PRP Records

Probable Primes Top 10000

(253466 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 ?
50016^115840-5590142Lelio R Paula05/2016
5002(5*10^90142-473)/990142Robert Price12/2017
50038*7^106659+590139Lelio R Paula10/2014
50042^299406-1665390131Enzo Doria05/2013
500510^90128+28867390129Patrick De Geest07/2019
5007208049#+(216091#)/(208049#)90128Makoto Morimoto04/2016
500610^90128-838790128Patrick De Geest09/2018
5008(F(5)^128941-F(4)^128941)/F(3)90126Wayne Halsdorf03/2012
50096^115819-5390125Lelio R Paula05/2016
501010^90123+631390124Patrick De Geest09/2018
50126^115816-1685390123Enzo Doria02/2013
501110^90123-2261790123Patrick De Geest07/2019
50136^115813-2390121Lelio R Paula05/2016
5014(22*10^90110+161)/390111Robert Price02/2017
5015(2^299330-509203)/6990106Lelio R Paula01/2013
501610^90105+91575990106Patrick De Geest07/2019
501810^90105-76790105Patrick De Geest09/2018
501710^90104+4818990105Patrick De Geest07/2019
501910^90104-770390104Patrick De Geest09/2018
502010^90103+915990104Patrick De Geest09/2018
502110^90103-20845790103Patrick De Geest07/2019
502210^90102+7301190103Patrick De Geest07/2019
502310^90102-60243390102Patrick De Geest07/2019
502410^90101+122553790102Patrick De Geest07/2019
502510^90101-320790101Patrick De Geest09/2018
5026(29*10^90096-17)/390097Erik Branger09/2014
502710^90089+14318190090Patrick De Geest07/2019
502810^90089-357390089Patrick De Geest09/2018
50292^299247+187052990083Enzo Doria05/2016
503010^90079+160990080Patrick De Geest09/2018
503110^90079-23004390079Patrick De Geest07/2019
50322^299229-279778390077Enzo Doria04/2016
50332^299220-1631790075Enzo Doria04/2013
503411^86491-135090072Enzo Doria12/2012
503510^90071+5233390072Patrick De Geest07/2019
503610^90071-123390071Patrick De Geest09/2018
503710^90069+15852790070Patrick De Geest07/2019
503810^90069-784190069Patrick De Geest09/2018
5039(31*10^90064-1)/390066Robert Price03/2017
504010^90060+14943190061Patrick De Geest07/2019
504110^90060-83990060Patrick De Geest09/2018
504210^90052+236190053Patrick De Geest09/2018
504310^90052-9092990052Patrick De Geest07/2019
504410^90047+61990048Patrick De Geest09/2018
504510^90047-15107190047Patrick De Geest07/2019
5046L(430949)/861899/144038756153990045Serge Batalov07/2017
50472^299112+7395190042Enzo Doria04/2016
50488^99702+7^(99702-1)90040Robert Price02/2016
504910^90038+15780390039Patrick De Geest07/2019
505010^90038-968790038Patrick De Geest09/2018
50515*10^90033+390034Dmitry Domanov11/2010
505210^90030+22581390031Patrick De Geest07/2019
505310^90030-146190030Patrick De Geest09/2018
5054243^37738+37738^24390029Norbert Schneider01/2015
505510^90025+7056990026Patrick De Geest07/2019
505610^90025-870390025Patrick De Geest09/2018
50572^299048-11329790023Enzo Doria07/2014
505810^90015+84990016Patrick De Geest09/2018
505910^90015-22838790015Patrick De Geest07/2019
506010^90010+681190011Patrick De Geest09/2018
506110^90010-18359790010Patrick De Geest11/2018
506210^90009+5832190010Patrick De Geest11/2018
506310^90008+84790009Patrick De Geest09/2018
506410^90009-35601390009Patrick De Geest11/2018
50663^188648+9290008Lelio R Paula12/2015
506510^90008-70604990008Patrick De Geest11/2018
50675*2^298991+790006Lelio R Paula08/2014
5068(25*2^298997+1)/326790005Lelio R Paula01/2013
506910^90000+886990001Patrick De Geest12/2009
507110^89999+8293990000Dirk Augustin04/2007
507010^90000-14034390000Patrick De Geest12/2009
507210^89999-19489189999Patrick De Geest11/2009
507319^70365-7889980Lelio R Paula12/2015
5074NaturalLogarithmOf2(89973)89973Eric W. Weisstein10/2015
50752^298852-6487589964Lelio R Paula11/2013
507618^71659+3789952Lelio R Paula12/2015
5077(2908*29^61501-3)/789942Curtis Bright05/2015
507817^73067+2089906Lelio R Paula11/2015
50792^298637-9989899Lelio R Paula10/2012
50809^94188+3*8^94188-2*4^94188-3*2^9418889879Mike Oakes01/2011
