PRP Records

Probable Primes Top 10000

(293016 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 ?
97522^303224+253391280Henri Lifchitz05/2005
9751(2^303226+1830)/291280Stefano Morozzi02/2021
97536^117302+14391279Lelio R Paula05/2016
97543^191306-11288091277Enzo Doria07/2014
9755(10052^22807-1)/1005191276Serge Batalov08/2020
97562^303207+1291591275Lelio R Paula02/2016
97572^303191-11125991270Enzo Doria05/2014
975881539!4+3291267Robert Price09/2019
9759(2^303116+3570)/291247Stefano Morozzi09/2020
976010^91230+9^(91230+1)91231Robert Price08/2016
976110^91230+792191231Patrick De Geest11/2016
976210^91230-91114191230Patrick De Geest11/2016
976310^91229+34879391230Patrick De Geest07/2019
976410^91229-247191229Patrick De Geest01/2019
97662996^26241+26241^299691228Norbert Schneider01/2020
97652^303249-49495391228Harrison Mesh06/2022
976810^91225+527191226Patrick De Geest01/2019
97672816^26445+26445^281691226Norbert Schneider02/2020
97706^117232-1742391225Enzo Doria02/2013
976910^91225-14721991225Patrick De Geest07/2019
97717*10^91215+391216Erik Branger11/2009
977210^91215+23061191216Patrick De Geest07/2019
977310^91215-453991215Patrick De Geest01/2019
9774(2^303007+606)/291214Stefano Morozzi09/2020
97759*10^91212-4791213Robert Price11/2021
9776(2^302998+3102)/291212Stefano Morozzi09/2020
977710^91210+242191211Patrick De Geest01/2019
977810^91210-173791210Patrick De Geest01/2019
977997*10^91205-391207Robert Price01/2017
97802^302979-16118191206Enzo Doria04/2013
9781(166*10^91199-7)/391201Robert Price11/2020
97822^302949+8191197Henri Lifchitz02/2007
978310^91194+20036191195Patrick De Geest07/2019
97854*6^117192-591194Lelio R Paula10/2014
978410^91194-866391194Patrick De Geest01/2019
97862^302918+9991188Lelio R Paula11/2012
978710^91186+26811191187Patrick De Geest07/2019
978810^91186-776391186Patrick De Geest01/2019
978910^91181+55047191182Patrick De Geest07/2019
9790(26*10^91181-83)/391182Robert Price12/2021
979110^91181-136791181Patrick De Geest01/2019
979210^91178+7188391179Patrick De Geest07/2019
979310^91178-471991178Patrick De Geest01/2019
979424686^4935+4935^2468691173Hans Havermann08/2020
979510^91165+304391166Patrick De Geest01/2019
979610^91165-39941391165Patrick De Geest07/2019
9797(19*10^91167+107)/9/11/11/15191164Alfred Reich11/2022
979810^91156+386191157Patrick De Geest01/2019
979910^91156-23149791156Patrick De Geest07/2019
98002^302797+186958791151Enzo Doria05/2016
9801265^37614+37614^26591148Norbert Schneider01/2015
98027^107852+8291146Lelio R Paula04/2016
9803(38*10^91144-11)/991145Robert Price05/2015
9804(55*10^91142+377)/991143Robert Price10/2017
980510^91128+996191129Patrick De Geest01/2019
9807249^38030+38030^24991128Norbert Schneider01/2015
980610^91128-18915391128Patrick De Geest07/2019
9808(2^302718+2814)/291127Stefano Morozzi02/2021
98096^117094-21104991117Mike Oakes05/2011
981021353^18472+18472^2135391103Hans Havermann05/2020
98122^302602-186718191093Enzo Doria03/2016
981110^91092+5612791093Patrick De Geest07/2019
981310^91092-910791092Patrick De Geest01/2019
9814(1017*2^302592-1)/5391091Lelio R Paula04/2015
981515^77445-1691083Lelio R Paula07/2016
981621656^16053+16053^2165691076Hans Havermann05/2020
98172^302505+8191064Henri Lifchitz02/2007
98182^302496-11234991061Enzo Doria06/2014
9819(2^302475+1790)/291054Stefano Morozzi01/2021
982017^73999-7291052Lelio R Paula07/2016
982110^91047+933191048Patrick De Geest01/2019
982210^91047-67116991047Patrick De Geest07/2019
982310^91044+207791045Patrick De Geest01/2019
982410^91044-13635991044Patrick De Geest07/2019
982510^91041+934991042Patrick De Geest01/2019
982610^91041-782391041Patrick De Geest01/2019
982710^91040+407791041Patrick De Geest01/2019
982810^91040-11942191040Patrick De Geest07/2019
982910^91037+276991038Patrick De Geest01/2019
983010^91037-2264991037Patrick De Geest07/2019
9831(16*10^91032+41)/391033Robert Price10/2017
983210^91023+5803991024Patrick De Geest07/2019
983310^91023-647191023Patrick De Geest01/2019
