PRP Records

Probable Primes Top 10000

(259919 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 ?
55017*3^186960-489204Lelio R Paula08/2014
55022^296290-11213389193Enzo Doria06/2014
55036^114620-1700389192Enzo Doria02/2013
5504(4*10^89189+41)/989189Robert Price11/2014
55052^296261-16118189184Enzo Doria04/2013
5506(19*2^296269-1)/53062389182Lelio R Paula02/2014
55073^186903-1089176Robert Price09/2013
55087*10^89169-389170Dmitry Domanov11/2010
5509(2^296221-1017)/3589170Lelio R Paula01/2013
5510(43*10^89169+47)/989170Robert Price12/2017
5511(10^89160+29)/389160Serge Batalov12/2014
5512(28*10^89141-97)/389142Robert Price07/2016
55132^296116-73463989140Paul Bourdelais04/2013
5514(2^296101+1250)/289135Stefano Morozzi01/2020
55156^114544-13389133Lelio R Paula12/2015
55162^296076-11329789128Enzo Doria07/2014
5517(11*2^296060-1)/21589122Lelio R Paula02/2014
55185*10^89118+8189119Robert Price08/2017
55192^296037-141189117Yves Minet01/2013
55202^296020-260480989111Enzo Doria05/2015
55212^296016+8189110Henri Lifchitz02/2007
55222^296010-1189108Lelio R Paula10/2012
55232^295998-11191189105Enzo Doria05/2014
5524(2^296014+47)/9399114989102Lelio R Paula01/2013
55252^295939-1662189087Enzo Doria04/2013
55262^295934-10969189086Enzo Doria04/2014
5527(2^295921+2246)/289081Stefano Morozzi01/2020
5528(185*10^89063+7)/389065Robert Price02/2017
55292^295831+14389055Lelio R Paula10/2012
553031^59713-3089054Theodore Burton02/2007
5531(7*2^295834-1)/2766389052Lelio R Paula02/2014
553279731!4-3289049Robert Price11/2019
5534123^42608+289047Lelio R Paula05/2013
55336^114433-114433^689047Norbert Schneider04/2017
55352^295800-45965989045Enzo Doria05/2015
5537(52*10^89037-1)/389039Robert Price02/2017
5536(2^295782+1870)/289039Stefano Morozzi01/2020
5538(6^114398-11)/589019Paul Bourdelais11/2011
553911^85470-585089008Enzo Doria02/2013
5540(2^295650+522)/289000Stefano Morozzi01/2020
5541(27*2^295634+1)/468788993Lelio R Paula01/2013
5542(p(18424)#-4)/288985Robert Price09/2017
55432^295564-18988974Lelio R Paula10/2012
55442^295557+7309788972Enzo Doria04/2016
554511^85433-576088970Enzo Doria01/2013
5546(2^295479+3050)/288948Stefano Morozzi01/2020
55476*10^88938-9188939Robert Price11/2017
554815^75619-8888935Lelio R Paula11/2015
5549(2^295433+2234)/288934Stefano Morozzi01/2020
55502^295385-8588920Lelio R Paula10/2012
55512^295385-1633388920Enzo Doria04/2013
555279617!4+3288909Robert Price09/2019
55532^295309+5988897Lelio R Paula10/2012
55542^295288-10979988891Enzo Doria04/2014
555510^88888+17037388889Stefano Morozzi07/2018
555610^88888+27139988889Stefano Morozzi07/2018
555710^88888+37539788889Stefano Morozzi07/2018
555810^88888+54882388889Stefano Morozzi07/2018
555910^88888+82086188889Stefano Morozzi07/2018
556010^88888+120634988889Stefano Morozzi07/2018
556110^88888+129204788889Stefano Morozzi07/2018
556210^88888+145602988889Stefano Morozzi07/2018
556310^88888-49028788888Patrick De Geest09/2018