50819*10^89858+1989859Robert Price05/2016
50822^298501+187006789858Enzo Doria05/2016
508311^86280-9889852Lelio R Paula11/2015
50842^298473-11005989850Enzo Doria04/2014
508519^70263-3289850Lelio R Paula12/2015
5086(299*10^89836-17)/389838Robert Price01/2017
50873^188286+1489836Robert Price09/2013
5088gcd(V(1091095),5*F(218219)*(F(218219)+1)+1)89822Serge Batalov04/2015
50892^298367+5890589818Lelio R Paula11/2013
50902^298319-10965789803Enzo Doria04/2014
50918*10^89800+8189801Robert Price05/2017
509218^71505-9189759Lelio R Paula12/2015
5093(7^106187+1)/889738Paul Bourdelais04/2008
50942^298079-10953189731Enzo Doria04/2014
5095117^43380+11689718Norbert Schneider08/2018
5096(22699*2^298016+1)/38589714Lelio R Paula06/2014
5097156*(10^(4*22427)-1)/101-189709Robert Price05/2014
50982^298003-6694589708Lelio R Paula11/2013
5099(23*10^89705-83)/389706Robert Price09/2017
510017^72900-5489700Lelio R Paula11/2015
51013*2^297956+589695Lelio R Paula08/2014
510220^68938-1189691Lelio R Paula01/2016
510389*10^89687-789689Robert Price03/2017
51042^297923+7778389684Enzo Doria05/2016
510511^86107-2457600089672Enzo Doria02/2013
51062^297878-11191189671Enzo Doria05/2014
51077^106084+4089652Lelio R Paula10/2015
5108(86*10^89640-311)/989641Robert Price10/2017
51093*10^89608-5989609Robert Price10/2017
51103^187780-1103889594Enzo Doria05/2014
5111(13*2^297560-1)/4915178789568Lelio R Paula02/2014
51125^128141-3689567Lelio R Paula10/2015
51134*7^105951+989540Lelio R Paula10/2014
5114(7*10^89539-439)/989539Robert Price09/2017
51152^297397+17725789526Enzo Doria05/2016
51162^297346-1624189511Enzo Doria04/2013
5117(5*10^89510+79)/389511Robert Price11/2017
51184^148663-3^14866389505Jean-Louis Charton11/2005
51192^297328-86968810589505Lelio R Paula07/2016
51202^297325-45904389504Enzo Doria05/2015
51212^297310-11239189500Enzo Doria06/2014
51222^297296-11215789496Enzo Doria06/2014
512357^50966-289490Lelio R Paula08/2013
5124(266*10^89482+1)/389484Robert Price02/2016
5125(14*10^89480-101)/389481Robert Price04/2017
51262^297122+9989443Lelio R Paula10/2012
5127(3^187435-5)/128689427Lelio R Paula01/2013
5128(25*10^89413+161)/389414Robert Price01/2017
51292^296990+187069989403Enzo Doria05/2016
51302^296972-101789398Lelio R Paula11/2013
5131(7*10^89383+167)/389384Robert Kinser10/2017
5132(85*10^89375-31)/989376Robert Price11/2015
51339*2^296870+789368Lelio R Paula08/2014
5134100^44683-99^4468389366Robert Price07/2013
51352^296810+7651989349Enzo Doria05/2016
51368^98928+7^(98928+1)89341Robert Price06/2016
5137(3^187247+4)/102789337Lelio R Paula01/2013
5138(3^187235-2)/204589331Lelio R Paula01/2013
51392^296736-43214989327Paul Bourdelais05/2013
51402^296737-11251989327Enzo Doria06/2014
51412^296718-364589322Lelio R Paula11/2013
51422^296681-1622189310Enzo Doria04/2013
51432^296669-1651389307Enzo Doria04/2013
51442^296619-1635789292Enzo Doria04/2013
51452^296614-11005189290Enzo Doria04/2014
5146(3^187138+8)/8314789283Lelio R Paula01/2013
5147(2*10^89279+457)/989279Robert Price01/2017
514815^75907-2889274Lelio R Paula11/2015
51492^296547-3789270Yves Minet01/2012
51502^296485+19189251Lelio R Paula10/2012
51512^296467-7589246Lelio R Paula10/2012
51522^296416-10953589231Enzo Doria04/2014
5153(23*2^296406+1)/389228Lelio R Paula01/2013
515466^49037-6589225Norbert Schneider11/2014
51552^296377-1624589219Enzo Doria04/2013
51562^296372-6487589217Lelio R Paula11/2013
51575*6^114648-789215Lelio R Paula10/2014
51583*10^89206+1389207Robert Price08/2017
51597*3^186960-489204Lelio R Paula08/2014
51602^296290-11213389193Enzo Doria06/2014
51616^114620-1700389192Enzo Doria02/2013
5162(4*10^89189+41)/989189Robert Price11/2014
51632^296261-16118189184Enzo Doria04/2013
5164(19*2^296269-1)/53062389182Lelio R Paula02/2014
51653^186903-1089176Robert Price09/2013
51677*10^89169-389170Dmitry Domanov11/2010
