PRP Records

Probable Primes Top 10000

(290751 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 ?
875110^90983+139390984Patrick De Geest01/2019
875211*10^90982+990984Robert Price08/2020
875310^90983-56238390983Patrick De Geest07/2019
8754(311^36497-1)/31090976Eric Chen09/2017
8755(2^302210+1014)/290974Stefano Morozzi09/2020
8756(3^190668+2)/8990970Lelio R Paula04/2013
87572^302188+9019590968Lelio R Paula02/2016
8758(53*10^90965-71)/990966Robert Price09/2015
875910^90965+57398790966Patrick De Geest07/2019
876010^90965-683390965Patrick De Geest01/2019
876110^90964+4878990965Patrick De Geest07/2019
876210^90964-5210390964Patrick De Geest07/2019
876310^90963+19188990964Patrick De Geest07/2019
876410^90963-365990963Patrick De Geest01/2019
876510^90962+765790963Patrick De Geest01/2019
876610^90962-21563390962Patrick De Geest07/2019
876710^90961+6747190962Patrick De Geest07/2019
876810^90961-21104390961Patrick De Geest07/2019
876910^90960+107211790961Patrick De Geest07/2019
877010^90959+879190960Patrick De Geest01/2019
877110^90960-61065990960Patrick De Geest07/2019
877210^90959-27521390959Patrick De Geest07/2019
8773(2^302129+3110)/290950Stefano Morozzi09/2020
877510^90948+986790949Patrick De Geest01/2019
877421665^15774+15774^2166590949Hans Havermann04/2020
877610^90948-10923990948Patrick De Geest07/2019
87772^302113+7410590946Enzo Doria04/2016
87782^302102-655590942Lelio R Paula02/2016
877910^90930+9522390931Patrick De Geest07/2019
878010^90930-362390930Patrick De Geest01/2019
8781156*(10^(4*22731)-1)/101-190925Robert Price05/2014
87823^190568+3890925Lelio R Paula04/2016
878310^90917+17986390918Patrick De Geest07/2019
878410^90917-669390917Patrick De Geest01/2019
87852^302009-1644990914Enzo Doria04/2013
878610^90908+318190909Patrick De Geest01/2019
878710^90908-13951190908Patrick De Geest07/2019
878810^90904+10694790905Patrick De Geest07/2019
878910^90904-516990904Patrick De Geest01/2019
879010^90903+12096390904Patrick De Geest07/2019
879110^90902+261390903Patrick De Geest01/2019
879210^90903-19073790903Patrick De Geest07/2019
879325174^4083+4083^2517490903Hans Havermann08/2020
879410^90902-95232990902Patrick De Geest07/2019
8795(17*2^301951-1)/16590896Lelio R Paula02/2014
87963^190497+7490891Lelio R Paula04/2016
8797(24737*2^301896+1)/39990882Lelio R Paula06/2014
879810^90880+570790881Patrick De Geest01/2019
879910^90880-15299390880Patrick De Geest07/2019
880018^72397+8990878Lelio R Paula06/2016
8801(2^301876+762)/290874Stefano Morozzi09/2020
8802134^42719-13390868Norbert Schneider03/2019
88036^116769-4790864Lelio R Paula05/2016
880410^90858+23343390859Patrick De Geest07/2019
880510^90858-830190858Patrick De Geest01/2019
880624298^5483+5483^2429890851Hans Havermann08/2020
880710^90849+4014190850Patrick De Geest07/2019
880810^90849-472190849Patrick De Geest01/2019
88092^301712-46590825Lelio R Paula02/2016
88102^301693-6990819Lelio R Paula11/2012
88112^301683-301683^290816Henri Lifchitz05/2005
881210^90807+727990808Patrick De Geest01/2019
881310^90807-16226390807Patrick De Geest07/2019
88146*10^90803+7990804Robert Price09/2020
881510^90800-645390800Patrick De Geest11/2018
881611^87187-171090796Enzo Doria12/2012
88175*10^90793+2190794Robert Price01/2017
8818(22*10^90792-13)/990793Robert Price03/2015
88192^301591-161590788Lelio R Paula02/2016
8820(52^52901+1)/5390777Paul Bourdelais08/2017
88212^301546-10903790775Enzo Doria04/2014
882210^90772+402990773Patrick De Geest11/2018
882310^90772-3662790772Patrick De Geest07/2019
882410^90771+6773790772Patrick De Geest07/2019
882510^90771-44100390771Patrick De Geest07/2019
882610^90770+2894190771Patrick De Geest07/2019
882710^90770-43190770Patrick De Geest11/2018
882814^79195-390768Lelio R Paula06/2016
882910^90766+87790767Patrick De Geest11/2018
88302^301517-186169390766Enzo Doria11/2015
883110^90766-10924190766Patrick De Geest07/2019
883210^90765+48536190766Patrick De Geest07/2019
883310^90765-479790765Patrick De Geest11/2018
