PRP Records

Probable Primes Top 10000

(291192 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 ?
90012^303224+253391280Henri Lifchitz05/2005
90026^117302+14391279Lelio R Paula05/2016
90033^191306-11288091277Enzo Doria07/2014
9004(10052^22807-1)/1005191276Serge Batalov08/2020
90052^303207+1291591275Lelio R Paula02/2016
90062^303191-11125991270Enzo Doria05/2014
900781539!4+3291267Robert Price09/2019
9008(2^303116+3570)/291247Stefano Morozzi09/2020
900910^91230+9^(91230+1)91231Robert Price08/2016
901010^91230+792191231Patrick De Geest11/2016
901110^91230-91114191230Patrick De Geest11/2016
901210^91229+34879391230Patrick De Geest07/2019
901310^91229-247191229Patrick De Geest01/2019
90142996^26241+26241^299691228Norbert Schneider01/2020
90152^303249-49495391228Harrison Mesh06/2022
901710^91225+527191226Patrick De Geest01/2019
90162816^26445+26445^281691226Norbert Schneider02/2020
90196^117232-1742391225Enzo Doria02/2013
901810^91225-14721991225Patrick De Geest07/2019
90207*10^91215+391216Erik Branger11/2009
902110^91215+23061191216Patrick De Geest07/2019
902210^91215-453991215Patrick De Geest01/2019
9023(2^303007+606)/291214Stefano Morozzi09/2020
90249*10^91212-4791213Robert Price11/2021
9025(2^302998+3102)/291212Stefano Morozzi09/2020
902610^91210+242191211Patrick De Geest01/2019
902710^91210-173791210Patrick De Geest01/2019
902897*10^91205-391207Robert Price01/2017
90292^302979-16118191206Enzo Doria04/2013
9030(166*10^91199-7)/391201Robert Price11/2020
90312^302949+8191197Henri Lifchitz02/2007
903210^91194+20036191195Patrick De Geest07/2019
90344*6^117192-591194Lelio R Paula10/2014
903310^91194-866391194Patrick De Geest01/2019
90352^302918+9991188Lelio R Paula11/2012
903610^91186+26811191187Patrick De Geest07/2019
903710^91186-776391186Patrick De Geest01/2019
903810^91181+55047191182Patrick De Geest07/2019
9039(26*10^91181-83)/391182Robert Price12/2021
904010^91181-136791181Patrick De Geest01/2019
904110^91178+7188391179Patrick De Geest07/2019
904210^91178-471991178Patrick De Geest01/2019
904324686^4935+4935^2468691173Hans Havermann08/2020
904410^91165+304391166Patrick De Geest01/2019
904510^91165-39941391165Patrick De Geest07/2019
904610^91156+386191157Patrick De Geest01/2019
904710^91156-23149791156Patrick De Geest07/2019
90482^302797+186958791151Enzo Doria05/2016
9049265^37614+37614^26591148Norbert Schneider01/2015
90507^107852+8291146Lelio R Paula04/2016
9051(38*10^91144-11)/991145Robert Price05/2015
9052(55*10^91142+377)/991143Robert Price10/2017
905310^91128+996191129Patrick De Geest01/2019
9055249^38030+38030^24991128Norbert Schneider01/2015
905410^91128-18915391128Patrick De Geest07/2019
9056(2^302718+2814)/291127Stefano Morozzi02/2021
90576^117094-21104991117Mike Oakes05/2011
905821353^18472+18472^2135391103Hans Havermann05/2020
90602^302602-186718191093Enzo Doria03/2016
905910^91092+5612791093Patrick De Geest07/2019
906110^91092-910791092Patrick De Geest01/2019
9062(1017*2^302592-1)/5391091Lelio R Paula04/2015
906315^77445-1691083Lelio R Paula07/2016
906421656^16053+16053^2165691076Hans Havermann05/2020
90652^302505+8191064Henri Lifchitz02/2007
90662^302496-11234991061Enzo Doria06/2014
9067(2^302475+1790)/291054Stefano Morozzi01/2021
906817^73999-7291052Lelio R Paula07/2016
906910^91047+933191048Patrick De Geest01/2019
907010^91047-67116991047Patrick De Geest07/2019
907110^91044+207791045Patrick De Geest01/2019
907210^91044-13635991044Patrick De Geest07/2019
907310^91041+934991042Patrick De Geest01/2019
907410^91041-782391041Patrick De Geest01/2019
907510^91040+407791041Patrick De Geest01/2019
907610^91040-11942191040Patrick De Geest07/2019
907710^91037+276991038Patrick De Geest01/2019
907810^91037-2264991037Patrick De Geest07/2019
9079(16*10^91032+41)/391033Robert Price10/2017
908010^91023+5803991024Patrick De Geest07/2019
908110^91023-647191023Patrick De Geest01/2019
908210^91018+787391019Patrick De Geest01/2019
908310^91018-33317791018Patrick De Geest07/2019
