PRP Records

Probable Primes Top 10000

(224660 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 ?
45019*2^296870+789368Lelio R Paula08/2014
4502100^44683-99^4468389366Robert Price07/2013
45032^296810+7651989349Enzo Doria05/2016
45048^98928+7^(98928+1)89341Robert Price06/2016
4505(3^187247+4)/102789337Lelio R Paula01/2013
4506(3^187235-2)/204589331Lelio R Paula01/2013
45072^296736-43214989327Paul Bourdelais05/2013
45082^296737-11251989327Enzo Doria06/2014
45092^296718-364589322Lelio R Paula11/2013
45102^296681-1622189310Enzo Doria04/2013
45112^296669-1651389307Enzo Doria04/2013
45122^296619-1635789292Enzo Doria04/2013
45132^296614-11005189290Enzo Doria04/2014
4514(3^187138+8)/8314789283Lelio R Paula01/2013
4515(2*10^89279+457)/989279Robert Price01/2017
451615^75907-2889274Lelio R Paula11/2015
45172^296547-3789270Yves Minet01/2012
45182^296485+19189251Lelio R Paula10/2012
45192^296467-7589246Lelio R Paula10/2012
45202^296416-10953589231Enzo Doria04/2014
4521(23*2^296406+1)/389228Lelio R Paula01/2013
452266^49037-6589225Norbert Schneider11/2014
45232^296377-1624589219Enzo Doria04/2013
45242^296372-6487589217Lelio R Paula11/2013
45255*6^114648-789215Lelio R Paula10/2014
45263*10^89206+1389207Robert Price08/2017
45277*3^186960-489204Lelio R Paula08/2014
45282^296290-11213389193Enzo Doria06/2014
45296^114620-1700389192Enzo Doria02/2013
4530(4*10^89189+41)/989189Robert Price11/2014
45312^296261-16118189184Enzo Doria04/2013
4532(19*2^296269-1)/53062389182Lelio R Paula02/2014
45333^186903-1089176Robert Price09/2013
45367*10^89169-389170Dmitry Domanov11/2010
4534(2^296221-1017)/3589170Lelio R Paula01/2013
4535(43*10^89169+47)/989170Robert Price12/2017
4537(10^89160+29)/389160Serge Batalov12/2014
4538(28*10^89141-97)/389142Robert Price07/2016
45392^296116-73463989140Paul Bourdelais04/2013
45406^114544-13389133Lelio R Paula12/2015
45412^296076-11329789128Enzo Doria07/2014
4542(11*2^296060-1)/21589122Lelio R Paula02/2014
45435*10^89118+8189119Robert Price08/2017
45442^296037-141189117Yves Minet01/2013
45452^296020-260480989111Enzo Doria05/2015
45462^296016+8189110Henri Lifchitz02/2007
45472^296010-1189108Lelio R Paula10/2012
45482^295998-11191189105Enzo Doria05/2014
4549(2^296014+47)/9399114989102Lelio R Paula01/2013
45502^295939-1662189087Enzo Doria04/2013
45512^295934-10969189086Enzo Doria04/2014
4552(185*10^89063+7)/389065Robert Price02/2017
45532^295831+14389055Lelio R Paula10/2012
455431^59713-3089054Theodore Burton02/2007
4555(7*2^295834-1)/2766389052Lelio R Paula02/2014
4556123^42608+289047Lelio R Paula05/2013
45576^114433-114433^689047Norbert Schneider04/2017
45582^295800-45965989045Enzo Doria05/2015
4559(52*10^89037-1)/389039Robert Price02/2017
4560(6^114398-11)/589019Paul Bourdelais11/2011
456111^85470-585089008Enzo Doria02/2013
4562(27*2^295634+1)/468788993Lelio R Paula01/2013
4563(p(18424)#-4)/288985Robert Price09/2017
45642^295564-18988974Lelio R Paula10/2012
45652^295557+7309788972Enzo Doria04/2016
456611^85433-576088970Enzo Doria01/2013
45676*10^88938-9188939Robert Price11/2017
456815^75619-8888935Lelio R Paula11/2015
45692^295385-8588920Lelio R Paula10/2012
45702^295385-1633388920Enzo Doria04/2013
45712^295309+5988897Lelio R Paula10/2012
45722^295288-10979988891Enzo Doria04/2014
457310^88888+17037388889Stefano Morozzi07/2018
457410^88888+27139988889Stefano Morozzi07/2018
457510^88888+37539788889Stefano Morozzi07/2018
457610^88888+54882388889Stefano Morozzi07/2018
457710^88888+82086188889Stefano Morozzi07/2018
457810^88888+120634988889Stefano Morozzi07/2018
457910^88888+129204788889Stefano Morozzi07/2018
458010^88888+145602988889Stefano Morozzi07/2018
458110^88888-49028788888Patrick De Geest09/2018
45822^295245+6588878Lelio R Paula10/2012
4583Padovan(727734)88874Eric W. Weisstein04/2011
