PRP Records

Probable Primes Top 10000

(280932 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 ?
675110^90930+9522390931Patrick De Geest07/2019
675210^90930-362390930Patrick De Geest01/2019
6753156*(10^(4*22731)-1)/101-190925Robert Price05/2014
67543^190568+3890925Lelio R Paula04/2016
675510^90917+17986390918Patrick De Geest07/2019
675610^90917-669390917Patrick De Geest01/2019
67572^302009-1644990914Enzo Doria04/2013
675810^90908+318190909Patrick De Geest01/2019
675910^90908-13951190908Patrick De Geest07/2019
676010^90904+10694790905Patrick De Geest07/2019
676110^90904-516990904Patrick De Geest01/2019
676210^90903+12096390904Patrick De Geest07/2019
676310^90902+261390903Patrick De Geest01/2019
676410^90903-19073790903Patrick De Geest07/2019
676525174^4083+4083^2517490903Hans Havermann08/2020
676610^90902-95232990902Patrick De Geest07/2019
6767(17*2^301951-1)/16590896Lelio R Paula02/2014
67683^190497+7490891Lelio R Paula04/2016
6769(24737*2^301896+1)/39990882Lelio R Paula06/2014
677010^90880+570790881Patrick De Geest01/2019
677110^90880-15299390880Patrick De Geest07/2019
677218^72397+8990878Lelio R Paula06/2016
6773(2^301876+762)/290874Stefano Morozzi09/2020
6774134^42719-13390868Norbert Schneider03/2019
67756^116769-4790864Lelio R Paula05/2016
677610^90858+23343390859Patrick De Geest07/2019
677710^90858-830190858Patrick De Geest01/2019
677824298^5483+5483^2429890851Hans Havermann08/2020
677910^90849+4014190850Patrick De Geest07/2019
678010^90849-472190849Patrick De Geest01/2019
67812^301712-46590825Lelio R Paula02/2016
67822^301693-6990819Lelio R Paula11/2012
67832^301683-301683^290816Henri Lifchitz05/2005
678410^90807+727990808Patrick De Geest01/2019
678510^90807-16226390807Patrick De Geest07/2019
67866*10^90803+7990804Robert Price09/2020
678710^90800-645390800Patrick De Geest11/2018
678811^87187-171090796Enzo Doria12/2012
67895*10^90793+2190794Robert Price01/2017
6790(22*10^90792-13)/990793Robert Price03/2015
67912^301591-161590788Lelio R Paula02/2016
6792(52^52901+1)/5390777Paul Bourdelais08/2017
67932^301546-10903790775Enzo Doria04/2014
679410^90772+402990773Patrick De Geest11/2018
679510^90772-3662790772Patrick De Geest07/2019
679610^90771+6773790772Patrick De Geest07/2019
679710^90771-44100390771Patrick De Geest07/2019
679810^90770+2894190771Patrick De Geest07/2019
679910^90770-43190770Patrick De Geest11/2018
680014^79195-390768Lelio R Paula06/2016
680110^90766+87790767Patrick De Geest11/2018
68042^301517-186169390766Enzo Doria11/2015
680210^90766-10924190766Patrick De Geest07/2019
680310^90765+48536190766Patrick De Geest07/2019
680510^90765-479790765Patrick De Geest11/2018
680610^90757+757390758Patrick De Geest11/2018
680710^90757-55497990757Patrick De Geest07/2019
680810^90756+43810990757Patrick De Geest07/2019
680910^90756-872790756Patrick De Geest11/2018
681010^90749+82390750Patrick De Geest11/2018
68132^301460-17390749Lelio R Paula11/2012
681110^90748+421390749Patrick De Geest11/2018
681210^90749-13041390749Patrick De Geest07/2019
681410^90748-7541190748Patrick De Geest07/2019
681510^90747+43847190748Patrick De Geest07/2019
681610^90747-927990747Patrick De Geest11/2018
6817(85*10^90745-103)/990746Robert Price10/2017
6818(2^301439+1206)/290742Stefano Morozzi09/2020
681910^90726+407790727Patrick De Geest11/2018
682010^90726-50495190726Patrick De Geest07/2019
682210^90721+18190722Patrick De Geest11/2018
6821(2^301372+2722)/290722Stefano Morozzi09/2020
682310^90721-17714990721Patrick De Geest07/2019
6824(2^301317+1146)/290706Stefano Morozzi09/2020
68252^301312-8990704Lelio R Paula11/2012
682610^90696+634990697Patrick De Geest11/2018
68282^301285-12990696Lelio R Paula11/2012
682710^90696-63504990696Patrick De Geest07/2019
68292^301282-10999190695Enzo Doria04/2014
683010^90690+887790691Patrick De Geest11/2018
683110^90690-22743390690Patrick De Geest07/2019
683210^90683+6141190684Patrick De Geest07/2019
6833(2^301244+1738)/290684Stefano Morozzi09/2020
