PRP Records

Probable Primes Top 10000

(205869 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 ?
4251100^44683-99^4468389366Robert Price07/2013
42522^296810+7651989349Enzo Doria05/2016
42538^98928+7^(98928+1)89341Robert Price06/2016
4254(3^187247+4)/102789337Lelio R Paula01/2013
4255(3^187235-2)/204589331Lelio R Paula01/2013
42572^296736-43214989327Paul Bourdelais05/2013
42562^296737-11251989327Enzo Doria06/2014
42582^296718-364589322Lelio R Paula11/2013
42592^296681-1622189310Enzo Doria04/2013
42602^296669-1651389307Enzo Doria04/2013
42612^296619-1635789292Enzo Doria04/2013
42622^296614-11005189290Enzo Doria04/2014
4263(3^187138+8)/8314789283Lelio R Paula01/2013
4264(2*10^89279+457)/989279Robert Price01/2017
426515^75907-2889274Lelio R Paula11/2015
42662^296547-3789270Yves Minet01/2012
42672^296485+19189251Lelio R Paula10/2012
42682^296467-7589246Lelio R Paula10/2012
42692^296416-10953589231Enzo Doria04/2014
4270(23*2^296406+1)/389228Lelio R Paula01/2013
427166^49037-6589225Norbert Schneider11/2014
42722^296377-1624589219Enzo Doria04/2013
42732^296372-6487589217Lelio R Paula11/2013
42745*6^114648-789215Lelio R Paula10/2014
42753*10^89206+1389207Robert Price08/2017
42767*3^186960-489204Lelio R Paula08/2014
42772^296290-11213389193Enzo Doria06/2014
42786^114620-1700389192Enzo Doria02/2013
4279(4*10^89189+41)/989189Robert Price11/2014
42802^296261-16118189184Enzo Doria04/2013
4281(19*2^296269-1)/53062389182Lelio R Paula02/2014
42823^186903-1089176Robert Price09/2013
42847*10^89169-389170Dmitry Domanov11/2010
4283(2^296221-1017)/3589170Lelio R Paula01/2013
4285(43*10^89169+47)/989170Robert Price12/2017
4286(10^89160+29)/389160Serge Batalov12/2014
4287(28*10^89141-97)/389142Robert Price07/2016
42882^296116-73463989140Paul Bourdelais04/2013
42896^114544-13389133Lelio R Paula12/2015
42902^296076-11329789128Enzo Doria07/2014
4291(11*2^296060-1)/21589122Lelio R Paula02/2014
42925*10^89118+8189119Robert Price08/2017
42932^296037-141189117Yves Minet01/2013
42942^296020-260480989111Enzo Doria05/2015
42952^296016+8189110Henri Lifchitz02/2007
42962^296010-1189108Lelio R Paula10/2012
42972^295998-11191189105Enzo Doria05/2014
4298(2^296014+47)/9399114989102Lelio R Paula01/2013
42992^295939-1662189087Enzo Doria04/2013
43002^295934-10969189086Enzo Doria04/2014
4301(185*10^89063+7)/389065Robert Price02/2017
43022^295831+14389055Lelio R Paula10/2012
430331^59713-3089054Theodore Burton02/2007
4304(7*2^295834-1)/2766389052Lelio R Paula02/2014
4305123^42608+289047Lelio R Paula05/2013
43066^114433-114433^689047Norbert Schneider04/2017
43072^295800-45965989045Enzo Doria05/2015
4308(52*10^89037-1)/389039Robert Price02/2017
4309(6^114398-11)/589019Paul Bourdelais11/2011
431011^85470-585089008Enzo Doria02/2013
4311(27*2^295634+1)/468788993Lelio R Paula01/2013
4312(p(18424)#-4)/288985Robert Price09/2017
43132^295564-18988974Lelio R Paula10/2012
43142^295557+7309788972Enzo Doria04/2016
431511^85433-576088970Enzo Doria01/2013
43166*10^88938-9188939Robert Price11/2017
431715^75619-8888935Lelio R Paula11/2015
43182^295385-8588920Lelio R Paula10/2012
43192^295385-1633388920Enzo Doria04/2013
43202^295309+5988897Lelio R Paula10/2012
43212^295288-10979988891Enzo Doria04/2014
43222^295245+6588878Lelio R Paula10/2012
4323Padovan(727734)88874Eric W. Weisstein04/2011
432418^70793-1788865Lelio R Paula11/2015
43256^114196-1757388862Enzo Doria02/2013
4326302^35829+35829^30288857Norbert Schneider12/2014
43273^186223+1688851Robert Price10/2013
43283*2^295139+788847Lelio R Paula08/2014
43293^186212-11300888846Enzo Doria07/2014
433087^45803-8688836Norbert Schneider11/2015
43312^295094-11027388833Enzo Doria05/2014
43322^295080+186915188828Enzo Doria05/2016
43332^295027-11340788812Enzo Doria07/2014
4334(2*10^88808-71)/388808Robert Price01/2017
