PRP Records

Probable Primes Top 10000

(252538 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 ?
47512^296810+7651989349Enzo Doria05/2016
47528^98928+7^(98928+1)89341Robert Price06/2016
4753(3^187247+4)/102789337Lelio R Paula01/2013
4754(3^187235-2)/204589331Lelio R Paula01/2013
47562^296736-43214989327Paul Bourdelais05/2013
47552^296737-11251989327Enzo Doria06/2014
47572^296718-364589322Lelio R Paula11/2013
47582^296681-1622189310Enzo Doria04/2013
47592^296669-1651389307Enzo Doria04/2013
47602^296619-1635789292Enzo Doria04/2013
47612^296614-11005189290Enzo Doria04/2014
4762(3^187138+8)/8314789283Lelio R Paula01/2013
4763(2*10^89279+457)/989279Robert Price01/2017
476415^75907-2889274Lelio R Paula11/2015
47652^296547-3789270Yves Minet01/2012
47662^296485+19189251Lelio R Paula10/2012
47672^296467-7589246Lelio R Paula10/2012
47682^296416-10953589231Enzo Doria04/2014
4769(23*2^296406+1)/389228Lelio R Paula01/2013
477066^49037-6589225Norbert Schneider11/2014
47712^296377-1624589219Enzo Doria04/2013
47722^296372-6487589217Lelio R Paula11/2013
47735*6^114648-789215Lelio R Paula10/2014
47743*10^89206+1389207Robert Price08/2017
47757*3^186960-489204Lelio R Paula08/2014
47762^296290-11213389193Enzo Doria06/2014
47776^114620-1700389192Enzo Doria02/2013
4778(4*10^89189+41)/989189Robert Price11/2014
47792^296261-16118189184Enzo Doria04/2013
4780(19*2^296269-1)/53062389182Lelio R Paula02/2014
47813^186903-1089176Robert Price09/2013
47847*10^89169-389170Dmitry Domanov11/2010
4783(2^296221-1017)/3589170Lelio R Paula01/2013
4782(43*10^89169+47)/989170Robert Price12/2017
4785(10^89160+29)/389160Serge Batalov12/2014
4786(28*10^89141-97)/389142Robert Price07/2016
47872^296116-73463989140Paul Bourdelais04/2013
47886^114544-13389133Lelio R Paula12/2015
47892^296076-11329789128Enzo Doria07/2014
4790(11*2^296060-1)/21589122Lelio R Paula02/2014
47915*10^89118+8189119Robert Price08/2017
47922^296037-141189117Yves Minet01/2013
47932^296020-260480989111Enzo Doria05/2015
47942^296016+8189110Henri Lifchitz02/2007
47952^296010-1189108Lelio R Paula10/2012
47962^295998-11191189105Enzo Doria05/2014
4797(2^296014+47)/9399114989102Lelio R Paula01/2013
47982^295939-1662189087Enzo Doria04/2013
47992^295934-10969189086Enzo Doria04/2014
4800(185*10^89063+7)/389065Robert Price02/2017
48012^295831+14389055Lelio R Paula10/2012
480231^59713-3089054Theodore Burton02/2007
4803(7*2^295834-1)/2766389052Lelio R Paula02/2014
4804123^42608+289047Lelio R Paula05/2013
48056^114433-114433^689047Norbert Schneider04/2017
48062^295800-45965989045Enzo Doria05/2015
4807(52*10^89037-1)/389039Robert Price02/2017
4808(6^114398-11)/589019Paul Bourdelais11/2011
480911^85470-585089008Enzo Doria02/2013
4810(27*2^295634+1)/468788993Lelio R Paula01/2013
4811(p(18424)#-4)/288985Robert Price09/2017
48122^295564-18988974Lelio R Paula10/2012
48132^295557+7309788972Enzo Doria04/2016
481411^85433-576088970Enzo Doria01/2013
48156*10^88938-9188939Robert Price11/2017
481615^75619-8888935Lelio R Paula11/2015
48172^295385-8588920Lelio R Paula10/2012
48182^295385-1633388920Enzo Doria04/2013
48192^295309+5988897Lelio R Paula10/2012
48202^295288-10979988891Enzo Doria04/2014
482110^88888+17037388889Stefano Morozzi07/2018
482210^88888+27139988889Stefano Morozzi07/2018
482310^88888+37539788889Stefano Morozzi07/2018
482410^88888+54882388889Stefano Morozzi07/2018
482510^88888+82086188889Stefano Morozzi07/2018
482610^88888+120634988889Stefano Morozzi07/2018
482710^88888+129204788889Stefano Morozzi07/2018
482810^88888+145602988889Stefano Morozzi07/2018
482910^88888-49028788888Patrick De Geest09/2018
48302^295245+6588878Lelio R Paula10/2012
4831Padovan(727734)88874Eric W. Weisstein04/2011
483218^70793-1788865Lelio R Paula11/2015
48336^114196-1757388862Enzo Doria02/2013