5166(2^296221-1017)/3589170Lelio R Paula01/2013
5168(43*10^89169+47)/989170Robert Price12/2017
5169(10^89160+29)/389160Serge Batalov12/2014
5170(28*10^89141-97)/389142Robert Price07/2016
51712^296116-73463989140Paul Bourdelais04/2013
51726^114544-13389133Lelio R Paula12/2015
51732^296076-11329789128Enzo Doria07/2014
5174(11*2^296060-1)/21589122Lelio R Paula02/2014
51755*10^89118+8189119Robert Price08/2017
51762^296037-141189117Yves Minet01/2013
51772^296020-260480989111Enzo Doria05/2015
51782^296016+8189110Henri Lifchitz02/2007
51792^296010-1189108Lelio R Paula10/2012
51802^295998-11191189105Enzo Doria05/2014
5181(2^296014+47)/9399114989102Lelio R Paula01/2013
51822^295939-1662189087Enzo Doria04/2013
51832^295934-10969189086Enzo Doria04/2014
5184(185*10^89063+7)/389065Robert Price02/2017
51852^295831+14389055Lelio R Paula10/2012
518631^59713-3089054Theodore Burton02/2007
5187(7*2^295834-1)/2766389052Lelio R Paula02/2014
5188123^42608+289047Lelio R Paula05/2013
51896^114433-114433^689047Norbert Schneider04/2017
51902^295800-45965989045Enzo Doria05/2015
5191(52*10^89037-1)/389039Robert Price02/2017
5192(6^114398-11)/589019Paul Bourdelais11/2011
519311^85470-585089008Enzo Doria02/2013
5194(27*2^295634+1)/468788993Lelio R Paula01/2013
5195(p(18424)#-4)/288985Robert Price09/2017
51962^295564-18988974Lelio R Paula10/2012
51972^295557+7309788972Enzo Doria04/2016
519811^85433-576088970Enzo Doria01/2013
51996*10^88938-9188939Robert Price11/2017
520015^75619-8888935Lelio R Paula11/2015
52012^295385-8588920Lelio R Paula10/2012
52022^295385-1633388920Enzo Doria04/2013
52032^295309+5988897Lelio R Paula10/2012
52042^295288-10979988891Enzo Doria04/2014
520510^88888+17037388889Stefano Morozzi07/2018
520610^88888+27139988889Stefano Morozzi07/2018
520710^88888+37539788889Stefano Morozzi07/2018
520810^88888+54882388889Stefano Morozzi07/2018
520910^88888+82086188889Stefano Morozzi07/2018
521010^88888+120634988889Stefano Morozzi07/2018
521110^88888+129204788889Stefano Morozzi07/2018
521210^88888+145602988889Stefano Morozzi07/2018
521310^88888-49028788888Patrick De Geest09/2018
52142^295245+6588878Lelio R Paula10/2012
5215Padovan(727734)88874Eric W. Weisstein04/2011
521618^70793-1788865Lelio R Paula11/2015
52176^114196-1757388862Enzo Doria02/2013
5218302^35829+35829^30288857Norbert Schneider12/2014
52193^186223+1688851Robert Price10/2013
52203*2^295139+788847Lelio R Paula08/2014
52213^186212-11300888846Enzo Doria07/2014
522287^45803-8688836Norbert Schneider11/2015
52232^295094-11027388833Enzo Doria05/2014
52242^295080+186915188828Enzo Doria05/2016
52252^295027-11340788812Enzo Doria07/2014
5226(2*10^88808-71)/388808Robert Price01/2017
522713^79722-8088806Lelio R Paula11/2015
52283^186103+10488794Lelio R Paula12/2015
5229(3*2^294971+1)/2556588792Lelio R Paula01/2013
52302^294937-11500388785Enzo Doria06/2015
52312^294868-10970988765Enzo Doria04/2014
52322^294864-298588763Yves Minet09/2014
5233(17*10^88761-41)/388762Robert Price09/2017
52342^294754+1501588730Lelio R Paula10/2013
5235(3^185951-7)/2088720Lelio R Paula01/2013
5236(2^294661+5)/44369338388694Lelio R Paula01/2013
5237(10^88680+11)/388680Robert Price11/2014
52382*7^104928-988675Lelio R Paula10/2014
523911^85150+1288675Lelio R Paula11/2015
52408*6^113951+588673Lelio R Paula10/2014
52416^113940-1856388663Enzo Doria03/2013
524238^56123-56123^3888663Norbert Schneider02/2017
52432^294492-6588651Lelio R Paula10/2012
524420^68120-5388627Lelio R Paula01/2016
5245122^42477-12188623Norbert Schneider10/2018
52462^294391-11325788621Enzo Doria07/2014
52475^126784-1547688619Enzo Doria02/2013
52482^294327+988602Lelio R Paula10/2012
52492^294320+1891588600Lelio R Paula10/2013
5250(98*10^88595-89)/9988595Ray Chandler07/2011


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 20 2019 14:10 (Time in France)

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