983410^91018+787391019Patrick De Geest01/2019
983510^91018-33317791018Patrick De Geest07/2019
983610^91017+6876791018Patrick De Geest07/2019
983710^91017-42832791017Patrick De Geest07/2019
983810^91016+7311191017Patrick De Geest07/2019
983910^91016-797391016Patrick De Geest01/2019
98401949^27666+27666^194991016Norbert Schneider04/2020
98412^302332+57729457591012Lelio R Paula08/2016
984210^91004+907391005Patrick De Geest01/2019
984310^91004-49151991004Patrick De Geest07/2019
984410^91003+7426991004Patrick De Geest07/2019
984510^91003-390391003Patrick De Geest01/2019
98462^302274+7420990994Enzo Doria04/2016
984710^90991+8114790992Patrick De Geest07/2019
984810^90991-627990991Patrick De Geest01/2019
984910^90983+139390984Patrick De Geest01/2019
985011*10^90982+990984Robert Price08/2020
985110^90983-56238390983Patrick De Geest07/2019
9852(311^36497-1)/31090976Eric Chen09/2017
9853(2^302210+1014)/290974Stefano Morozzi09/2020
9854(3^190668+2)/8990970Lelio R Paula04/2013
98552^302188+9019590968Lelio R Paula02/2016
9856(53*10^90965-71)/990966Robert Price09/2015
985710^90965+57398790966Patrick De Geest07/2019
985810^90965-683390965Patrick De Geest01/2019
985910^90964+4878990965Patrick De Geest07/2019
986010^90964-5210390964Patrick De Geest07/2019
986110^90963+19188990964Patrick De Geest07/2019
986210^90963-365990963Patrick De Geest01/2019
986310^90962+765790963Patrick De Geest01/2019
986410^90962-21563390962Patrick De Geest07/2019
986510^90961+6747190962Patrick De Geest07/2019
986610^90961-21104390961Patrick De Geest07/2019
986710^90960+107211790961Patrick De Geest07/2019
986810^90959+879190960Patrick De Geest01/2019
986910^90960-61065990960Patrick De Geest07/2019
987010^90959-27521390959Patrick De Geest07/2019
9871(2^302129+3110)/290950Stefano Morozzi09/2020
987310^90948+986790949Patrick De Geest01/2019
987221665^15774+15774^2166590949Hans Havermann04/2020
987410^90948-10923990948Patrick De Geest07/2019
98752^302113+7410590946Enzo Doria04/2016
98762^302102-655590942Lelio R Paula02/2016
987710^90930+9522390931Patrick De Geest07/2019
987810^90930-362390930Patrick De Geest01/2019
9879156*(10^(4*22731)-1)/101-190925Robert Price05/2014
98803^190568+3890925Lelio R Paula04/2016
988110^90917+17986390918Patrick De Geest07/2019
988210^90917-669390917Patrick De Geest01/2019
98832^302009-1644990914Enzo Doria04/2013
988410^90908+318190909Patrick De Geest01/2019
988510^90908-13951190908Patrick De Geest07/2019
988610^90904+10694790905Patrick De Geest07/2019
988710^90904-516990904Patrick De Geest01/2019
988810^90903+12096390904Patrick De Geest07/2019
988910^90902+261390903Patrick De Geest01/2019
989010^90903-19073790903Patrick De Geest07/2019
989125174^4083+4083^2517490903Hans Havermann08/2020
989210^90902-95232990902Patrick De Geest07/2019
9893(17*2^301951-1)/16590896Lelio R Paula02/2014
98943^190497+7490891Lelio R Paula04/2016
9895(24737*2^301896+1)/39990882Lelio R Paula06/2014
989610^90880+570790881Patrick De Geest01/2019
989710^90880-15299390880Patrick De Geest07/2019
989818^72397+8990878Lelio R Paula06/2016
9899(2^301876+762)/290874Stefano Morozzi09/2020
9900134^42719-13390868Norbert Schneider03/2019
99016^116769-4790864Lelio R Paula05/2016
990210^90858+23343390859Patrick De Geest07/2019
990310^90858-830190858Patrick De Geest01/2019
990424298^5483+5483^2429890851Hans Havermann08/2020
990510^90849+4014190850Patrick De Geest07/2019
990610^90849-472190849Patrick De Geest01/2019
99072^301712-46590825Lelio R Paula02/2016
99082^301693-6990819Lelio R Paula11/2012
99092^301683-301683^290816Henri Lifchitz05/2005
991010^90807+727990808Patrick De Geest01/2019
991110^90807-16226390807Patrick De Geest07/2019
99126*10^90803+7990804Robert Price09/2020
991310^90800-645390800Patrick De Geest11/2018
991411^87187-171090796Enzo Doria12/2012
99155*10^90793+2190794Robert Price01/2017
9916(22*10^90792-13)/990793Robert Price03/2015
99172^301591-161590788Lelio R Paula02/2016