4834302^35829+35829^30288857Norbert Schneider12/2014
48353^186223+1688851Robert Price10/2013
48363*2^295139+788847Lelio R Paula08/2014
48373^186212-11300888846Enzo Doria07/2014
483887^45803-8688836Norbert Schneider11/2015
48392^295094-11027388833Enzo Doria05/2014
48402^295080+186915188828Enzo Doria05/2016
48412^295027-11340788812Enzo Doria07/2014
4842(2*10^88808-71)/388808Robert Price01/2017
484313^79722-8088806Lelio R Paula11/2015
48443^186103+10488794Lelio R Paula12/2015
4845(3*2^294971+1)/2556588792Lelio R Paula01/2013
48462^294937-11500388785Enzo Doria06/2015
48472^294868-10970988765Enzo Doria04/2014
48482^294864-298588763Yves Minet09/2014
4849(17*10^88761-41)/388762Robert Price09/2017
48502^294754+1501588730Lelio R Paula10/2013
4851(3^185951-7)/2088720Lelio R Paula01/2013
4852(2^294661+5)/44369338388694Lelio R Paula01/2013
4853(10^88680+11)/388680Robert Price11/2014
48542*7^104928-988675Lelio R Paula10/2014
485511^85150+1288675Lelio R Paula11/2015
48568*6^113951+588673Lelio R Paula10/2014
48586^113940-1856388663Enzo Doria03/2013
485738^56123-56123^3888663Norbert Schneider02/2017
48592^294492-6588651Lelio R Paula10/2012
486020^68120-5388627Lelio R Paula01/2016
4861122^42477-12188623Norbert Schneider10/2018
48622^294391-11325788621Enzo Doria07/2014
48635^126784-1547688619Enzo Doria02/2013
48642^294327+988602Lelio R Paula10/2012
48652^294320+1891588600Lelio R Paula10/2013
4866(98*10^88595-89)/9988595Ray Chandler07/2011
4867(17*2^294262-1)/1388582Lelio R Paula02/2014
4869(2*10^88545+7)/988545Erik Branger03/2011
48682^294137-13388545Lelio R Paula10/2012
4870(2^294092-1017)/117188528Lelio R Paula01/2013
48714^147036+147036^4+188525Robert Price04/2014
4872(14^77213-5^77213)/988496Robert Price04/2013
48732^293965+279337788493Enzo Doria03/2016
487411^84971-15088489Enzo Doria08/2012
487548^52626-4788478Norbert Schneider08/2018
4876(2^293956-1017)/3985137669667788476Lelio R Paula01/2013
487711^84958-219088475Enzo Doria12/2012
48782^293880-11134788467Enzo Doria05/2014
4879(106*10^88459-1)/388461Serge Batalov12/2014
488010^88457+27873388458Patrick De Geest07/2017
488110^88457-40188457Robert Price06/2017
488211^84908-168088423Enzo Doria12/2012
48832^293679-11207588407Enzo Doria06/2014
48846^113608-6588405Lelio R Paula12/2015
48852^293624+8287588390Lelio R Paula10/2013
48862^293612-11233788387Enzo Doria06/2014
4887758^30693+30693^75888386Norbert Schneider05/2017
4888gcd(V(1062695),5*F(212539)*(F(212539)-1)+1)88383Serge Batalov04/2015
48895*10^88377+7788378Robert Price06/2016
4890(5*2^293526+1)/30388359Lelio R Paula01/2013
48912^293461-278584388341Enzo Doria03/2016
48922^293416-103788328Yves Minet11/2012
4893(2^293384-7)/388317Lelio R Paula01/2013
4894(3^185092-5)/488311Lelio R Paula01/2013
4895(5*10^88303-173)/388304Robert Price11/2017
489614^77039-5788297Lelio R Paula11/2015
48973*10^88293-5988294Robert Price10/2017
48985^126303+4288283Lelio R Paula10/2015
489919^69025-1888266Theodore Burton01/2006
49005*10^88261-388262Dmitry Domanov11/2010
49018^97731-7^(97731-1)88260Robert Price04/2016
49025*10^88254+5988255Robert Price09/2016
49034*3^184968-788253Lelio R Paula08/2014
49047^104426+8888251Lelio R Paula10/2015
49052^293142+9988245Lelio R Paula10/2012
490611^84736-213088244Enzo Doria12/2012
49072^293068-8988223Lelio R Paula10/2012
49082^293014-10965588207Enzo Doria04/2014
49098*7^104371-388205Lelio R Paula10/2014
49102^292995-214588201Lelio R Paula10/2013
49115*10^88182+7788183Robert Price06/2016
49132^292929+4387788181Donovan Johnson04/2005
49126^113321+13188181Lelio R Paula12/2015
49142^292904-58394988173Paul Bourdelais04/2013
49152^292894-11185188170Enzo Doria05/2014
49162^292872-279734988164Enzo Doria03/2016
49172^292860-10968588160Enzo Doria04/2014
49189*6^113288-588157Lelio R Paula10/2014
4919(2*10^88112-23)/388112Robert Price09/2017
