Geest09/2018
615310^90010-18359790010Patrick De Geest11/2018
615410^90009+5832190010Patrick De Geest11/2018
615510^90008+84790009Patrick De Geest09/2018
615610^90009-35601390009Patrick De Geest11/2018
615725696^3183+3183^2569690009Hans Havermann08/2020
61583^188648+9290008Lelio R Paula12/2015
615910^90008-70604990008Patrick De Geest11/2018
61605*2^298991+790006Lelio R Paula08/2014
6161(25*2^298997+1)/326790005Lelio R Paula01/2013
616210^90000+886990001Patrick De Geest12/2009
616410^89999+8293990000Dirk Augustin04/2007
616310^90000-14034390000Patrick De Geest12/2009
616510^89999-19489189999Patrick De Geest11/2009
6166(2^298918+1798)/289983Stefano Morozzi01/2020
616719^70365-7889980Lelio R Paula12/2015
6168NaturalLogarithmOf2(89973)89973Eric W. Weisstein10/2015
61692^298852-6487589964Lelio R Paula11/2013
6170(2^298825+1010)/289955Stefano Morozzi01/2020
617118^71659+3789952Lelio R Paula12/2015
6172(2908*29^61501-3)/789942Curtis Bright05/2015
6173(2^298769+1202)/289939Stefano Morozzi01/2020
6174(5941^23827-1)/594089916Serge Batalov08/2020
617517^73067+2089906Lelio R Paula11/2015
61762^298637-9989899Lelio R Paula10/2012
617725513^3336+3336^2551389889Hans Havermann08/2020
617829748^1051+1051^2974889887Hans Havermann08/2020
61799^94188+3*8^94188-2*4^94188-3*2^9418889879Mike Oakes01/2011
6180(2^298558+3654)/289875Stefano Morozzi01/2020
61819*10^89858+1989859Robert Price05/2016
61822^298501+187006789858Enzo Doria05/2016
618311^86280-9889852Lelio R Paula11/2015
61842^298473-11005989850Enzo Doria04/2014
618519^70263-3289850Lelio R Paula12/2015
618621208^17221+17221^2120889839Hans Havermann08/2020
6187(299*10^89836-17)/389838Robert Price01/2017
61883^188286+1489836Robert Price09/2013
6189(2^298408+450)/289830Stefano Morozzi01/2020
6190gcd(V(1091095),5*F(218219)*(F(218219)+1)+1)89822Serge Batalov04/2015
61912^298367+5890589818Lelio R Paula11/2013
619221966^12269+12269^2196689815Hans Havermann08/2020
6193(2^298333+3126)/289807Stefano Morozzi01/2020
61942^298319-10965789803Enzo Doria04/2014
61958*10^89800+8189801Robert Price05/2017
619621354^16037+16037^2135489797Hans Havermann08/2020
6197(2^298249+714)/289782Stefano Morozzi01/2020
619821227^16954+16954^2122789775Hans Havermann08/2020
6199(733^31333-1)/73289770Serge Batalov08/2020
620218^71505-9189759Lelio R Paula12/2015
6200(2^298171+1586)/289759Stefano Morozzi01/2020
6201(4788^24391-1)/478789759Serge Batalov08/2020
6203(2^298161+3530)/289756Stefano Morozzi01/2020
6204(7^106187+1)/889738Paul Bourdelais04/2008
62052^298079-10953189731Enzo Doria04/2014
6206(9255^22621-1)/925489720Serge Batalov08/2020
6207117^43380+11689718Norbert Schneider08/2018
6208(22699*2^298016+1)/38589714Lelio R Paula06/2014
6209156*(10^(4*22427)-1)/101-189709Robert Price05/2014
62102^298003-6694589708Lelio R Paula11/2013
6211(23*10^89705-83)/389706Robert Price09/2017
621217^72900-5489700Lelio R Paula11/2015
6213(2^297968+2482)/289698Stefano Morozzi01/2020
62143*2^297956+589695Lelio R Paula08/2014
6215(2^297952+3558)/289693Stefano Morozzi01/2020
6216(3992^24907-1)/399189692Serge Batalov08/2020
621720^68938-1189691Lelio R Paula01/2016
621889*10^89687-789689Robert Price03/2017
6219(6882^23371-1)/688189688Serge Batalov08/2020
6220(297847^16384+1)/289686Richard Fischer08/2019
62212^297923+7778389684Enzo Doria05/2016
6222(2^297893+1694)/289675Stefano Morozzi01/2020
622311^86107-2457600089672Enzo Doria02/2013
62242^297878-11191189671Enzo Doria05/2014
622520823^20236+20236^2082389667Hans Havermann08/2020
622625708^3075+3075^2570889666Hans Havermann08/2020
622721002^18585+18585^2100289661Hans Havermann08/2020
6228(2^297830+3670)/289656Stefano Morozzi01/2020
62297^106084+4089652Lelio R Paula10/2015
6230(2^297815+618)/289651Stefano Morozzi01/2020
623121223^16752+16752^2122389648Hans Havermann08/2020
6233(86*10^89640-311)/989641Robert Price10/2017
6232(2^297781+2094)/289641Stefano Morozzi01/2020
6234(2^297741+3326)/289629Stefano Morozzi01/2020
6235(2^297724+3606)/289624Stefano Morozzi01/2020
62363*10^89608-5989609Robert Price10/2017
6237(2^297650+3250)/289602Stefano Morozzi01/2020
62383^187780-1103889594Enzo Doria05/2014
6239(13*2^297560-1)/4915178789568Lelio R Paula02/2014
62405^128141-3689567Lelio R Paula10/2015
62414*7^105951+989540Lelio R Paula10/2014
6242(7*10^89539-439)/989539Robert Price09/2017
6243(9772^22441-1)/977189536Serge Batalov08/2020
624422823^8374+8374^2282389534Hans Havermann08/2020
6245(2^297401+2954)/289527Stefano Morozzi01/2020
6246(2^297403+1670)/289527Stefano Morozzi01/2020
62472^297397+17725789526Enzo Doria05/2016
62492^297346-1624189511Enzo Doria04/2013
6248(5*10^89510+79)/389511Robert Price11/2017
62504^148663-3^14866389505Jean-Louis Charton11/2005


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2020 00:24 (Time in France)

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