PRP Records

Probable Primes Top 10000

(259919 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 ?
500110^91092+5612791093Patrick De Geest07/2019
500210^91092-910791092Patrick De Geest01/2019
5003(1017*2^302592-1)/5391091Lelio R Paula04/2015
500415^77445-1691083Lelio R Paula07/2016
50052^302505+8191064Henri Lifchitz02/2007
50062^302496-11234991061Enzo Doria06/2014
500717^73999-7291052Lelio R Paula07/2016
500810^91047+933191048Patrick De Geest01/2019
500910^91047-67116991047Patrick De Geest07/2019
501010^91044+207791045Patrick De Geest01/2019
501110^91044-13635991044Patrick De Geest07/2019
501210^91041+934991042Patrick De Geest01/2019
501310^91041-782391041Patrick De Geest01/2019
501410^91040+407791041Patrick De Geest01/2019
501510^91040-11942191040Patrick De Geest07/2019
501610^91037+276991038Patrick De Geest01/2019
501710^91037-2264991037Patrick De Geest07/2019
5018(16*10^91032+41)/391033Robert Price10/2017
501910^91023+5803991024Patrick De Geest07/2019
502010^91023-647191023Patrick De Geest01/2019
502110^91018+787391019Patrick De Geest01/2019
502210^91018-33317791018Patrick De Geest07/2019
502310^91017+6876791018Patrick De Geest07/2019
502410^91017-42832791017Patrick De Geest07/2019
502510^91016+7311191017Patrick De Geest07/2019
502610^91016-797391016Patrick De Geest01/2019
50272^302332+57729457591012Lelio R Paula08/2016
502810^91004+907391005Patrick De Geest01/2019
502910^91004-49151991004Patrick De Geest07/2019
503010^91003+7426991004Patrick De Geest07/2019
503110^91003-390391003Patrick De Geest01/2019
50322^302274+7420990994Enzo Doria04/2016
503310^90991+8114790992Patrick De Geest07/2019
503410^90991-627990991Patrick De Geest01/2019
503510^90983+139390984Patrick De Geest01/2019
503610^90983-56238390983Patrick De Geest07/2019
5037(311^36497-1)/31090976Eric Chen09/2017
5038(3^190668+2)/8990970Lelio R Paula04/2013
50392^302188+9019590968Lelio R Paula02/2016
5041(53*10^90965-71)/990966Robert Price09/2015
504010^90965+57398790966Patrick De Geest07/2019
504210^90965-683390965Patrick De Geest01/2019
504310^90964+4878990965Patrick De Geest07/2019
504410^90964-5210390964Patrick De Geest07/2019
504510^90963+19188990964Patrick De Geest07/2019
504610^90963-365990963Patrick De Geest01/2019
504710^90962+765790963Patrick De Geest01/2019
504810^90962-21563390962Patrick De Geest07/2019
504910^90961+6747190962Patrick De Geest07/2019
505010^90961-21104390961Patrick De Geest07/2019
505110^90960+107211790961Patrick De Geest07/2019
505210^90959+879190960Patrick De Geest01/2019
505310^90960-61065990960Patrick De Geest07/2019
505410^90959-27521390959Patrick De Geest07/2019
505510^90948+986790949Patrick De Geest01/2019
505610^90948-10923990948Patrick De Geest07/2019
50572^302113+7410590946Enzo Doria04/2016
50582^302102-655590942Lelio R Paula02/2016
505910^90930+9522390931Patrick De Geest07/2019
506010^90930-362390930Patrick De Geest01/2019
5062156*(10^(4*22731)-1)/101-190925Robert Price05/2014
50613^190568+3890925Lelio R Paula04/2016
506310^90917+17986390918Patrick De Geest07/2019
506410^90917-669390917Patrick De Geest01/2019
50652^302009-1644990914Enzo Doria04/2013
506610^90908+318190909Patrick De Geest01/2019
506710^90908-13951190908Patrick De Geest07/2019
506810^90904+10694790905Patrick De Geest07/2019
506910^90904-516990904Patrick De Geest01/2019
507010^90903+12096390904Patrick De Geest07/2019
507110^90902+261390903Patrick De Geest01/2019
507210^90903-19073790903Patrick De Geest07/2019
507310^90902-95232990902Patrick De Geest07/2019
5074(17*2^301951-1)/16590896Lelio R Paula02/2014
50753^190497+7490891Lelio R Paula04/2016
5076(24737*2^301896+1)/39990882Lelio R Paula06/2014
507710^90880+570790881Patrick De Geest01/2019
507810^90880-15299390880Patrick De Geest07/2019
507918^72397+8990878Lelio R Paula06/2016
5080134^42719-13390868Norbert Schneider03/2019
50816^116769-4790864Lelio R Paula05/2016
508210^90858+23343390859Patrick De Geest07/2019
