PRP Records

Probable Primes Top 10000

(288949 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 ?
80012^299868-10961390270Enzo Doria04/2014
800210^90259+35929990260Patrick De Geest07/2019
800310^90259-944390259Patrick De Geest09/2018
8004(2^299831+3786)/290258Stefano Morozzi01/2020
800510^90252+10287390253Patrick De Geest07/2019
800610^90252-810390252Patrick De Geest09/2018
80075*2^299799-390250Lelio R Paula08/2014
8008(2^299803+3326)/290250Stefano Morozzi01/2020
800913^81008-290239Lelio R Paula09/2013
801080697!4-25690234Robert Price11/2019
801264^49957-63^4995790232Robert Price07/2013
8011(2^299745+2994)/290232Stefano Morozzi01/2020
801310^90227+5628190228Patrick De Geest06/2016
80162^299725+31590227Lelio R Paula11/2013
801410^90227-100000000190227Robert Price05/2016
801510^90227-6876390227Patrick De Geest06/2016
80175^129082+4890225Lelio R Paula03/2016
80182^299699+19590219Lelio R Paula10/2012
8019(55*10^90211-1)/990212Ray Chandler02/2012
802022131^11918+11918^2213190211Hans Havermann08/2020
802110^90209+897190210Patrick De Geest09/2018
802210^90209-72479790209Patrick De Geest07/2019
802310^90208+18953190209Patrick De Geest07/2019
802410^90208-224790208Patrick De Geest09/2018
8025(629^32233-1)/62890207Michael Stocker05/2020
8026116^43693-11590203Norbert Schneider08/2018
802710^90202+355390203Patrick De Geest09/2018
80283^189053+28090202Lelio R Paula04/2016
802910^90202-6779390202Patrick De Geest07/2019
80302^299639-18790201Lelio R Paula10/2012
803110^90199+25403190200Patrick De Geest07/2019
803210^90199-289190199Patrick De Geest09/2018
80332^299631+18390198Lelio R Paula10/2012
803421567^15212+15212^2156790198Hans Havermann08/2020
803510^90196+18753990197Patrick De Geest07/2019
803710^90196-968390196Patrick De Geest09/2018
803621708^14287+14287^2170890196Hans Havermann08/2020
803810^90193+10497390194Patrick De Geest07/2019
803910^90193-980990193Patrick De Geest09/2018
8040(21*2^299611-1)/2990192Lelio R Paula02/2014
8041(2277^26863-1)/227690186Serge Batalov08/2020
80422^299567+11390179Lelio R Paula10/2012
80432^299550+18990174Lelio R Paula10/2012
804410^90170+37606390171Patrick De Geest07/2019
804510^90170-674990170Patrick De Geest09/2018
8046(2^299535+3)/2990168Lelio R Paula01/2013
8047(2^299521+13)/1590164Stefano Morozzi03/2020
804822316^10971+10971^2231690163Hans Havermann08/2020
804910^90160+27194790161Patrick De Geest07/2019
805010^90160-561390160Patrick De Geest09/2018
8051(97*10^90155-1)/390157Serge Batalov12/2014
8052(29*10^90153+583)/990154Robert Price06/2021
80543^188938+868090147Lelio R Paula04/2016
805310^90146+16020990147Patrick De Geest07/2019
805510^90146-202790146Patrick De Geest09/2018
80566^115840-5590142Lelio R Paula05/2016
8057(5*10^90142-473)/990142Robert Price12/2017
80588*7^106659+590139Lelio R Paula10/2014
80592^299406-1665390131Enzo Doria05/2013
8060(317057^16384+1)/290131Richard Fischer10/2019
8061(2^299409+834)/290131Stefano Morozzi01/2020
806210^90128+28867390129Patrick De Geest07/2019