908410^91017+6876791018Patrick De Geest07/2019
908510^91017-42832791017Patrick De Geest07/2019
908610^91016+7311191017Patrick De Geest07/2019
908710^91016-797391016Patrick De Geest01/2019
90881949^27666+27666^194991016Norbert Schneider04/2020
90892^302332+57729457591012Lelio R Paula08/2016
909010^91004+907391005Patrick De Geest01/2019
909110^91004-49151991004Patrick De Geest07/2019
909210^91003+7426991004Patrick De Geest07/2019
909310^91003-390391003Patrick De Geest01/2019
90942^302274+7420990994Enzo Doria04/2016
909510^90991+8114790992Patrick De Geest07/2019
909610^90991-627990991Patrick De Geest01/2019
909710^90983+139390984Patrick De Geest01/2019
909811*10^90982+990984Robert Price08/2020
909910^90983-56238390983Patrick De Geest07/2019
9100(311^36497-1)/31090976Eric Chen09/2017
9101(2^302210+1014)/290974Stefano Morozzi09/2020
9102(3^190668+2)/8990970Lelio R Paula04/2013
91032^302188+9019590968Lelio R Paula02/2016
9104(53*10^90965-71)/990966Robert Price09/2015
910510^90965+57398790966Patrick De Geest07/2019
910610^90965-683390965Patrick De Geest01/2019
910710^90964+4878990965Patrick De Geest07/2019
910810^90964-5210390964Patrick De Geest07/2019
910910^90963+19188990964Patrick De Geest07/2019
911010^90963-365990963Patrick De Geest01/2019
911110^90962+765790963Patrick De Geest01/2019
911210^90962-21563390962Patrick De Geest07/2019
911310^90961+6747190962Patrick De Geest07/2019
911410^90961-21104390961Patrick De Geest07/2019
911510^90960+107211790961Patrick De Geest07/2019
911610^90959+879190960Patrick De Geest01/2019
911710^90960-61065990960Patrick De Geest07/2019
911810^90959-27521390959Patrick De Geest07/2019
9119(2^302129+3110)/290950Stefano Morozzi09/2020
912110^90948+986790949Patrick De Geest01/2019
912021665^15774+15774^2166590949Hans Havermann04/2020
912210^90948-10923990948Patrick De Geest07/2019
91232^302113+7410590946Enzo Doria04/2016
91242^302102-655590942Lelio R Paula02/2016
912510^90930+9522390931Patrick De Geest07/2019
912610^90930-362390930Patrick De Geest01/2019
9127156*(10^(4*22731)-1)/101-190925Robert Price05/2014
91283^190568+3890925Lelio R Paula04/2016
912910^90917+17986390918Patrick De Geest07/2019
913010^90917-669390917Patrick De Geest01/2019
91312^302009-1644990914Enzo Doria04/2013
913210^90908+318190909Patrick De Geest01/2019
913310^90908-13951190908Patrick De Geest07/2019
913410^90904+10694790905Patrick De Geest07/2019
913510^90904-516990904Patrick De Geest01/2019
913610^90903+12096390904Patrick De Geest07/2019
913710^90902+261390903Patrick De Geest01/2019
913810^90903-19073790903Patrick De Geest07/2019
913925174^4083+4083^2517490903Hans Havermann08/2020
914010^90902-95232990902Patrick De Geest07/2019
9141(17*2^301951-1)/16590896Lelio R Paula02/2014
91423^190497+7490891Lelio R Paula04/2016
9143(24737*2^301896+1)/39990882Lelio R Paula06/2014
914410^90880+570790881Patrick De Geest01/2019
914510^90880-15299390880Patrick De Geest07/2019
914618^72397+8990878Lelio R Paula06/2016
9147(2^301876+762)/290874Stefano Morozzi09/2020
9148134^42719-13390868Norbert Schneider03/2019
91496^116769-4790864Lelio R Paula05/2016
915010^90858+23343390859Patrick De Geest07/2019
915110^90858-830190858Patrick De Geest01/2019
915224298^5483+5483^2429890851Hans Havermann08/2020
915310^90849+4014190850Patrick De Geest07/2019
915410^90849-472190849Patrick De Geest01/2019
91552^301712-46590825Lelio R Paula02/2016
91562^301693-6990819Lelio R Paula11/2012
91572^301683-301683^290816Henri Lifchitz05/2005
915810^90807+727990808Patrick De Geest01/2019
915910^90807-16226390807Patrick De Geest07/2019
91606*10^90803+7990804Robert Price09/2020
916110^90800-645390800Patrick De Geest11/2018
916211^87187-171090796Enzo Doria12/2012
91635*10^90793+2190794Robert Price01/2017
9164(22*10^90792-13)/990793Robert Price03/2015
91652^301591-161590788Lelio R Paula02/2016
9166(52^52901+1)/5390777Paul Bourdelais08/2017
91672^301546-10903790775Enzo Doria04/2014