508310^90858-830190858Patrick De Geest01/2019
508410^90849+4014190850Patrick De Geest07/2019
508510^90849-472190849Patrick De Geest01/2019
50862^301712-46590825Lelio R Paula02/2016
50872^301693-6990819Lelio R Paula11/2012
50882^301683-301683^290816Henri Lifchitz05/2005
508910^90807+727990808Patrick De Geest01/2019
509010^90807-16226390807Patrick De Geest07/2019
509110^90800-645390800Patrick De Geest11/2018
509211^87187-171090796Enzo Doria12/2012
50935*10^90793+2190794Robert Price01/2017
5094(22*10^90792-13)/990793Robert Price03/2015
50952^301591-161590788Lelio R Paula02/2016
5096(52^52901+1)/5390777Paul Bourdelais08/2017
50972^301546-10903790775Enzo Doria04/2014
509810^90772+402990773Patrick De Geest11/2018
509910^90772-3662790772Patrick De Geest07/2019
510010^90771+6773790772Patrick De Geest07/2019
510110^90771-44100390771Patrick De Geest07/2019
510210^90770+2894190771Patrick De Geest07/2019
510310^90770-43190770Patrick De Geest11/2018
510414^79195-390768Lelio R Paula06/2016
510510^90766+87790767Patrick De Geest11/2018
51082^301517-186169390766Enzo Doria11/2015
510610^90766-10924190766Patrick De Geest07/2019
510710^90765+48536190766Patrick De Geest07/2019
510910^90765-479790765Patrick De Geest11/2018
511010^90757+757390758Patrick De Geest11/2018
511110^90757-55497990757Patrick De Geest07/2019
511210^90756+43810990757Patrick De Geest07/2019
511310^90756-872790756Patrick De Geest11/2018
511410^90749+82390750Patrick De Geest11/2018
51172^301460-17390749Lelio R Paula11/2012
511510^90748+421390749Patrick De Geest11/2018
511610^90749-13041390749Patrick De Geest07/2019
511810^90748-7541190748Patrick De Geest07/2019
511910^90747+43847190748Patrick De Geest07/2019
512010^90747-927990747Patrick De Geest11/2018
5121(85*10^90745-103)/990746Robert Price10/2017
512210^90726+407790727Patrick De Geest11/2018
512310^90726-50495190726Patrick De Geest07/2019
512410^90721+18190722Patrick De Geest11/2018
512510^90721-17714990721Patrick De Geest07/2019
51262^301312-8990704Lelio R Paula11/2012
512710^90696+634990697Patrick De Geest11/2018
51292^301285-12990696Lelio R Paula11/2012
512810^90696-63504990696Patrick De Geest07/2019
51302^301282-10999190695Enzo Doria04/2014
513110^90690+887790691Patrick De Geest11/2018
513210^90690-22743390690Patrick De Geest07/2019
513310^90683+6141190684Patrick De Geest07/2019
513410^90683-257790683Patrick De Geest11/2018
51352^301228-185426990679Enzo Doria09/2015
5136(151*10^90669-1)/390671Robert Price04/2017
5137(32*10^90669+13)/990670Robert Price04/2015
513810^90669+979390670Patrick De Geest11/2018
513910^90669-22393190669Patrick De Geest07/2019
514010^90665+1098990666Patrick De Geest07/2019
514110^90665-308790665Patrick De Geest11/2018
514210^90662+8963790663Patrick De Geest07/2019
514310^90662-951990662Patrick De Geest11/2018
514410^90661+237390662Patrick De Geest11/2018
514510^90661-19478190661Patrick De Geest07/2019
51463*5^129698+890656Lelio R Paula10/2014
5147F(433781)90655Henri Lifchitz09/2003
514819^70891+8290653Lelio R Paula06/2016
5149(29*2^301124-1)/1390648Lelio R Paula02/2014
515010^90636+6415990637Patrick De Geest07/2019
515110^90636-310190636Patrick De Geest11/2018
51527*3^189953-890632Lelio R Paula08/2014
515310^90626+33928990627Patrick De Geest07/2019
515410^90626-113190626Patrick De Geest11/2018
515511^87022-180090625Enzo Doria12/2012
515610^90623+86190624Patrick De Geest11/2018
515710^90623-30584190623Patrick De Geest07/2019
5158(2^301042+47)/1203696990616Lelio R Paula06/2013
51602^301004-278693990612Enzo Doria03/2016
515910^90611+16997790612Patrick De Geest07/2019
516210^90611-973790611Patrick De Geest11/2018
516110^90610+3674790611Patrick De Geest07/2019
516310^90609+682390610Patrick De Geest11/2018
516410^90610-2657390610Patrick De Geest07/2019
516510^90609-22817390609Patrick De Geest07/2019
51662^300980-2790605Lelio R Paula11/2012
51672*10^90597-790598Dmitry Domanov11/2010
5168197^39485+290597Lelio R Paula06/2013