8064208049#+(216091#)/(208049#)90128Makoto Morimoto04/2016
806310^90128-838790128Patrick De Geest09/2018
8065(F(5)^128941-F(4)^128941)/F(3)90126Wayne Halsdorf03/2012
80666^115819-5390125Lelio R Paula05/2016
806710^90123+631390124Patrick De Geest09/2018
80696^115816-1685390123Enzo Doria02/2013
806810^90123-2261790123Patrick De Geest07/2019
80706^115813-2390121Lelio R Paula05/2016
80712^299351-93307590114Paul Bourdelais04/2021
8072(22*10^90110+161)/390111Robert Price02/2017
8073(2^299330-509203)/6990106Lelio R Paula01/2013
807410^90105+91575990106Patrick De Geest07/2019
807710^90105-76790105Patrick De Geest09/2018
807510^90104+4818990105Patrick De Geest07/2019
8076(6050^23827-1)/604990105Serge Batalov08/2020
807810^90104-770390104Patrick De Geest09/2018
807910^90103+915990104Patrick De Geest09/2018
8080(797*10^90102-23)/990104Robert Price01/2022
808110^90103-20845790103Patrick De Geest07/2019
808210^90102+7301190103Patrick De Geest07/2019
808310^90102-60243390102Patrick De Geest07/2019
808410^90101+122553790102Patrick De Geest07/2019
808610^90101-320790101Patrick De Geest09/2018
808521730^14007+14007^2173090101Hans Havermann08/2020
8087(29*10^90096-17)/390097Erik Branger09/2014
808810^90089+14318190090Patrick De Geest07/2019
808910^90089-357390089Patrick De Geest09/2018
80902^299247+187052990083Enzo Doria05/2016
809110^90079+160990080Patrick De Geest09/2018
809210^90079-23004390079Patrick De Geest07/2019
80932^299229-279778390077Enzo Doria04/2016
80942^299220-1631790075Enzo Doria04/2013
809511^86491-135090072Enzo Doria12/2012
809610^90071+5233390072Patrick De Geest07/2019
809810^90071-123390071Patrick De Geest09/2018
8097(314401^16384+1)/290071Richard Fischer10/2019
809910^90069+15852790070Patrick De Geest07/2019
810010^90069-784190069Patrick De Geest09/2018
8101(31*10^90064-1)/390066Robert Price03/2017
810210^90060+14943190061Patrick De Geest07/2019
810310^90060-83990060Patrick De Geest09/2018
810410^90052+236190053Patrick De Geest09/2018
810510^90052-9092990052Patrick De Geest07/2019
810610^90047+61990048Patrick De Geest09/2018
810710^90047-15107190047Patrick De Geest07/2019
8108L(430949)/861899/144038756153990045Serge Batalov07/2017
810922996^8233+8233^2299690043Hans Havermann08/2020
81102^299112+7395190042Enzo Doria04/2016
81118^99702+7^(99702-1)90040Robert Price02/2016
811210^90038+15780390039Patrick De Geest07/2019
811310^90038-968790038Patrick De Geest09/2018
81145*10^90033+390034Dmitry Domanov11/2010
8115(17574^21211-1)/1757390034Serge Batalov08/2020
811610^90030+22581390031Patrick De Geest07/2019
811710^90030-146190030Patrick De Geest09/2018
8118243^37738+37738^24390029Norbert Schneider01/2015
811910^90025+7056990026Patrick De Geest07/2019
812010^90025-870390025Patrick De Geest09/2018
81212^299048-11329790023Enzo Doria07/2014
812210^90015+84990016Patrick De Geest09/2018
812310^90015-22838790015Patrick De Geest07/2019
812410^90010+681190011Patrick De Geest09/2018
812510^90010-18359790010Patrick De Geest11/2018
812610^90009+5832190010Patrick De Geest11/2018