9918(52^52901+1)/5390777Paul Bourdelais08/2017
99192^301546-10903790775Enzo Doria04/2014
992010^90772+402990773Patrick De Geest11/2018
992110^90772-3662790772Patrick De Geest07/2019
992210^90771+6773790772Patrick De Geest07/2019
992310^90771-44100390771Patrick De Geest07/2019
992410^90770+2894190771Patrick De Geest07/2019
992510^90770-43190770Patrick De Geest11/2018
992614^79195-390768Lelio R Paula06/2016
992710^90766+87790767Patrick De Geest11/2018
99282^301517-186169390766Enzo Doria11/2015
992910^90766-10924190766Patrick De Geest07/2019
993010^90765+48536190766Patrick De Geest07/2019
993110^90765-479790765Patrick De Geest11/2018
993210^90757+757390758Patrick De Geest11/2018
993310^90757-55497990757Patrick De Geest07/2019
993410^90756+43810990757Patrick De Geest07/2019
993510^90756-872790756Patrick De Geest11/2018
993610^90749+82390750Patrick De Geest11/2018
99392^301460-17390749Lelio R Paula11/2012
993710^90748+421390749Patrick De Geest11/2018
993810^90749-13041390749Patrick De Geest07/2019
994010^90748-7541190748Patrick De Geest07/2019
994110^90747+43847190748Patrick De Geest07/2019
994210^90747-927990747Patrick De Geest11/2018
9943(85*10^90745-103)/990746Robert Price10/2017
9944(2^301439+1206)/290742Stefano Morozzi09/2020
994510^90726+407790727Patrick De Geest11/2018
994610^90726-50495190726Patrick De Geest07/2019
994810^90721+18190722Patrick De Geest11/2018
9947(2^301372+2722)/290722Stefano Morozzi09/2020
994910^90721-17714990721Patrick De Geest07/2019
9950(2^301317+1146)/290706Stefano Morozzi09/2020
99512^301312-8990704Lelio R Paula11/2012
995210^90696+634990697Patrick De Geest11/2018
99532^301285-12990696Lelio R Paula11/2012
995410^90696-63504990696Patrick De Geest07/2019
99552^301282-10999190695Enzo Doria04/2014
995610^90690+887790691Patrick De Geest11/2018
995710^90690-22743390690Patrick De Geest07/2019
995810^90683+6141190684Patrick De Geest07/2019
9959(2^301244+1738)/290684Stefano Morozzi09/2020
996010^90683-257790683Patrick De Geest11/2018
99612^301228-185426990679Enzo Doria09/2015
996210^90674+13845390675Patrick De Geest10/2022
996310^90674-500000190674Robert Price12/2021
996410^90674-5945190674Patrick De Geest10/2022
9966(151*10^90669-1)/390671Robert Price04/2017
9965(2^301201+2046)/290671Stefano Morozzi09/2020
9968(32*10^90669+13)/990670Robert Price04/2015
996710^90669+979390670Patrick De Geest11/2018
996910^90669-22393190669Patrick De Geest07/2019
9970(2^301191+2510)/290668Stefano Morozzi09/2020
99715*10^90666-6390667Robert Price04/2021
997210^90665+1098990666Patrick De Geest07/2019
997310^90665-308790665Patrick De Geest11/2018
99742^301177-22771390664Harrison Mesh06/2022
997510^90662+8963790663Patrick De Geest07/2019
997610^90662-951990662Patrick De Geest11/2018
997710^90661+237390662Patrick De Geest11/2018
997810^90661-19478190661Patrick De Geest07/2019
99793*5^129698+890656Lelio R Paula10/2014
9980F(433781)90655Henri Lifchitz09/2003
998119^70891+8290653Lelio R Paula06/2016
9982(29*2^301124-1)/1390648Lelio R Paula02/2014
998310^90636+6415990637Patrick De Geest07/2019
998410^90636-310190636Patrick De Geest11/2018
99857*3^189953-890632Lelio R Paula08/2014
998610^90626+33928990627Patrick De Geest07/2019
998710^90626-113190626Patrick De Geest11/2018
998811^87022-180090625Enzo Doria12/2012
998910^90623+86190624Patrick De Geest11/2018
999010^90623-30584190623Patrick De Geest07/2019
9991(2^301042+47)/1203696990616Lelio R Paula06/2013
99922^301004-278693990612Enzo Doria03/2016
999310^90611+16997790612Patrick De Geest07/2019
999510^90611-973790611Patrick De Geest11/2018
999410^90610+3674790611Patrick De Geest07/2019
999610^90609+682390610Patrick De Geest11/2018
999710^90610-2657390610Patrick De Geest07/2019
999810^90609-22817390609Patrick De Geest07/2019
99992^300980-2790605Lelio R Paula11/2012
100002*10^90597-790598Dmitry Domanov11/2010


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 04 2023 08:38 (Time in France)

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