916810^90772+402990773Patrick De Geest11/2018
916910^90772-3662790772Patrick De Geest07/2019
917010^90771+6773790772Patrick De Geest07/2019
917110^90771-44100390771Patrick De Geest07/2019
917210^90770+2894190771Patrick De Geest07/2019
917310^90770-43190770Patrick De Geest11/2018
917414^79195-390768Lelio R Paula06/2016
917510^90766+87790767Patrick De Geest11/2018
91762^301517-186169390766Enzo Doria11/2015
917710^90766-10924190766Patrick De Geest07/2019
917810^90765+48536190766Patrick De Geest07/2019
917910^90765-479790765Patrick De Geest11/2018
918010^90757+757390758Patrick De Geest11/2018
918110^90757-55497990757Patrick De Geest07/2019
918210^90756+43810990757Patrick De Geest07/2019
918310^90756-872790756Patrick De Geest11/2018
918410^90749+82390750Patrick De Geest11/2018
91872^301460-17390749Lelio R Paula11/2012
918510^90748+421390749Patrick De Geest11/2018
918610^90749-13041390749Patrick De Geest07/2019
918810^90748-7541190748Patrick De Geest07/2019
918910^90747+43847190748Patrick De Geest07/2019
919010^90747-927990747Patrick De Geest11/2018
9191(85*10^90745-103)/990746Robert Price10/2017
9192(2^301439+1206)/290742Stefano Morozzi09/2020
919310^90726+407790727Patrick De Geest11/2018
919410^90726-50495190726Patrick De Geest07/2019
919610^90721+18190722Patrick De Geest11/2018
9195(2^301372+2722)/290722Stefano Morozzi09/2020
919710^90721-17714990721Patrick De Geest07/2019
9198(2^301317+1146)/290706Stefano Morozzi09/2020
91992^301312-8990704Lelio R Paula11/2012
920010^90696+634990697Patrick De Geest11/2018
92012^301285-12990696Lelio R Paula11/2012
920210^90696-63504990696Patrick De Geest07/2019
92032^301282-10999190695Enzo Doria04/2014
920410^90690+887790691Patrick De Geest11/2018
920510^90690-22743390690Patrick De Geest07/2019
920610^90683+6141190684Patrick De Geest07/2019
9207(2^301244+1738)/290684Stefano Morozzi09/2020
920810^90683-257790683Patrick De Geest11/2018
92092^301228-185426990679Enzo Doria09/2015
921010^90674-500000190674Robert Price12/2021
9212(151*10^90669-1)/390671Robert Price04/2017
9211(2^301201+2046)/290671Stefano Morozzi09/2020
9214(32*10^90669+13)/990670Robert Price04/2015
921310^90669+979390670Patrick De Geest11/2018
921510^90669-22393190669Patrick De Geest07/2019
9216(2^301191+2510)/290668Stefano Morozzi09/2020
92175*10^90666-6390667Robert Price04/2021
921810^90665+1098990666Patrick De Geest07/2019
921910^90665-308790665Patrick De Geest11/2018
92202^301177-22771390664Harrison Mesh06/2022
922110^90662+8963790663Patrick De Geest07/2019
922210^90662-951990662Patrick De Geest11/2018
922310^90661+237390662Patrick De Geest11/2018
922410^90661-19478190661Patrick De Geest07/2019
92253*5^129698+890656Lelio R Paula10/2014
9226F(433781)90655Henri Lifchitz09/2003
922719^70891+8290653Lelio R Paula06/2016
9228(29*2^301124-1)/1390648Lelio R Paula02/2014
922910^90636+6415990637Patrick De Geest07/2019
923010^90636-310190636Patrick De Geest11/2018
92317*3^189953-890632Lelio R Paula08/2014
923210^90626+33928990627Patrick De Geest07/2019
923310^90626-113190626Patrick De Geest11/2018
923411^87022-180090625Enzo Doria12/2012
923510^90623+86190624Patrick De Geest11/2018
923610^90623-30584190623Patrick De Geest07/2019
9237(2^301042+47)/1203696990616Lelio R Paula06/2013
92382^301004-278693990612Enzo Doria03/2016
923910^90611+16997790612Patrick De Geest07/2019
924110^90611-973790611Patrick De Geest11/2018
924010^90610+3674790611Patrick De Geest07/2019
924210^90609+682390610Patrick De Geest11/2018
924310^90610-2657390610Patrick De Geest07/2019
924410^90609-22817390609Patrick De Geest07/2019
92452^300980-2790605Lelio R Paula11/2012
92462*10^90597-790598Dmitry Domanov11/2010
9247197^39485+290597Lelio R Paula06/2013
92487^107198+4890593Lelio R Paula04/2016
9249(86*10^90588+121)/990589Robert Price03/2017
92502^300923+5390587Lelio R Paula11/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 22 2022 18:03 (Time in France)

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