55642^295245+6588878Lelio R Paula10/2012
5565Padovan(727734)88874Eric W. Weisstein04/2011
5566(2^295231+1554)/288874Stefano Morozzi01/2020
556779585!4-3288870Robert Price11/2019
556818^70793-1788865Lelio R Paula11/2015
55696^114196-1757388862Enzo Doria02/2013
5570302^35829+35829^30288857Norbert Schneider12/2014
55713^186223+1688851Robert Price10/2013
55723*2^295139+788847Lelio R Paula08/2014
55733^186212-11300888846Enzo Doria07/2014
557487^45803-8688836Norbert Schneider11/2015
55752^295094-11027388833Enzo Doria05/2014
55762^295080+186915188828Enzo Doria05/2016
5577(2^295061+2174)/288822Stefano Morozzi01/2020
55782^295027-11340788812Enzo Doria07/2014
5579(2*10^88808-71)/388808Robert Price01/2017
5580(2^295009+2102)/288807Stefano Morozzi01/2020
558113^79722-8088806Lelio R Paula11/2015
55823^186103+10488794Lelio R Paula12/2015
5583(3*2^294971+1)/2556588792Lelio R Paula01/2013
55842^294937-11500388785Enzo Doria06/2015
5585(2^294923+3134)/288781Stefano Morozzi01/2020
55862551^26056+26056^255188766Norbert Schneider01/2020
55872^294868-10970988765Enzo Doria04/2014
55882^294864-298588763Yves Minet09/2014
5589(17*10^88761-41)/388762Robert Price09/2017
5590(2^294834+2854)/288754Stefano Morozzi01/2020
5591(2^294823+2466)/288751Stefano Morozzi01/2020
5592(2^294764+642)/288733Stefano Morozzi01/2020
55932^294754+1501588730Lelio R Paula10/2013
5594(3^185951-7)/2088720Lelio R Paula01/2013
5595(2^294688+3186)/288710Stefano Morozzi01/2020
5596(2^294673+3906)/288706Stefano Morozzi01/2020
5597(2^294661+5)/44369338388694Lelio R Paula01/2013
5598(2^294631+2514)/288693Stefano Morozzi01/2020
5599(10^88680+11)/388680Robert Price11/2014
56002*7^104928-988675Lelio R Paula10/2014
560111^85150+1288675Lelio R Paula11/2015
56028*6^113951+588673Lelio R Paula10/2014
5603(2^294549+3110)/288668Stefano Morozzi01/2020
56056^113940-1856388663Enzo Doria03/2013
560438^56123-56123^3888663Norbert Schneider02/2017
56062^294492-6588651Lelio R Paula10/2012
5607(2^294481+2822)/288648Stefano Morozzi01/2020
5608(2^294469+1466)/288644Stefano Morozzi01/2020
56097*10^88634-2788635Dylan Delgado08/2019
561020^68120-5388627Lelio R Paula01/2016
5611122^42477-12188623Norbert Schneider10/2018
56122^294391-11325788621Enzo Doria07/2014
56135^126784-1547688619Enzo Doria02/2013
5614(2^294335+554)/288604Stefano Morozzi01/2020
56152^294327+988602Lelio R Paula10/2012
56162^294320+1891588600Lelio R Paula10/2013
5617(98*10^88595-89)/9988595Ray Chandler07/2011
5618(2^294268+1402)/288584Stefano Morozzi01/2020
5619(17*2^294262-1)/1388582Lelio R Paula02/2014
5620(2^294145+1346)/288547Stefano Morozzi01/2020
5621(2*10^88545+7)/988545Erik Branger03/2011
56222^294137-13388545Lelio R Paula10/2012
5623(2^294109+3494)/288536Stefano Morozzi01/2020
5624(2^294092-1017)/117188528Lelio R Paula01/2013
56254^147036+147036^4+188525Robert Price04/2014
5626(14^77213-5^77213)/988496Robert Price04/2013