883410^90757+757390758Patrick De Geest11/2018
883510^90757-55497990757Patrick De Geest07/2019
883610^90756+43810990757Patrick De Geest07/2019
883710^90756-872790756Patrick De Geest11/2018
883810^90749+82390750Patrick De Geest11/2018
88412^301460-17390749Lelio R Paula11/2012
883910^90748+421390749Patrick De Geest11/2018
884010^90749-13041390749Patrick De Geest07/2019
884210^90748-7541190748Patrick De Geest07/2019
884310^90747+43847190748Patrick De Geest07/2019
884410^90747-927990747Patrick De Geest11/2018
8845(85*10^90745-103)/990746Robert Price10/2017
8846(2^301439+1206)/290742Stefano Morozzi09/2020
884710^90726+407790727Patrick De Geest11/2018
884810^90726-50495190726Patrick De Geest07/2019
885010^90721+18190722Patrick De Geest11/2018
8849(2^301372+2722)/290722Stefano Morozzi09/2020
885110^90721-17714990721Patrick De Geest07/2019
8852(2^301317+1146)/290706Stefano Morozzi09/2020
88532^301312-8990704Lelio R Paula11/2012
885410^90696+634990697Patrick De Geest11/2018
88552^301285-12990696Lelio R Paula11/2012
885610^90696-63504990696Patrick De Geest07/2019
88572^301282-10999190695Enzo Doria04/2014
885810^90690+887790691Patrick De Geest11/2018
885910^90690-22743390690Patrick De Geest07/2019
886010^90683+6141190684Patrick De Geest07/2019
8861(2^301244+1738)/290684Stefano Morozzi09/2020
886210^90683-257790683Patrick De Geest11/2018
88632^301228-185426990679Enzo Doria09/2015
886410^90674-500000190674Robert Price12/2021
8866(151*10^90669-1)/390671Robert Price04/2017
8865(2^301201+2046)/290671Stefano Morozzi09/2020
8868(32*10^90669+13)/990670Robert Price04/2015
886710^90669+979390670Patrick De Geest11/2018
886910^90669-22393190669Patrick De Geest07/2019
8870(2^301191+2510)/290668Stefano Morozzi09/2020
88715*10^90666-6390667Robert Price04/2021
887210^90665+1098990666Patrick De Geest07/2019
887310^90665-308790665Patrick De Geest11/2018
88742^301177-22771390664Harrison Mesh06/2022
887510^90662+8963790663Patrick De Geest07/2019
887610^90662-951990662Patrick De Geest11/2018
887710^90661+237390662Patrick De Geest11/2018
887810^90661-19478190661Patrick De Geest07/2019
88793*5^129698+890656Lelio R Paula10/2014
8880F(433781)90655Henri Lifchitz09/2003
888119^70891+8290653Lelio R Paula06/2016
8882(29*2^301124-1)/1390648Lelio R Paula02/2014
888310^90636+6415990637Patrick De Geest07/2019
888410^90636-310190636Patrick De Geest11/2018
88857*3^189953-890632Lelio R Paula08/2014
888610^90626+33928990627Patrick De Geest07/2019
888710^90626-113190626Patrick De Geest11/2018
888811^87022-180090625Enzo Doria12/2012
888910^90623+86190624Patrick De Geest11/2018
889010^90623-30584190623Patrick De Geest07/2019
8891(2^301042+47)/1203696990616Lelio R Paula06/2013
88922^301004-278693990612Enzo Doria03/2016
889310^90611+16997790612Patrick De Geest07/2019
889510^90611-973790611Patrick De Geest11/2018
889410^90610+3674790611Patrick De Geest07/2019
889610^90609+682390610Patrick De Geest11/2018
889710^90610-2657390610Patrick De Geest07/2019
889810^90609-22817390609Patrick De Geest07/2019
88992^300980-2790605Lelio R Paula11/2012
89002*10^90597-790598Dmitry Domanov11/2010
8901197^39485+290597Lelio R Paula06/2013
89027^107198+4890593Lelio R Paula04/2016
8903(86*10^90588+121)/990589Robert Price03/2017
89042^300923+5390587Lelio R Paula11/2012
89052^300874+790573Lelio R Paula10/2012
890610^90567+948990568Patrick De Geest11/2018
890710^90567-23135390567Patrick De Geest07/2019
8908(2^300857+2214)/290567Stefano Morozzi01/2020
89095^129568-5690565Lelio R Paula04/2016
89102^300847-11283190564Enzo Doria06/2014
891110^90562+79019790563Patrick De Geest07/2019
891210^90562-298190562Patrick De Geest11/2018
8913(7796^23269-1)/779590557Serge Batalov08/2020
8914(31*10^90554+257)/990555Robert Price12/2021
891510^90549+381190550Patrick De Geest11/2018
891610^90549-63030390549Patrick De Geest07/2019
89172^300790-454190547Yves Minet03/2019
891810^90532+816990533Patrick De Geest11/2018
891910^90531+983190532Patrick De Geest11/2018