812710^90008+84790009Patrick De Geest09/2018
812810^90009-35601390009Patrick De Geest11/2018
812925696^3183+3183^2569690009Hans Havermann08/2020
81313^188648+9290008Lelio R Paula12/2015
813010^90008-70604990008Patrick De Geest11/2018
81325*2^298991+790006Lelio R Paula08/2014
8133(25*2^298997+1)/326790005Lelio R Paula01/2013
813410^90000+886990001Patrick De Geest12/2009
813610^89999+8293990000Dirk Augustin04/2007
813510^90000-14034390000Patrick De Geest12/2009
813710^89999-19489189999Patrick De Geest11/2009
8138(2^298918+1798)/289983Stefano Morozzi01/2020
813919^70365-7889980Lelio R Paula12/2015
8140Phi(186062,10)/13460963248300334700445189977Makoto Kamada04/2021
8141NaturalLogarithmOf2(89973)89973Eric W. Weisstein10/2015
81422^298852-6487589964Lelio R Paula11/2013
8143(2^298825+1010)/289955Stefano Morozzi01/2020
814418^71659+3789952Lelio R Paula12/2015
8145(2908*29^61501-3)/789942Curtis Bright05/2015
8146(2^298769+1202)/289939Stefano Morozzi01/2020
8147(5941^23827-1)/594089916Serge Batalov08/2020
814817^73067+2089906Lelio R Paula11/2015
81492^298637-9989899Lelio R Paula10/2012
815025513^3336+3336^2551389889Hans Havermann08/2020
815129748^1051+1051^2974889887Hans Havermann08/2020
81529*10^89882-9189883Robert Price06/2021
81539^94188+3*8^94188-2*4^94188-3*2^9418889879Mike Oakes01/2011
81542*10^89876+8389877Robert Price12/2021
8155(2^298558+3654)/289875Stefano Morozzi01/2020
81569*10^89858+1989859Robert Price05/2016
81572^298501+187006789858Enzo Doria05/2016
8158(286*10^89852-1)/389854Robert Price11/2020
815911^86280-9889852Lelio R Paula11/2015
81602^298473-11005989850Enzo Doria04/2014
816119^70263-3289850Lelio R Paula12/2015
816221208^17221+17221^2120889839Hans Havermann08/2020
8163(299*10^89836-17)/389838Robert Price01/2017
81643^188286+1489836Robert Price09/2013
8165(2^298408+450)/289830Stefano Morozzi01/2020
8166gcd(V(1091095),5*F(218219)*(F(218219)+1)+1)89822Serge Batalov04/2015
81672^298367+5890589818Lelio R Paula11/2013
816821966^12269+12269^2196689815Hans Havermann08/2020
8169(2^298333+3126)/289807Stefano Morozzi01/2020
81702^298319-10965789803Enzo Doria04/2014
81717*10^89801+1389802Robert Price03/2021
81728*10^89800+8189801Robert Price05/2017
817321354^16037+16037^2135489797Hans Havermann08/2020
8174(2^298249+714)/289782Stefano Morozzi01/2020
817521227^16954+16954^2122789775Hans Havermann08/2020
8176(733^31333-1)/73289770Serge Batalov08/2020
817918^71505-9189759Lelio R Paula12/2015
8177(2^298171+1586)/289759Stefano Morozzi01/2020
8178(4788^24391-1)/478789759Serge Batalov08/2020
8180(2^298161+3530)/289756Stefano Morozzi01/2020
8181(7^106187+1)/889738Paul Bourdelais04/2008
81822^298079-10953189731Enzo Doria04/2014
8183(9255^22621-1)/925489720Serge Batalov08/2020
8184117^43380+11689718Norbert Schneider08/2018
8185(22699*2^298016+1)/38589714Lelio R Paula06/2014
8186156*(10^(4*22427)-1)/101-189709Robert Price05/2014
81872^298003-6694589708Lelio R Paula11/2013
8188(23*10^89705-83)/389706Robert Price09/2017
818917^72900-5489700Lelio R Paula11/2015