683410^90683-257790683Patrick De Geest11/2018
68352^301228-185426990679Enzo Doria09/2015
6837(151*10^90669-1)/390671Robert Price04/2017
6836(2^301201+2046)/290671Stefano Morozzi09/2020
6838(32*10^90669+13)/990670Robert Price04/2015
683910^90669+979390670Patrick De Geest11/2018
684010^90669-22393190669Patrick De Geest07/2019
6841(2^301191+2510)/290668Stefano Morozzi09/2020
68425*10^90666-6390667Robert Price04/2021
684310^90665+1098990666Patrick De Geest07/2019
684410^90665-308790665Patrick De Geest11/2018
684510^90662+8963790663Patrick De Geest07/2019
684610^90662-951990662Patrick De Geest11/2018
684710^90661+237390662Patrick De Geest11/2018
684810^90661-19478190661Patrick De Geest07/2019
68493*5^129698+890656Lelio R Paula10/2014
6850F(433781)90655Henri Lifchitz09/2003
685119^70891+8290653Lelio R Paula06/2016
6852(29*2^301124-1)/1390648Lelio R Paula02/2014
685310^90636+6415990637Patrick De Geest07/2019
685410^90636-310190636Patrick De Geest11/2018
68557*3^189953-890632Lelio R Paula08/2014
685610^90626+33928990627Patrick De Geest07/2019
685710^90626-113190626Patrick De Geest11/2018
685811^87022-180090625Enzo Doria12/2012
685910^90623+86190624Patrick De Geest11/2018
686010^90623-30584190623Patrick De Geest07/2019
6861(2^301042+47)/1203696990616Lelio R Paula06/2013
68632^301004-278693990612Enzo Doria03/2016
686210^90611+16997790612Patrick De Geest07/2019
686510^90611-973790611Patrick De Geest11/2018
686410^90610+3674790611Patrick De Geest07/2019
686610^90609+682390610Patrick De Geest11/2018
686710^90610-2657390610Patrick De Geest07/2019
686810^90609-22817390609Patrick De Geest07/2019
68692^300980-2790605Lelio R Paula11/2012
68702*10^90597-790598Dmitry Domanov11/2010
6871197^39485+290597Lelio R Paula06/2013
68727^107198+4890593Lelio R Paula04/2016
6873(86*10^90588+121)/990589Robert Price03/2017
68742^300923+5390587Lelio R Paula11/2012
68752^300874+790573Lelio R Paula10/2012
687610^90567+948990568Patrick De Geest11/2018
687710^90567-23135390567Patrick De Geest07/2019
6878(2^300857+2214)/290567Stefano Morozzi01/2020
68795^129568-5690565Lelio R Paula04/2016
68802^300847-11283190564Enzo Doria06/2014
688110^90562+79019790563Patrick De Geest07/2019
688210^90562-298190562Patrick De Geest11/2018
6883(7796^23269-1)/779590557Serge Batalov08/2020
688410^90549+381190550Patrick De Geest11/2018
688510^90549-63030390549Patrick De Geest07/2019
68862^300790-454190547Yves Minet03/2019
688710^90532+816990533Patrick De Geest11/2018
688810^90531+983190532Patrick De Geest11/2018
688910^90532-15488990532Patrick De Geest07/2019
689010^90531-106058990531Patrick De Geest07/2019
68922^300718+25525590526Lelio R Paula02/2016
6891(2^300719+938)/290526Stefano Morozzi01/2020
689310^90516+21591790517Patrick De Geest07/2019
689410^90516-678390516Patrick De Geest11/2018
689510^90511+3017790512Patrick De Geest07/2019
689610^90511-697790511Patrick De Geest11/2018
6897(8573^23011-1)/857290502Serge Batalov08/2020
68982^300637+9590501Lelio R Paula11/2012
68997^107087-2490500Lelio R Paula04/2016
690010^90499+19154790500Patrick De Geest07/2019
690110^90499-582390499Patrick De Geest11/2018
6903(10^90499+3^90499)/1390498Robert Price01/2013
690213^81241+9090498Lelio R Paula06/2016
6904(2^300600+1222)/290490Stefano Morozzi01/2020
690510^90480+513190481Patrick De Geest11/2018
690610^90480-8572190480Patrick De Geest07/2019
6907(34*10^90478-547)/990479Robert Price03/2021
69086^116273-8590478Lelio R Paula05/2016
690910^90473+313990474Patrick De Geest11/2018
691010^90473-15059990473Patrick De Geest07/2019
691110^90470+231990471Patrick De Geest11/2018
691210^90470-7163790470Patrick De Geest07/2019
69136^116256-1757390465Enzo Doria02/2013
69142^300502+5461590461Lelio R Paula02/2016
6915(13*2^300487+1)/4590456Lelio R Paula09/2013
691610^90453+14184390454Patrick De Geest07/2019
691710^90453-396990453Patrick De Geest11/2018
691810^90452-8000000190452Robert Price04/2021
691910^90440+135990441Patrick De Geest11/2018