4920(73*10^88105+17)/988106Robert Price10/2015
492111^84588+7888090Lelio R Paula11/2015
4922(265*10^88077+11)/388079Robert Price03/2017
492391^44959-90^4495988077Robert Price07/2015
49246^113177-5^11317788069Jean-Louis Charton01/2009
4925(10^88020+101)/388020Robert Price04/2016
492652^51285-5188006Norbert Schneider09/2018
4927(10^(2*43982+1)-6*10^43982-1)/387965Robert Price02/2016
4928(424*10^87930-1)/987932Robert Price11/2017
4929p(18225)#/2+12887929Robert Price04/2017
49304*6^112977+787914Lelio R Paula10/2014
493114^76677+6987882Lelio R Paula11/2015
4932(22*10^87863-1)/387864Robert Price12/2014
49332^291822-279781187848Enzo Doria04/2016
49342^291716-11138987816Enzo Doria05/2014
4935(782*10^87809-71)/987811Robert Price06/2017
49363^184039+182087809Lelio R Paula12/2015
493712^81356+4187798Lelio R Paula11/2015
49386^112792-1898387770Enzo Doria03/2013
49393*6^112787-587766Lelio R Paula10/2014
49407^103848+8287762Lelio R Paula10/2015
4941(19*2^291534-1)/17869639587754Lelio R Paula02/2014
4942(3^183915+5)/12887748Lelio R Paula01/2013
494319^68619+2487747Lelio R Paula12/2015
49452^291480+118587745Lelio R Paula10/2013
49442^291482+186736987745Enzo Doria03/2016
49462^291467-93787741Yves Minet05/2013
4947(25*10^87726+161)/387727Robert Price01/2017
494811^84239-285087726Enzo Doria12/2012
494910^87720+21554187721Patrick De Geest01/2011
495010^87720-387720Markus Tervooren07/2010
4951(5*10^87712-473)/987712Robert Price12/2017
4952(2^291357+5)/684787704Lelio R Paula01/2013
495393^44541-287679Lelio R Paula09/2013
49542^291261-10956187679Enzo Doria04/2014
4955(4*10^87669+149)/987669Robert Price03/2017
49562^291217+425787666Lelio R Paula10/2013
49572*12^81214-5^8121487645Mike Oakes12/2010
4958(5*10^87622-473)/987622Robert Price12/2017
495912^81188+8587617Lelio R Paula11/2015
4960(21*2^290980-1)/587595Lelio R Paula02/2014
49612^290958+12787588Lelio R Paula09/2012
49622^290923-6787577Lelio R Paula09/2012
49633*10^87573-9787574Robert Price08/2017
4964(13*10^87565+11)/387566Robert Price05/2015
4965(2^290857-7)/5587555Lelio R Paula01/2013
49662^290802+8287587541Lelio R Paula10/2013
4967(509203*2^290792-1)/756098787536Lelio R Paula04/2015
49683^183441+23687524Lelio R Paula12/2015
49692^290618-3387485Lelio R Paula09/2012
4970(184*10^87473-1)/387475Robert Price02/2017
49712^290534-11515187460Enzo Doria06/2015
49722^290512-10975787453Enzo Doria04/2014
4973(32*10^87448-41)/987449Robert Price05/2015
4974(2^290491+9)/317987444Lelio R Paula01/2013
4975(25*2^290489-1)/5180987443Lelio R Paula02/2014
49762^290426+8287587427Lelio R Paula11/2013
49773*2^290415-787425Lelio R Paula08/2014
497910^87408+5787409Robert Price03/2011
49782^290366+7477987409Enzo Doria04/2016
498010^87408-12356987408Patrick De Geest07/2013
49812^290265+5890587379Lelio R Paula10/2013
49827^103391+1687376Lelio R Paula10/2015
4983(115*10^87368-7)/987370Robert Price11/2017
4984(92^44491-1)/9187369Paul Bourdelais08/2017
49858*7^103379+387367Lelio R Paula10/2014
4986(2^290226+7)/7187365Lelio R Paula01/2013
498713^78407-3087341Lelio R Paula11/2015
49884*10^87337-9987338Robert Price12/2016
49897*10^87319+3987320Robert Price07/2016
49903*5^124921+287317Lelio R Paula10/2014
49913^182984+8887306Lelio R Paula12/2015
4992(10^87323-1)/(9*33909262597306826117)87303Alfred Reich02/2019
49934*10^87287-9987288Robert Price12/2016
499411^83813-186087283Enzo Doria12/2012
4995734^30453+30453^73487270Norbert Schneider04/2017
499612^80855+2987258Lelio R Paula11/2015
49973*6^112119-587247Lelio R Paula10/2014
499812^80806+7987205Lelio R Paula11/2015
499991382^9+9^9138287201Andrey Kulsha11/2004
5000(21181*2^289657+1)/8187198Lelio R Paula06/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 14 2019 10:37 (Time in France)

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