458418^70793-1788865Lelio R Paula11/2015
45856^114196-1757388862Enzo Doria02/2013
4586302^35829+35829^30288857Norbert Schneider12/2014
45873^186223+1688851Robert Price10/2013
45883*2^295139+788847Lelio R Paula08/2014
45893^186212-11300888846Enzo Doria07/2014
459087^45803-8688836Norbert Schneider11/2015
45912^295094-11027388833Enzo Doria05/2014
45922^295080+186915188828Enzo Doria05/2016
45932^295027-11340788812Enzo Doria07/2014
4594(2*10^88808-71)/388808Robert Price01/2017
459513^79722-8088806Lelio R Paula11/2015
45963^186103+10488794Lelio R Paula12/2015
4597(3*2^294971+1)/2556588792Lelio R Paula01/2013
45982^294937-11500388785Enzo Doria06/2015
45992^294868-10970988765Enzo Doria04/2014
46002^294864-298588763Yves Minet09/2014
4601(17*10^88761-41)/388762Robert Price09/2017
46022^294754+1501588730Lelio R Paula10/2013
4603(3^185951-7)/2088720Lelio R Paula01/2013
4604(2^294661+5)/44369338388694Lelio R Paula01/2013
4605(10^88680+11)/388680Robert Price11/2014
46062*7^104928-988675Lelio R Paula10/2014
460711^85150+1288675Lelio R Paula11/2015
46088*6^113951+588673Lelio R Paula10/2014
46096^113940-1856388663Enzo Doria03/2013
461038^56123-56123^3888663Norbert Schneider02/2017
46112^294492-6588651Lelio R Paula10/2012
461220^68120-5388627Lelio R Paula01/2016
46132^294391-11325788621Enzo Doria07/2014
46145^126784-1547688619Enzo Doria02/2013
46152^294327+988602Lelio R Paula10/2012
46162^294320+1891588600Lelio R Paula10/2013
4617(98*10^88595-89)/9988595Ray Chandler07/2011
4618(17*2^294262-1)/1388582Lelio R Paula02/2014
4619(2*10^88545+7)/988545Erik Branger03/2011
46202^294137-13388545Lelio R Paula10/2012
4621(2^294092-1017)/117188528Lelio R Paula01/2013
46224^147036+147036^4+188525Robert Price04/2014
4623(14^77213-5^77213)/988496Robert Price04/2013
46242^293965+279337788493Enzo Doria03/2016
462511^84971-15088489Enzo Doria08/2012
462648^52626-4788478Norbert Schneider08/2018
4627(2^293956-1017)/3985137669667788476Lelio R Paula01/2013
462811^84958-219088475Enzo Doria12/2012
46292^293880-11134788467Enzo Doria05/2014
4630(106*10^88459-1)/388461Serge Batalov12/2014
463110^88457+27873388458Patrick De Geest07/2017
463210^88457-40188457Robert Price06/2017
463311^84908-168088423Enzo Doria12/2012
46342^293679-11207588407Enzo Doria06/2014
46356^113608-6588405Lelio R Paula12/2015
46362^293624+8287588390Lelio R Paula10/2013
46372^293612-11233788387Enzo Doria06/2014
4638758^30693+30693^75888386Norbert Schneider05/2017
4639gcd(V(1062695),5*F(212539)*(F(212539)-1)+1)88383Serge Batalov04/2015
46405*10^88377+7788378Robert Price06/2016
4641(5*2^293526+1)/30388359Lelio R Paula01/2013
46422^293461-278584388341Enzo Doria03/2016
46432^293416-103788328Yves Minet11/2012
4644(2^293384-7)/388317Lelio R Paula01/2013
4645(3^185092-5)/488311Lelio R Paula01/2013
4646(5*10^88303-173)/388304Robert Price11/2017
464714^77039-5788297Lelio R Paula11/2015
46483*10^88293-5988294Robert Price10/2017
46495^126303+4288283Lelio R Paula10/2015
465019^69025-1888266Theodore Burton01/2006
46515*10^88261-388262Dmitry Domanov11/2010
46528^97731-7^(97731-1)88260Robert Price04/2016
46535*10^88254+5988255Robert Price09/2016
46544*3^184968-788253Lelio R Paula08/2014
46557^104426+8888251Lelio R Paula10/2015
46562^293142+9988245Lelio R Paula10/2012
465711^84736-213088244Enzo Doria12/2012
46582^293068-8988223Lelio R Paula10/2012
46592^293014-10965588207Enzo Doria04/2014
46608*7^104371-388205Lelio R Paula10/2014
46612^292995-214588201Lelio R Paula10/2013
46625*10^88182+7788183Robert Price06/2016
46632^292929+4387788181Donovan Johnson04/2005
46646^113321+13188181Lelio R Paula12/2015
46652^292904-58394988173Paul Bourdelais04/2013
46662^292894-11185188170Enzo Doria05/2014
46672^292872-279734988164Enzo Doria03/2016
46682^292860-10968588160Enzo Doria04/2014