51697^107198+4890593Lelio R Paula04/2016
5170(86*10^90588+121)/990589Robert Price03/2017
51712^300923+5390587Lelio R Paula11/2012
51722^300874+790573Lelio R Paula10/2012
517310^90567+948990568Patrick De Geest11/2018
517510^90567-23135390567Patrick De Geest07/2019
5174(2^300857+2214)/290567Stefano Morozzi01/2020
51765^129568-5690565Lelio R Paula04/2016
51772^300847-11283190564Enzo Doria06/2014
517810^90562+79019790563Patrick De Geest07/2019
517910^90562-298190562Patrick De Geest11/2018
518010^90549+381190550Patrick De Geest11/2018
518110^90549-63030390549Patrick De Geest07/2019
51822^300790-454190547Yves Minet03/2019
518310^90532+816990533Patrick De Geest11/2018
518410^90531+983190532Patrick De Geest11/2018
518510^90532-15488990532Patrick De Geest07/2019
518610^90531-106058990531Patrick De Geest07/2019
51872^300718+25525590526Lelio R Paula02/2016
5188(2^300719+938)/290526Stefano Morozzi01/2020
518910^90516+21591790517Patrick De Geest07/2019
519010^90516-678390516Patrick De Geest11/2018
519110^90511+3017790512Patrick De Geest07/2019
519210^90511-697790511Patrick De Geest11/2018
51932^300637+9590501Lelio R Paula11/2012
51957^107087-2490500Lelio R Paula04/2016
519410^90499+19154790500Patrick De Geest07/2019
519610^90499-582390499Patrick De Geest11/2018
5198(10^90499+3^90499)/1390498Robert Price01/2013
519713^81241+9090498Lelio R Paula06/2016
5199(2^300600+1222)/290490Stefano Morozzi01/2020
520010^90480+513190481Patrick De Geest11/2018
520110^90480-8572190480Patrick De Geest07/2019
52026^116273-8590478Lelio R Paula05/2016
520310^90473+313990474Patrick De Geest11/2018
520410^90473-15059990473Patrick De Geest07/2019
520510^90470+231990471Patrick De Geest11/2018
520610^90470-7163790470Patrick De Geest07/2019
52076^116256-1757390465Enzo Doria02/2013
52082^300502+5461590461Lelio R Paula02/2016
5209(13*2^300487+1)/4590456Lelio R Paula09/2013
521010^90453+14184390454Patrick De Geest07/2019
521110^90453-396990453Patrick De Geest11/2018
521210^90440+135990441Patrick De Geest11/2018
521310^90440-1882190440Patrick De Geest07/2019
5214(3^189545-8)/590436Lelio R Paula01/2013
5215(7*2^300406-1)/390432Lelio R Paula02/2014
521610^90430+333990431Patrick De Geest11/2018
521710^90430-6347790430Patrick De Geest07/2019
521810^90414+22959390415Patrick De Geest07/2019
521910^90414-154790414Patrick De Geest11/2018
522010^90404+4704190405Patrick De Geest07/2019
522110^90404-642990404Patrick De Geest11/2018
522210^90401+207790402Patrick De Geest11/2018
522310^90401-36863790401Patrick De Geest07/2019
52244*5^129332+390400Lelio R Paula10/2014
522510^90397+1978390398Patrick De Geest07/2019
522710^90397-32390397Patrick De Geest11/2018
5226(2^300293+2762)/290397Stefano Morozzi01/2020
52282^300249-1624590384Enzo Doria04/2013
5229(7*10^90371-313)/990371Robert Price11/2016
523010^90363+5867790364Patrick De Geest07/2019
523110^90363-355790363Patrick De Geest11/2018
523210^90358+10464190359Patrick De Geest07/2019
52342*6^116118+790358Lelio R Paula10/2014
523510^90358-497990358Patrick De Geest11/2018
523310^90357+11283790358Patrick De Geest07/2019
523610^90357-18959390357Patrick De Geest07/2019
523710^90356+5311390357Patrick De Geest07/2019
523810^90356-719790356Patrick De Geest11/2018
523910^90353+60321190354Patrick De Geest07/2019
524010^90353-108990353Patrick De Geest11/2018
5241(24737*2^300101+1)/2590343Lelio R Paula06/2014
52424*10^90334-2190335Robert Price04/2016
524310^90322+13769190323Patrick De Geest07/2019
524410^90322-955190322Patrick De Geest11/2018
524510^90316+999190317Patrick De Geest11/2018
524610^90316-4562790316Patrick De Geest07/2019
524710^90315+3288990316Patrick De Geest07/2019
52482^300019-11033590315Enzo Doria05/2014
524910^90315-856190315Patrick De Geest11/2018
5250FAB2(300001,5032)90310Robert Price05/2019


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 29 2020 17:41 (Time in France)

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