433513^79722-8088806Lelio R Paula11/2015
43363^186103+10488794Lelio R Paula12/2015
4337(3*2^294971+1)/2556588792Lelio R Paula01/2013
43382^294937-11500388785Enzo Doria06/2015
43392^294868-10970988765Enzo Doria04/2014
43402^294864-298588763Yves Minet09/2014
4341(17*10^88761-41)/388762Robert Price09/2017
43422^294754+1501588730Lelio R Paula10/2013
4343(3^185951-7)/2088720Lelio R Paula01/2013
4344(2^294661+5)/44369338388694Lelio R Paula01/2013
4345(10^88680+11)/388680Robert Price11/2014
43462*7^104928-988675Lelio R Paula10/2014
434711^85150+1288675Lelio R Paula11/2015
43488*6^113951+588673Lelio R Paula10/2014
43496^113940-1856388663Enzo Doria03/2013
435038^56123-56123^3888663Norbert Schneider02/2017
43512^294492-6588651Lelio R Paula10/2012
435220^68120-5388627Lelio R Paula01/2016
43532^294391-11325788621Enzo Doria07/2014
43545^126784-1547688619Enzo Doria02/2013
43552^294327+988602Lelio R Paula10/2012
43562^294320+1891588600Lelio R Paula10/2013
4357(98*10^88595-89)/9988595Ray Chandler07/2011
4358(17*2^294262-1)/1388582Lelio R Paula02/2014
4359(2*10^88545+7)/988545Erik Branger03/2011
43602^294137-13388545Lelio R Paula10/2012
4361(2^294092-1017)/117188528Lelio R Paula01/2013
43624^147036+147036^4+188525Robert Price04/2014
4363(14^77213-5^77213)/988496Robert Price04/2013
43642^293965+279337788493Enzo Doria03/2016
436511^84971-15088489Enzo Doria08/2012
4366(2^293956-1017)/3985137669667788476Lelio R Paula01/2013
436711^84958-219088475Enzo Doria12/2012
43682^293880-11134788467Enzo Doria05/2014
4369(106*10^88459-1)/388461Serge Batalov12/2014
437010^88457+27873388458Patrick De Geest07/2017
437110^88457-40188457Robert Price06/2017
437211^84908-168088423Enzo Doria12/2012
43732^293679-11207588407Enzo Doria06/2014
43746^113608-6588405Lelio R Paula12/2015
43752^293624+8287588390Lelio R Paula10/2013
43762^293612-11233788387Enzo Doria06/2014
4377758^30693+30693^75888386Norbert Schneider05/2017
4378gcd(V(1062695),5*F(212539)*(F(212539)-1)+1)88383Serge Batalov04/2015
43795*10^88377+7788378Robert Price06/2016
4380(5*2^293526+1)/30388359Lelio R Paula01/2013
43812^293461-278584388341Enzo Doria03/2016
43822^293416-103788328Yves Minet11/2012
4383(2^293384-7)/388317Lelio R Paula01/2013
4384(3^185092-5)/488311Lelio R Paula01/2013
4385(5*10^88303-173)/388304Robert Price11/2017
438614^77039-5788297Lelio R Paula11/2015
43873*10^88293-5988294Robert Price10/2017
43885^126303+4288283Lelio R Paula10/2015
438919^69025-1888266Theodore Burton01/2006
43905*10^88261-388262Dmitry Domanov11/2010
43918^97731-7^(97731-1)88260Robert Price04/2016
43925*10^88254+5988255Robert Price09/2016
43934*3^184968-788253Lelio R Paula08/2014
43947^104426+8888251Lelio R Paula10/2015
43952^293142+9988245Lelio R Paula10/2012
439611^84736-213088244Enzo Doria12/2012
43972^293068-8988223Lelio R Paula10/2012
43982^293014-10965588207Enzo Doria04/2014
43998*7^104371-388205Lelio R Paula10/2014
44002^292995-214588201Lelio R Paula10/2013
44015*10^88182+7788183Robert Price06/2016
44032^292929+4387788181Donovan Johnson04/2005
44026^113321+13188181Lelio R Paula12/2015
44042^292904-58394988173Paul Bourdelais04/2013
44052^292894-11185188170Enzo Doria05/2014
44062^292872-279734988164Enzo Doria03/2016
44072^292860-10968588160Enzo Doria04/2014
44089*6^113288-588157Lelio R Paula10/2014
4409(2*10^88112-23)/388112Robert Price09/2017
4410(73*10^88105+17)/988106Robert Price10/2015
441111^84588+7888090Lelio R Paula11/2015
4412(265*10^88077+11)/388079Robert Price03/2017
441391^44959-90^4495988077Robert Price07/2015
44146^113177-5^11317788069Jean-Louis Charton01/2009
4415(10^88020+101)/388020Robert Price04/2016
4416(10^(2*43982+1)-6*10^43982-1)/387965Robert Price02/2016
4417(424*10^87930-1)/987932Robert Price11/2017
4418p(18225)#/2+12887929Robert Price04/2017