56272^293965+279337788493Enzo Doria03/2016
5628(2^293956+3306)/288490Stefano Morozzi01/2020
562911^84971-15088489Enzo Doria08/2012
5630(2^293944+1066)/288486Stefano Morozzi01/2020
563148^52626-4788478Norbert Schneider08/2018
5632(2^293956-1017)/3985137669667788476Lelio R Paula01/2013
563311^84958-219088475Enzo Doria12/2012
5634(2^293902+3070)/288474Stefano Morozzi01/2020
56352^293880-11134788467Enzo Doria05/2014
5636(106*10^88459-1)/388461Serge Batalov12/2014
563710^88457+27873388458Patrick De Geest07/2017
563810^88457-40188457Robert Price06/2017
5639(2^293834+3018)/288453Stefano Morozzi01/2020
5640(2^293747+1626)/288427Stefano Morozzi01/2020
564111^84908-168088423Enzo Doria12/2012
5642(2^293703+3486)/288414Stefano Morozzi01/2020
56432^293679-11207588407Enzo Doria06/2014
56446^113608-6588405Lelio R Paula12/2015
56452^293624+8287588390Lelio R Paula10/2013
5646(2^293618+918)/288388Stefano Morozzi01/2020
56472^293612-11233788387Enzo Doria06/2014
5648758^30693+30693^75888386Norbert Schneider05/2017
5649gcd(V(1062695),5*F(212539)*(F(212539)-1)+1)88383Serge Batalov04/2015
56515*10^88377+7788378Robert Price06/2016
5650(2^293584+1558)/288378Stefano Morozzi01/2020
5652(5*2^293526+1)/30388359Lelio R Paula01/2013
5653(2^293499+2390)/288352Stefano Morozzi01/2020
56542^293461-278584388341Enzo Doria03/2016
56552^293416-103788328Yves Minet11/2012
5656(2^293384-7)/388317Lelio R Paula01/2013
5657(3^185092-5)/488311Lelio R Paula01/2013
5658(5*10^88303-173)/388304Robert Price11/2017
565914^77039-5788297Lelio R Paula11/2015
56603*10^88293-5988294Robert Price10/2017
56615^126303+4288283Lelio R Paula10/2015
566319^69025-1888266Theodore Burton01/2006
5662140^41128+13988266Norbert Schneider04/2019
56645*10^88261-388262Dmitry Domanov11/2010
5665(2^293195+2238)/288261Stefano Morozzi01/2020
56668^97731-7^(97731-1)88260Robert Price04/2016
56675*10^88254+5988255Robert Price09/2016
56684*3^184968-788253Lelio R Paula08/2014
56697^104426+8888251Lelio R Paula10/2015
56702^293142+9988245Lelio R Paula10/2012
567111^84736-213088244Enzo Doria12/2012
5672(10^110315+1)/(10^22063+1)/582481268216764857846028164188225Makoto Kamada04/2019
56732^293068-8988223Lelio R Paula10/2012
56742126^26511+26511^212688218Norbert Schneider02/2020
56752^293014-10965588207Enzo Doria04/2014
56768*7^104371-388205Lelio R Paula10/2014
56772^292995-214588201Lelio R Paula10/2013
56785*10^88182+7788183Robert Price06/2016
56802^292929+4387788181Donovan Johnson04/2005
56796^113321+13188181Lelio R Paula12/2015
5681(2^292919+3366)/288178Stefano Morozzi01/2020
56822^292904-58394988173Paul Bourdelais04/2013
56832^292894-11185188170Enzo Doria05/2014
56842^292872-279734988164Enzo Doria03/2016
5685(2^292864+1042)/288161Stefano Morozzi01/2020
56862^292860-10968588160Enzo Doria04/2014
56879*6^113288-588157Lelio R Paula10/2014
5688(2^292735+2166)/288122Stefano Morozzi01/2020
5689(2^292735+2346)/288122Stefano Morozzi01/2020