892010^90532-15488990532Patrick De Geest07/2019
892110^90531-106058990531Patrick De Geest07/2019
89232^300718+25525590526Lelio R Paula02/2016
8922(2^300719+938)/290526Stefano Morozzi01/2020
892410^90516+21591790517Patrick De Geest07/2019
892510^90516-678390516Patrick De Geest11/2018
892610^90511+3017790512Patrick De Geest07/2019
892710^90511-697790511Patrick De Geest11/2018
8928(8573^23011-1)/857290502Serge Batalov08/2020
89292^300637+9590501Lelio R Paula11/2012
89307^107087-2490500Lelio R Paula04/2016
893110^90499+19154790500Patrick De Geest07/2019
893210^90499-582390499Patrick De Geest11/2018
8934(10^90499+3^90499)/1390498Robert Price01/2013
893313^81241+9090498Lelio R Paula06/2016
8935(2^300600+1222)/290490Stefano Morozzi01/2020
893610^90480+513190481Patrick De Geest11/2018
893710^90480-8572190480Patrick De Geest07/2019
8938(34*10^90478-547)/990479Robert Price03/2021
89396^116273-8590478Lelio R Paula05/2016
894010^90473+313990474Patrick De Geest11/2018
894110^90473-15059990473Patrick De Geest07/2019
894210^90470+231990471Patrick De Geest11/2018
894310^90470-7163790470Patrick De Geest07/2019
89446^116256-1757390465Enzo Doria02/2013
89452^300502+5461590461Lelio R Paula02/2016
8946(13*2^300487+1)/4590456Lelio R Paula09/2013
894710^90453+14184390454Patrick De Geest07/2019
894910^90453-396990453Patrick De Geest11/2018
894810^90452+5931790453Patrick De Geest05/2021
895010^90452-8000000190452Robert Price04/2021
895110^90452-8471390452Patrick De Geest05/2021
895210^90440+135990441Patrick De Geest11/2018
895310^90440-1882190440Patrick De Geest07/2019
8954(3^189545-8)/590436Lelio R Paula01/2013
8955(7*2^300406-1)/390432Lelio R Paula02/2014
895610^90430+333990431Patrick De Geest11/2018
895710^90430-6347790430Patrick De Geest07/2019
8958(5408^24223-1)/540790422Serge Batalov08/2020
895910^90414+22959390415Patrick De Geest07/2019
896010^90414-154790414Patrick De Geest11/2018
896110^90404+4704190405Patrick De Geest07/2019
896210^90404-642990404Patrick De Geest11/2018
896310^90401+207790402Patrick De Geest11/2018
896410^90401-36863790401Patrick De Geest07/2019
896524900^4271+4271^2490090401Hans Havermann08/2020
89664*5^129332+390400Lelio R Paula10/2014
896810^90397+1978390398Patrick De Geest07/2019
896723380^7353+7353^2338090398Hans Havermann08/2020
897010^90397-32390397Patrick De Geest11/2018
8969(2^300293+2762)/290397Stefano Morozzi01/2020
897124058^5719+5719^2405890394Hans Havermann08/2020
89722^300249-1624590384Enzo Doria04/2013
897324414^5035+5035^2441490381Hans Havermann08/2020
8974(7*10^90371-313)/990371Robert Price11/2016
897510^90363+5867790364Patrick De Geest07/2019
897610^90363-355790363Patrick De Geest11/2018
897710^90358+10464190359Patrick De Geest07/2019
89802*6^116118+790358Lelio R Paula10/2014
897910^90358-497990358Patrick De Geest11/2018
897810^90357+11283790358Patrick De Geest07/2019
898110^90357-18959390357Patrick De Geest07/2019
898210^90356+5311390357Patrick De Geest07/2019
898310^90356-719790356Patrick De Geest11/2018
898410^90353+60321190354Patrick De Geest07/2019
898510^90353-108990353Patrick De Geest11/2018
8986(24737*2^300101+1)/2590343Lelio R Paula06/2014
89874*10^90334-2190335Robert Price04/2016
8988(4546^24697-1)/454590329Serge Batalov08/2020
898910^90322+13769190323Patrick De Geest07/2019
899010^90322-955190322Patrick De Geest11/2018
899110^90316+999190317Patrick De Geest11/2018
8992(4550^24691-1)/454990317Serge Batalov08/2020
899310^90316-4562790316Patrick De Geest07/2019
899410^90315+3288990316Patrick De Geest07/2019
89962^300019-11033590315Enzo Doria05/2014
899510^90315-856190315Patrick De Geest11/2018
8997FAB2(300001,5032)90310Robert Price05/2019
8998FAB2(300001,29405)90310Robert Price05/2019
8999(2^299965+2774)/290299Stefano Morozzi01/2020
900023679^6506+6506^2367990296Hans Havermann08/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 23 2022 21:24 (Time in France)

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