46699*6^113288-588157Lelio R Paula10/2014
4670(2*10^88112-23)/388112Robert Price09/2017
4671(73*10^88105+17)/988106Robert Price10/2015
467211^84588+7888090Lelio R Paula11/2015
4673(265*10^88077+11)/388079Robert Price03/2017
467491^44959-90^4495988077Robert Price07/2015
46756^113177-5^11317788069Jean-Louis Charton01/2009
4676(10^88020+101)/388020Robert Price04/2016
467752^51285-5188006Norbert Schneider09/2018
4678(10^(2*43982+1)-6*10^43982-1)/387965Robert Price02/2016
4679(424*10^87930-1)/987932Robert Price11/2017
4680p(18225)#/2+12887929Robert Price04/2017
46814*6^112977+787914Lelio R Paula10/2014
468214^76677+6987882Lelio R Paula11/2015
4683(22*10^87863-1)/387864Robert Price12/2014
46842^291822-279781187848Enzo Doria04/2016
46852^291716-11138987816Enzo Doria05/2014
4686(782*10^87809-71)/987811Robert Price06/2017
46873^184039+182087809Lelio R Paula12/2015
468812^81356+4187798Lelio R Paula11/2015
46896^112792-1898387770Enzo Doria03/2013
46903*6^112787-587766Lelio R Paula10/2014
46917^103848+8287762Lelio R Paula10/2015
4692(19*2^291534-1)/17869639587754Lelio R Paula02/2014
4693(3^183915+5)/12887748Lelio R Paula01/2013
469419^68619+2487747Lelio R Paula12/2015
46962^291480+118587745Lelio R Paula10/2013
46952^291482+186736987745Enzo Doria03/2016
46972^291467-93787741Yves Minet05/2013
4698(25*10^87726+161)/387727Robert Price01/2017
469911^84239-285087726Enzo Doria12/2012
470010^87720+21554187721Patrick De Geest01/2011
470110^87720-387720Markus Tervooren07/2010
4702(5*10^87712-473)/987712Robert Price12/2017
4703(2^291357+5)/684787704Lelio R Paula01/2013
470493^44541-287679Lelio R Paula09/2013
47052^291261-10956187679Enzo Doria04/2014
4706(4*10^87669+149)/987669Robert Price03/2017
47072^291217+425787666Lelio R Paula10/2013
47082*12^81214-5^8121487645Mike Oakes12/2010
4709(5*10^87622-473)/987622Robert Price12/2017
471012^81188+8587617Lelio R Paula11/2015
4711(21*2^290980-1)/587595Lelio R Paula02/2014
47122^290958+12787588Lelio R Paula09/2012
47132^290923-6787577Lelio R Paula09/2012
47143*10^87573-9787574Robert Price08/2017
4715(13*10^87565+11)/387566Robert Price05/2015
4716(2^290857-7)/5587555Lelio R Paula01/2013
47172^290802+8287587541Lelio R Paula10/2013
4718(509203*2^290792-1)/756098787536Lelio R Paula04/2015
47193^183441+23687524Lelio R Paula12/2015
47202^290618-3387485Lelio R Paula09/2012
4721(184*10^87473-1)/387475Robert Price02/2017
47222^290534-11515187460Enzo Doria06/2015
47232^290512-10975787453Enzo Doria04/2014
4724(32*10^87448-41)/987449Robert Price05/2015
4725(2^290491+9)/317987444Lelio R Paula01/2013
4726(25*2^290489-1)/5180987443Lelio R Paula02/2014
47272^290426+8287587427Lelio R Paula11/2013
47283*2^290415-787425Lelio R Paula08/2014
472910^87408+5787409Robert Price03/2011
47302^290366+7477987409Enzo Doria04/2016
473110^87408-12356987408Patrick De Geest07/2013
47322^290265+5890587379Lelio R Paula10/2013
47337^103391+1687376Lelio R Paula10/2015
4734(115*10^87368-7)/987370Robert Price11/2017
4735(92^44491-1)/9187369Paul Bourdelais08/2017
47368*7^103379+387367Lelio R Paula10/2014
4737(2^290226+7)/7187365Lelio R Paula01/2013
473813^78407-3087341Lelio R Paula11/2015
47394*10^87337-9987338Robert Price12/2016
47407*10^87319+3987320Robert Price07/2016
47413*5^124921+287317Lelio R Paula10/2014
47423^182984+8887306Lelio R Paula12/2015
47434*10^87287-9987288Robert Price12/2016
474411^83813-186087283Enzo Doria12/2012
4745734^30453+30453^73487270Norbert Schneider04/2017
474612^80855+2987258Lelio R Paula11/2015
47473*6^112119-587247Lelio R Paula10/2014
474812^80806+7987205Lelio R Paula11/2015
474991382^9+9^9138287201Andrey Kulsha11/2004
4750(21181*2^289657+1)/8187198Lelio R Paula06/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 15 2018 21:33 (Time in France)

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