44194*6^112977+787914Lelio R Paula10/2014
442014^76677+6987882Lelio R Paula11/2015
4421(22*10^87863-1)/387864Robert Price12/2014
44222^291822-279781187848Enzo Doria04/2016
44232^291716-11138987816Enzo Doria05/2014
4424(782*10^87809-71)/987811Robert Price06/2017
44253^184039+182087809Lelio R Paula12/2015
442612^81356+4187798Lelio R Paula11/2015
44276^112792-1898387770Enzo Doria03/2013
44283*6^112787-587766Lelio R Paula10/2014
44297^103848+8287762Lelio R Paula10/2015
4430(19*2^291534-1)/17869639587754Lelio R Paula02/2014
4431(3^183915+5)/12887748Lelio R Paula01/2013
443219^68619+2487747Lelio R Paula12/2015
44342^291480+118587745Lelio R Paula10/2013
44332^291482+186736987745Enzo Doria03/2016
44352^291467-93787741Yves Minet05/2013
4436(25*10^87726+161)/387727Robert Price01/2017
443711^84239-285087726Enzo Doria12/2012
443810^87720+21554187721Patrick De Geest01/2011
443910^87720-387720Markus Tervooren07/2010
4440(5*10^87712-473)/987712Robert Price12/2017
4441(2^291357+5)/684787704Lelio R Paula01/2013
444293^44541-287679Lelio R Paula09/2013
44432^291261-10956187679Enzo Doria04/2014
4444(4*10^87669+149)/987669Robert Price03/2017
44452^291217+425787666Lelio R Paula10/2013
44462*12^81214-5^8121487645Mike Oakes12/2010
4447(5*10^87622-473)/987622Robert Price12/2017
444812^81188+8587617Lelio R Paula11/2015
4449(21*2^290980-1)/587595Lelio R Paula02/2014
44502^290958+12787588Lelio R Paula09/2012
44512^290923-6787577Lelio R Paula09/2012
44523*10^87573-9787574Robert Price08/2017
4453(13*10^87565+11)/387566Robert Price05/2015
4454(2^290857-7)/5587555Lelio R Paula01/2013
44552^290802+8287587541Lelio R Paula10/2013
4456(509203*2^290792-1)/756098787536Lelio R Paula04/2015
44573^183441+23687524Lelio R Paula12/2015
44582^290618-3387485Lelio R Paula09/2012
4459(184*10^87473-1)/387475Robert Price02/2017
44602^290534-11515187460Enzo Doria06/2015
44612^290512-10975787453Enzo Doria04/2014
4462(32*10^87448-41)/987449Robert Price05/2015
4463(2^290491+9)/317987444Lelio R Paula01/2013
4464(25*2^290489-1)/5180987443Lelio R Paula02/2014
44652^290426+8287587427Lelio R Paula11/2013
44663*2^290415-787425Lelio R Paula08/2014
446710^87408+5787409Robert Price03/2011
44682^290366+7477987409Enzo Doria04/2016
446910^87408-12356987408Patrick De Geest07/2013
44702^290265+5890587379Lelio R Paula10/2013
44717^103391+1687376Lelio R Paula10/2015
4472(115*10^87368-7)/987370Robert Price11/2017
4473(92^44491-1)/9187369Paul Bourdelais08/2017
44748*7^103379+387367Lelio R Paula10/2014
4475(2^290226+7)/7187365Lelio R Paula01/2013
447613^78407-3087341Lelio R Paula11/2015
44774*10^87337-9987338Robert Price12/2016
44787*10^87319+3987320Robert Price07/2016
44793*5^124921+287317Lelio R Paula10/2014
44803^182984+8887306Lelio R Paula12/2015
44814*10^87287-9987288Robert Price12/2016
448211^83813-186087283Enzo Doria12/2012
4483734^30453+30453^73487270Norbert Schneider04/2017
448412^80855+2987258Lelio R Paula11/2015
44853*6^112119-587247Lelio R Paula10/2014
448612^80806+7987205Lelio R Paula11/2015
448791382^9+9^9138287201Andrey Kulsha11/2004
4488(21181*2^289657+1)/8187198Lelio R Paula06/2014
44896^112054-4787195Lelio R Paula12/2015
4490(55459*2^289632+1)/5587191Lelio R Paula06/2014
449115^74131-6887185Lelio R Paula11/2015
44922^289583-74187174Lelio R Paula10/2013
44937^103146+1287169Lelio R Paula10/2015
44945*2^289556-387166Lelio R Paula08/2014
44952^289543-11273587162Enzo Doria06/2014
44968*3^182655-787150Lelio R Paula08/2014
44972*10^87144+8187145Robert Price01/2017
44987^103106+2*3^10310687135Mike Oakes08/2010
44998*3^182614+787130Lelio R Paula08/2014
4500(2^289368-509203)/987108Lelio R Paula01/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 22 2018 09:48 (Time in France)

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