PRP Records

Probable Primes Top 10000

(211563 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 (> 30000) Who ? When ?
42518^99702+7^(99702-1)90040Robert Price02/2016
42525*10^90033+390034Dmitry Domanov11/2010
4253243^37738+37738^24390029Norbert Schneider01/2015
42542^299048-11329790023Enzo Doria07/2014
42553^188648+9290008Lelio R Paula12/2015
42565*2^298991+790006Lelio R Paula08/2014
4257(25*2^298997+1)/326790005Lelio R Paula01/2013
425810^90000+886990001Patrick De Geest12/2009
426010^89999+8293990000Dirk Augustin04/2007
425910^90000-14034390000Patrick De Geest12/2009
426110^89999-19489189999Patrick De Geest11/2009
426219^70365-7889980Lelio R Paula12/2015
4263NaturalLogarithmOf2(89973)89973Eric W. Weisstein10/2015
42642^298852-6487589964Lelio R Paula11/2013
426518^71659+3789952Lelio R Paula12/2015
4266(2908*29^61501-3)/789942Curtis Bright05/2015
426717^73067+2089906Lelio R Paula11/2015
42682^298637-9989899Lelio R Paula10/2012
42699^94188+3*8^94188-2*4^94188-3*2^9418889879Mike Oakes01/2011
42709*10^89858+1989859Robert Price05/2016
42712^298501+187006789858Enzo Doria05/2016
427211^86280-9889852Lelio R Paula11/2015
42732^298473-11005989850Enzo Doria04/2014
427419^70263-3289850Lelio R Paula12/2015
4275(299*10^89836-17)/389838Robert Price01/2017
42763^188286+1489836Robert Price09/2013
4277gcd(V(1091095),5*F(218219)*(F(218219)+1)+1)89822Serge Batalov04/2015
42782^298367+5890589818Lelio R Paula11/2013
42792^298319-10965789803Enzo Doria04/2014
42808*10^89800+8189801Robert Price05/2017
428118^71505-9189759Lelio R Paula12/2015
4282(7^106187+1)/889738Paul Bourdelais04/2008
42832^298079-10953189731Enzo Doria04/2014
4284(22699*2^298016+1)/38589714Lelio R Paula06/2014
4285156*(10^(4*22427)-1)/101-189709Robert Price05/2014
42862^298003-6694589708Lelio R Paula11/2013
4287(23*10^89705-83)/389706Robert Price09/2017
428817^72900-5489700Lelio R Paula11/2015
42893*2^297956+589695Lelio R Paula08/2014
429020^68938-1189691Lelio R Paula01/2016
429189*10^89687-789689Robert Price03/2017
42922^297923+7778389684Enzo Doria05/2016
429311^86107-2457600089672Enzo Doria02/2013
42942^297878-11191189671Enzo Doria05/2014
42957^106084+4089652Lelio R Paula10/2015
4296(86*10^89640-311)/989641Robert Price10/2017
42973*10^89608-5989609Robert Price10/2017
42983^187780-1103889594Enzo Doria05/2014
4299(13*2^297560-1)/4915178789568Lelio R Paula02/2014
43005^128141-3689567Lelio R Paula10/2015
43014*7^105951+989540Lelio R Paula10/2014
4302(7*10^89539-439)/989539Robert Price09/2017
43032^297397+17725789526Enzo Doria05/2016
43042^297346-1624189511Enzo Doria04/2013
4305(5*10^89510+79)/389511Robert Price11/2017
43074^148663-3^14866389505Jean-Louis Charton11/2005
43062^297328-86968810589505Lelio R Paula07/2016
43082^297325-45904389504Enzo Doria05/2015
43092^297310-11239189500Enzo Doria06/2014
43102^297296-11215789496Enzo Doria06/2014
431157^50966-289490Lelio R Paula08/2013
4312(266*10^89482+1)/389484Robert Price02/2016
4313(14*10^89480-101)/389481Robert Price04/2017
43142^297122+9989443Lelio R Paula10/2012
4315(3^187435-5)/128689427Lelio R Paula01/2013
4316(25*10^89413+161)/389414Robert Price01/2017
43172^296990+187069989403Enzo Doria05/2016
43182^296972-101789398Lelio R Paula11/2013
4319(7*10^89383+167)/389384Robert Kinser10/2017
4320(85*10^89375-31)/989376Robert Price11/2015
43219*2^296870+789368Lelio R Paula08/2014
4322100^44683-99^4468389366Robert Price07/2013
43232^296810+7651989349Enzo Doria05/2016
43248^98928+7^(98928+1)89341Robert Price06/2016
4325(3^187247+4)/102789337Lelio R Paula01/2013
4326(3^187235-2)/204589331Lelio R Paula01/2013
43272^296736-43214989327Paul Bourdelais05/2013
43282^296737-11251989327Enzo Doria06/2014
43292^296718-364589322Lelio R Paula11/2013
43302^296681-1622189310Enzo Doria04/2013
43312^296669-1651389307Enzo Doria04/2013