692010^90440-1882190440Patrick De Geest07/2019
6921(3^189545-8)/590436Lelio R Paula01/2013
6922(7*2^300406-1)/390432Lelio R Paula02/2014
692310^90430+333990431Patrick De Geest11/2018
692410^90430-6347790430Patrick De Geest07/2019
6925(5408^24223-1)/540790422Serge Batalov08/2020
692610^90414+22959390415Patrick De Geest07/2019
692710^90414-154790414Patrick De Geest11/2018
692810^90404+4704190405Patrick De Geest07/2019
692910^90404-642990404Patrick De Geest11/2018
693010^90401+207790402Patrick De Geest11/2018
693110^90401-36863790401Patrick De Geest07/2019
693224900^4271+4271^2490090401Hans Havermann08/2020
69334*5^129332+390400Lelio R Paula10/2014
693410^90397+1978390398Patrick De Geest07/2019
693523380^7353+7353^2338090398Hans Havermann08/2020
693710^90397-32390397Patrick De Geest11/2018
6936(2^300293+2762)/290397Stefano Morozzi01/2020
693824058^5719+5719^2405890394Hans Havermann08/2020
69392^300249-1624590384Enzo Doria04/2013
694024414^5035+5035^2441490381Hans Havermann08/2020
6941(7*10^90371-313)/990371Robert Price11/2016
694210^90363+5867790364Patrick De Geest07/2019
694310^90363-355790363Patrick De Geest11/2018
694410^90358+10464190359Patrick De Geest07/2019
69472*6^116118+790358Lelio R Paula10/2014
694610^90358-497990358Patrick De Geest11/2018
694510^90357+11283790358Patrick De Geest07/2019
694810^90357-18959390357Patrick De Geest07/2019
694910^90356+5311390357Patrick De Geest07/2019
695010^90356-719790356Patrick De Geest11/2018
695110^90353+60321190354Patrick De Geest07/2019
695210^90353-108990353Patrick De Geest11/2018
6953(24737*2^300101+1)/2590343Lelio R Paula06/2014
69544*10^90334-2190335Robert Price04/2016
6955(4546^24697-1)/454590329Serge Batalov08/2020
695610^90322+13769190323Patrick De Geest07/2019
695710^90322-955190322Patrick De Geest11/2018
695810^90316+999190317Patrick De Geest11/2018
6959(4550^24691-1)/454990317Serge Batalov08/2020
696010^90316-4562790316Patrick De Geest07/2019
696110^90315+3288990316Patrick De Geest07/2019
69622^300019-11033590315Enzo Doria05/2014
696310^90315-856190315Patrick De Geest11/2018
6964FAB2(300001,5032)90310Robert Price05/2019
6965FAB2(300001,29405)90310Robert Price05/2019
6966(2^299965+2774)/290299Stefano Morozzi01/2020
696723679^6506+6506^2367990296Hans Havermann08/2020
69682^299949-100590294Lelio R Paula11/2013
6969(2^299947+2054)/290293Stefano Morozzi01/2020
697021740^14229+14229^2174090291Hans Havermann08/2020
697110^90279+6245790280Patrick De Geest07/2019
697210^90279-155190279Patrick De Geest09/2018
6973(2^299892+1986)/290277Stefano Morozzi01/2020
6974(2^299893+3866)/290277Stefano Morozzi01/2020
69752^299868-10961390270Enzo Doria04/2014
697610^90259+35929990260Patrick De Geest07/2019
697710^90259-944390259Patrick De Geest09/2018
6978(2^299831+3786)/290258Stefano Morozzi01/2020
697910^90252+10287390253Patrick De Geest07/2019
698010^90252-810390252Patrick De Geest09/2018
69825*2^299799-390250Lelio R Paula08/2014
6981(2^299803+3326)/290250Stefano Morozzi01/2020
698313^81008-290239Lelio R Paula09/2013
698480697!4-25690234Robert Price11/2019
698664^49957-63^4995790232Robert Price07/2013
6985(2^299745+2994)/290232Stefano Morozzi01/2020
698710^90227+5628190228Patrick De Geest06/2016
69902^299725+31590227Lelio R Paula11/2013
698810^90227-100000000190227Robert Price05/2016
698910^90227-6876390227Patrick De Geest06/2016
69915^129082+4890225Lelio R Paula03/2016
69922^299699+19590219Lelio R Paula10/2012
6993(55*10^90211-1)/990212Ray Chandler02/2012
699422131^11918+11918^2213190211Hans Havermann08/2020
699510^90209+897190210Patrick De Geest09/2018
699610^90209-72479790209Patrick De Geest07/2019
699710^90208+18953190209Patrick De Geest07/2019
699810^90208-224790208Patrick De Geest09/2018
6999(629^32233-1)/62890207Michael Stocker05/2020
7000116^43693-11590203Norbert Schneider08/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 13 2021 12:02 (Time in France)

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