5690(2^292705+1934)/288113Stefano Morozzi01/2020
5691(2*10^88112-23)/388112Robert Price09/2017
5692(73*10^88105+17)/988106Robert Price10/2015
5693(2^292673+3026)/288104Stefano Morozzi01/2020
569411^84588+7888090Lelio R Paula11/2015
5695(265*10^88077+11)/388079Robert Price03/2017
569691^44959-90^4495988077Robert Price07/2015
56976^113177-5^11317788069Jean-Louis Charton01/2009
5698(2^292543+2234)/288064Stefano Morozzi01/2020
5699(10^88020+101)/388020Robert Price04/2016
570052^51285-5188006Norbert Schneider09/2018
5701(2^292324+2346)/287998Stefano Morozzi01/2020
5702(10^(2*43982+1)-6*10^43982-1)/387965Robert Price02/2016
5703(424*10^87930-1)/987932Robert Price11/2017
5704(2^292100+3070)/287931Stefano Morozzi01/2020
5705p(18225)#/2+12887929Robert Price04/2017
5706(2^292047+1550)/287915Stefano Morozzi01/2020
57074*6^112977+787914Lelio R Paula10/2014
5708(2^292016+1062)/287906Stefano Morozzi01/2020
570914^76677+6987882Lelio R Paula11/2015
5710(22*10^87863-1)/387864Robert Price12/2014
57112^291822-279781187848Enzo Doria04/2016
5712(2^291730+1614)/287820Stefano Morozzi01/2020
57132^291716-11138987816Enzo Doria05/2014
5714(782*10^87809-71)/987811Robert Price06/2017
57153^184039+182087809Lelio R Paula12/2015
571612^81356+4187798Lelio R Paula11/2015
5717(2^291596+1986)/287779Stefano Morozzi01/2020
57186^112792-1898387770Enzo Doria03/2013
57193*6^112787-587766Lelio R Paula10/2014
57207^103848+8287762Lelio R Paula10/2015
5721(19*2^291534-1)/17869639587754Lelio R Paula02/2014
5722(2^291506+918)/287752Stefano Morozzi01/2020
5723(3^183915+5)/12887748Lelio R Paula01/2013
572419^68619+2487747Lelio R Paula12/2015
57262^291480+118587745Lelio R Paula10/2013
57252^291482+186736987745Enzo Doria03/2016
57272^291467-93787741Yves Minet05/2013
5728(25*10^87726+161)/387727Robert Price01/2017
572911^84239-285087726Enzo Doria12/2012
573010^87720+21554187721Patrick De Geest01/2011
573110^87720-387720Markus Tervooren07/2010
5732(2^291383+3078)/287715Stefano Morozzi01/2020
5734(5*10^87712-473)/987712Robert Price12/2017
5733(2^291373+2946)/287712Stefano Morozzi01/2020
5735(2^291357+5)/684787704Lelio R Paula01/2013
5736(2^291280+462)/287684Stefano Morozzi01/2020
573893^44541-287679Lelio R Paula09/2013
57372^291261-10956187679Enzo Doria04/2014
5739(4*10^87669+149)/987669Robert Price03/2017
57402^291217+425787666Lelio R Paula10/2013
57412*12^81214-5^8121487645Mike Oakes12/2010
5742(5*10^87622-473)/987622Robert Price12/2017
574312^81188+8587617Lelio R Paula11/2015
5744(2^291030+3462)/287609Stefano Morozzi01/2020
5745(21*2^290980-1)/587595Lelio R Paula02/2014
5746(2^290980+1150)/287594Stefano Morozzi01/2020
57472^290958+12787588Lelio R Paula09/2012
574878531!4-887580Robert Price11/2019
57492^290923-6787577Lelio R Paula09/2012
57503*10^87573-9787574Robert Price08/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 29 2020 17:41 (Time in France)

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