8190(2^297968+2482)/289698Stefano Morozzi01/2020
81913*2^297956+589695Lelio R Paula08/2014
8192(2^297952+3558)/289693Stefano Morozzi01/2020
8193(3992^24907-1)/399189692Serge Batalov08/2020
819420^68938-1189691Lelio R Paula01/2016
819589*10^89687-789689Robert Price03/2017
8196(6882^23371-1)/688189688Serge Batalov08/2020
8197(297847^16384+1)/289686Richard Fischer08/2019
81982^297923+7778389684Enzo Doria05/2016
8199(2^297893+1694)/289675Stefano Morozzi01/2020
820011^86107-2457600089672Enzo Doria02/2013
82012^297878-11191189671Enzo Doria05/2014
820220823^20236+20236^2082389667Hans Havermann08/2020
820325708^3075+3075^2570889666Hans Havermann08/2020
820421002^18585+18585^2100289661Hans Havermann08/2020
8205(2^297830+3670)/289656Stefano Morozzi01/2020
82067^106084+4089652Lelio R Paula10/2015
8207(2^297815+618)/289651Stefano Morozzi01/2020
820821223^16752+16752^2122389648Hans Havermann08/2020
8210(86*10^89640-311)/989641Robert Price10/2017
8209(2^297781+2094)/289641Stefano Morozzi01/2020
8211(2^297741+3326)/289629Stefano Morozzi01/2020
8212(2^297724+3606)/289624Stefano Morozzi01/2020
82133*10^89608-5989609Robert Price10/2017
8214(2^297650+3250)/289602Stefano Morozzi01/2020
8215(34*10^89599+191)/989600Robert Price08/2021
82163^187780-1103889594Enzo Doria05/2014
8217(13*2^297560-1)/4915178789568Lelio R Paula02/2014
82185^128141-3689567Lelio R Paula10/2015
82194*7^105951+989540Lelio R Paula10/2014
8220(7*10^89539-439)/989539Robert Price09/2017
8221(9772^22441-1)/977189536Serge Batalov08/2020
822222823^8374+8374^2282389534Hans Havermann08/2020
8223(2^297401+2954)/289527Stefano Morozzi01/2020
8224(2^297403+1670)/289527Stefano Morozzi01/2020
82252^297397+17725789526Enzo Doria05/2016
8226(77*10^89518+247)/989519Robert Price03/2021
82272^297346-1624189511Enzo Doria04/2013
8228(5*10^89510+79)/389511Robert Price11/2017
82304^148663-3^14866389505Jean-Louis Charton11/2005
82292^297328-86968810589505Lelio R Paula07/2016
82312^297325-45904389504Enzo Doria05/2015
82322^297310-11239189500Enzo Doria06/2014
82332^297296-11215789496Enzo Doria06/2014
823457^50966-289490Lelio R Paula08/2013
8235(266*10^89482+1)/389484Robert Price02/2016
8236(14*10^89480-101)/389481Robert Price04/2017
82372618^26175+26175^261889466Norbert Schneider01/2020
8238(2^297150+3922)/289451Stefano Morozzi01/2020
8239(2^297141+1842)/289449Stefano Morozzi01/2020
8240(2^297140+1458)/289448Stefano Morozzi01/2020
8241(2^297129+726)/289445Stefano Morozzi01/2020
82422^297122+9989443Lelio R Paula10/2012
8243(3^187435-5)/128689427Lelio R Paula01/2013
8244(28*10^89425+101)/389426Robert Price09/2020
8245(2^297037+3522)/289417Stefano Morozzi01/2020
8246(25*10^89413+161)/389414Robert Price01/2017
8247(89*10^89411-737)/989412Robert Price01/2022
824829080^1187+1187^2908089406Hans Havermann08/2020
82492^296990+187069989403Enzo Doria05/2016
82502^296972-101789398Lelio R Paula11/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 19 2022 17:15 (Time in France)

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