43322^296619-1635789292Enzo Doria04/2013
43332^296614-11005189290Enzo Doria04/2014
4334(3^187138+8)/8314789283Lelio R Paula01/2013
4335(2*10^89279+457)/989279Robert Price01/2017
433615^75907-2889274Lelio R Paula11/2015
43372^296547-3789270Yves Minet01/2012
43382^296485+19189251Lelio R Paula10/2012
43392^296467-7589246Lelio R Paula10/2012
43402^296416-10953589231Enzo Doria04/2014
4341(23*2^296406+1)/389228Lelio R Paula01/2013
434266^49037-6589225Norbert Schneider11/2014
43432^296377-1624589219Enzo Doria04/2013
43442^296372-6487589217Lelio R Paula11/2013
43455*6^114648-789215Lelio R Paula10/2014
43463*10^89206+1389207Robert Price08/2017
43477*3^186960-489204Lelio R Paula08/2014
43482^296290-11213389193Enzo Doria06/2014
43496^114620-1700389192Enzo Doria02/2013
4350(4*10^89189+41)/989189Robert Price11/2014
43512^296261-16118189184Enzo Doria04/2013
4352(19*2^296269-1)/53062389182Lelio R Paula02/2014
43533^186903-1089176Robert Price09/2013
43567*10^89169-389170Dmitry Domanov11/2010
4354(2^296221-1017)/3589170Lelio R Paula01/2013
4355(43*10^89169+47)/989170Robert Price12/2017
4357(10^89160+29)/389160Serge Batalov12/2014
4358(28*10^89141-97)/389142Robert Price07/2016
43592^296116-73463989140Paul Bourdelais04/2013
43606^114544-13389133Lelio R Paula12/2015
43612^296076-11329789128Enzo Doria07/2014
4362(11*2^296060-1)/21589122Lelio R Paula02/2014
43635*10^89118+8189119Robert Price08/2017
43642^296037-141189117Yves Minet01/2013
43652^296020-260480989111Enzo Doria05/2015
43662^296016+8189110Henri Lifchitz02/2007
43672^296010-1189108Lelio R Paula10/2012
43682^295998-11191189105Enzo Doria05/2014
4369(2^296014+47)/9399114989102Lelio R Paula01/2013
43702^295939-1662189087Enzo Doria04/2013
43712^295934-10969189086Enzo Doria04/2014
4372(185*10^89063+7)/389065Robert Price02/2017
43732^295831+14389055Lelio R Paula10/2012
437431^59713-3089054Theodore Burton02/2007
4375(7*2^295834-1)/2766389052Lelio R Paula02/2014
4376123^42608+289047Lelio R Paula05/2013
43776^114433-114433^689047Norbert Schneider04/2017
43782^295800-45965989045Enzo Doria05/2015
4379(52*10^89037-1)/389039Robert Price02/2017
4380(6^114398-11)/589019Paul Bourdelais11/2011
438111^85470-585089008Enzo Doria02/2013
4382(27*2^295634+1)/468788993Lelio R Paula01/2013
4383(p(18424)#-4)/288985Robert Price09/2017
43842^295564-18988974Lelio R Paula10/2012
43852^295557+7309788972Enzo Doria04/2016
438611^85433-576088970Enzo Doria01/2013
43876*10^88938-9188939Robert Price11/2017
438815^75619-8888935Lelio R Paula11/2015
43892^295385-8588920Lelio R Paula10/2012
43902^295385-1633388920Enzo Doria04/2013
43912^295309+5988897Lelio R Paula10/2012
43922^295288-10979988891Enzo Doria04/2014
43932^295245+6588878Lelio R Paula10/2012
4394Padovan(727734)88874Eric W. Weisstein04/2011
439518^70793-1788865Lelio R Paula11/2015
43966^114196-1757388862Enzo Doria02/2013
4397302^35829+35829^30288857Norbert Schneider12/2014
43983^186223+1688851Robert Price10/2013
43993*2^295139+788847Lelio R Paula08/2014
44003^186212-11300888846Enzo Doria07/2014
440187^45803-8688836Norbert Schneider11/2015
44022^295094-11027388833Enzo Doria05/2014
44032^295080+186915188828Enzo Doria05/2016
44042^295027-11340788812Enzo Doria07/2014
4405(2*10^88808-71)/388808Robert Price01/2017
440613^79722-8088806Lelio R Paula11/2015
44073^186103+10488794Lelio R Paula12/2015
4408(3*2^294971+1)/2556588792Lelio R Paula01/2013
44092^294937-11500388785Enzo Doria06/2015
44102^294868-10970988765Enzo Doria04/2014
44112^294864-298588763Yves Minet09/2014
4412(17*10^88761-41)/388762Robert Price09/2017
44132^294754+1501588730Lelio R Paula10/2013
4414(3^185951-7)/2088720Lelio R Paula01/2013
4415(2^294661+5)/44369338388694Lelio R Paula01/2013
4416(10^88680+11)/388680Robert Price11/2014
44172*7^104928-988675Lelio R Paula10/2014
441811^85150+1288675Lelio R Paula11/2015
44198*6^113951+588673Lelio R Paula10/2014
44206^113940-1856388663Enzo Doria03/2013
442138^56123-56123^3888663Norbert Schneider02/2017
44222^294492-6588651Lelio R Paula10/2012
442320^68120-5388627Lelio R Paula01/2016
44242^294391-11325788621Enzo Doria07/2014
44255^126784-1547688619Enzo Doria02/2013
44262^294327+988602Lelio R Paula10/2012
44272^294320+1891588600Lelio R Paula10/2013
4428(98*10^88595-89)/9988595Ray Chandler07/2011
4429(17*2^294262-1)/1388582Lelio R Paula02/2014
4430(2*10^88545+7)/988545Erik Branger03/2011
44312^294137-13388545Lelio R Paula10/2012
4432(2^294092-1017)/117188528Lelio R Paula01/2013
44334^147036+147036^4+188525Robert Price04/2014
4434(14^77213-5^77213)/988496Robert Price04/2013
44352^293965+279337788493Enzo Doria03/2016
443611^84971-15088489Enzo Doria08/2012
4437(2^293956-1017)/3985137669667788476Lelio R Paula01/2013
443811^84958-219088475Enzo Doria12/2012
44392^293880-11134788467Enzo Doria05/2014
4440(106*10^88459-1)/388461Serge Batalov12/2014
444110^88457+27873388458Patrick De Geest07/2017
444210^88457-40188457Robert Price06/2017
444311^84908-168088423Enzo Doria12/2012
44442^293679-11207588407Enzo Doria06/2014
44456^113608-6588405Lelio R Paula12/2015
44462^293624+8287588390Lelio R Paula10/2013
44472^293612-11233788387Enzo Doria06/2014
4448758^30693+30693^75888386Norbert Schneider05/2017
4449gcd(V(1062695),5*F(212539)*(F(212539)-1)+1)88383Serge Batalov04/2015
44505*10^88377+7788378Robert Price06/2016
4451(5*2^293526+1)/30388359Lelio R Paula01/2013
44522^293461-278584388341Enzo Doria03/2016
44532^293416-103788328Yves Minet11/2012
4454(2^293384-7)/388317Lelio R Paula01/2013
4455(3^185092-5)/488311Lelio R Paula01/2013
4456(5*10^88303-173)/388304Robert Price11/2017
445714^77039-5788297Lelio R Paula11/2015
44583*10^88293-5988294Robert Price10/2017
44595^126303+4288283Lelio R Paula10/2015
446019^69025-1888266Theodore Burton01/2006
44615*10^88261-388262Dmitry Domanov11/2010
44628^97731-7^(97731-1)88260Robert Price04/2016
44635*10^88254+5988255Robert Price09/2016
44644*3^184968-788253Lelio R Paula08/2014
44657^104426+8888251Lelio R Paula10/2015
44662^293142+9988245Lelio R Paula10/2012
446711^84736-213088244Enzo Doria12/2012
44682^293068-8988223Lelio R Paula10/2012
44692^293014-10965588207Enzo Doria04/2014
44708*7^104371-388205Lelio R Paula10/2014
44712^292995-214588201Lelio R Paula10/2013
44725*10^88182+7788183Robert Price06/2016
44742^292929+4387788181Donovan Johnson04/2005
44736^113321+13188181Lelio R Paula12/2015
44752^292904-58394988173Paul Bourdelais04/2013
44762^292894-11185188170Enzo Doria05/2014
44772^292872-279734988164Enzo Doria03/2016
44782^292860-10968588160Enzo Doria04/2014
44799*6^113288-588157Lelio R Paula10/2014
4480(2*10^88112-23)/388112Robert Price09/2017
4481(73*10^88105+17)/988106Robert Price10/2015
448211^84588+7888090Lelio R Paula11/2015
4483(265*10^88077+11)/388079Robert Price03/2017
448491^44959-90^4495988077Robert Price07/2015
44856^113177-5^11317788069Jean-Louis Charton01/2009
4486(10^88020+101)/388020Robert Price04/2016
4487(10^(2*43982+1)-6*10^43982-1)/387965Robert Price02/2016
4488(424*10^87930-1)/987932Robert Price11/2017
4489p(18225)#/2+12887929Robert Price04/2017
44904*6^112977+787914Lelio R Paula10/2014
449114^76677+6987882Lelio R Paula11/2015
4492(22*10^87863-1)/387864Robert Price12/2014
44932^291822-279781187848Enzo Doria04/2016
44942^291716-11138987816Enzo Doria05/2014
4495(782*10^87809-71)/987811Robert Price06/2017
44963^184039+182087809Lelio R Paula12/2015
449712^81356+4187798Lelio R Paula11/2015
44986^112792-1898387770Enzo Doria03/2013
44993*6^112787-587766Lelio R Paula10/2014
45007^103848+8287762Lelio R Paula10/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2018 23:06 (Time in France)

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