PRP Records

Probable Primes Top 10000

(291192 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 ?
9501(2908*29^61501-3)/789942Curtis Bright05/2015
9502(2^298769+1202)/289939Stefano Morozzi01/2020
9503(5941^23827-1)/594089916Serge Batalov08/2020
950417^73067+2089906Lelio R Paula11/2015
95052^298637-9989899Lelio R Paula10/2012
950625513^3336+3336^2551389889Hans Havermann08/2020
950729748^1051+1051^2974889887Hans Havermann08/2020
95089*10^89882-9189883Robert Price06/2021
95099^94188+3*8^94188-2*4^94188-3*2^9418889879Mike Oakes01/2011
95102*10^89876+8389877Robert Price12/2021
9511(2^298558+3654)/289875Stefano Morozzi01/2020
95129*10^89858+1989859Robert Price05/2016
95132^298501+187006789858Enzo Doria05/2016
9514(286*10^89852-1)/389854Robert Price11/2020
951511^86280-9889852Lelio R Paula11/2015
95162^298473-11005989850Enzo Doria04/2014
951719^70263-3289850Lelio R Paula12/2015
951821208^17221+17221^2120889839Hans Havermann08/2020
9519(299*10^89836-17)/389838Robert Price01/2017
95203^188286+1489836Robert Price09/2013
9521(2^298408+450)/289830Stefano Morozzi01/2020
9522gcd(V(1091095),5*F(218219)*(F(218219)+1)+1)89822Serge Batalov04/2015
95232^298367+5890589818Lelio R Paula11/2013
952421966^12269+12269^2196689815Hans Havermann08/2020
9525(2^298333+3126)/289807Stefano Morozzi01/2020
95262^298319-10965789803Enzo Doria04/2014
95277*10^89801+1389802Robert Price03/2021
95288*10^89800+8189801Robert Price05/2017
952921354^16037+16037^2135489797Hans Havermann08/2020
9530(2^298249+714)/289782Stefano Morozzi01/2020
953121227^16954+16954^2122789775Hans Havermann08/2020
9532(733^31333-1)/73289770Serge Batalov08/2020
953518^71505-9189759Lelio R Paula12/2015
9533(2^298171+1586)/289759Stefano Morozzi01/2020
9534(4788^24391-1)/478789759Serge Batalov08/2020
9536(2^298161+3530)/289756Stefano Morozzi01/2020
9537(7^106187+1)/889738Paul Bourdelais04/2008
95382^298079-10953189731Enzo Doria04/2014
9539(9255^22621-1)/925489720Serge Batalov08/2020
9540117^43380+11689718Norbert Schneider08/2018
9541(22699*2^298016+1)/38589714Lelio R Paula06/2014
9542156*(10^(4*22427)-1)/101-189709Robert Price05/2014
95432^298003-6694589708Lelio R Paula11/2013
9544(23*10^89705-83)/389706Robert Price09/2017
954517^72900-5489700Lelio R Paula11/2015
9546(2^297968+2482)/289698Stefano Morozzi01/2020
95473*2^297956+589695Lelio R Paula08/2014
9548(2^297952+3558)/289693Stefano Morozzi01/2020
9549(3992^24907-1)/399189692Serge Batalov08/2020
955020^68938-1189691Lelio R Paula01/2016
955189*10^89687-789689Robert Price03/2017
9552(6882^23371-1)/688189688Serge Batalov08/2020
9553(297847^16384+1)/289686Richard Fischer08/2019
95542^297923+7778389684Enzo Doria05/2016
9555(2^297893+1694)/289675Stefano Morozzi01/2020
955611^86107-2457600089672Enzo Doria02/2013
95572^297878-11191189671Enzo Doria05/2014
955820823^20236+20236^2082389667Hans Havermann08/2020
955925708^3075+3075^2570889666Hans Havermann08/2020
956021002^18585+18585^2100289661Hans Havermann08/2020
9561(2^297830+3670)/289656Stefano Morozzi01/2020
95627^106084+4089652Lelio R Paula10/2015
9563(2^297815+618)/289651Stefano Morozzi01/2020
956421223^16752+16752^2122389648Hans Havermann08/2020
9566(86*10^89640-311)/989641Robert Price10/2017
9565(2^297781+2094)/289641Stefano Morozzi01/2020
9567(2^297741+3326)/289629Stefano Morozzi01/2020
9568(2^297724+3606)/289624Stefano Morozzi01/2020
95693*10^89608-5989609Robert Price10/2017
9570(2^297650+3250)/289602Stefano Morozzi01/2020
9571(34*10^89599+191)/989600Robert Price08/2021
95723^187780-1103889594Enzo Doria05/2014
9573(13*2^297560-1)/4915178789568Lelio R Paula02/2014
95745^128141-3689567Lelio R Paula10/2015
95754*7^105951+989540Lelio R Paula10/2014
9576(7*10^89539-439)/989539Robert Price09/2017
9577(9772^22441-1)/977189536Serge Batalov08/2020
957822823^8374+8374^2282389534Hans Havermann08/2020
9579(2^297401+2954)/289527Stefano Morozzi01/2020
9580(2^297403+1670)/289527Stefano Morozzi01/2020
95812^297397+17725789526Enzo Doria05/2016
9582(77*10^89518+247)/989519Robert Price03/2021
95832^297346-1624189511Enzo Doria04/2013
9584(5*10^89510+79)/389511Robert Price11/2017
95864^148663-3^14866389505Jean-Louis Charton11/2005
95852^297328-86968810589505Lelio R Paula07/2016
95872^297325-45904389504Enzo Doria05/2015
95882^297310-11239189500Enzo Doria06/2014
95892^297296-11215789496Enzo Doria06/2014
959057^50966-289490Lelio R Paula08/2013
9591(266*10^89482+1)/389484Robert Price02/2016
9592(14*10^89480-101)/389481Robert Price04/2017
95932618^26175+26175^261889466Norbert Schneider01/2020
9594(2^297150+3922)/289451Stefano Morozzi01/2020
9595(2^297141+1842)/289449Stefano Morozzi01/2020
9596(2^297140+1458)/289448Stefano Morozzi01/2020
9597(2^297129+726)/289445Stefano Morozzi01/2020
95982^297122+9989443Lelio R Paula10/2012
9599(3^187435-5)/128689427Lelio R Paula01/2013
9600(28*10^89425+101)/389426Robert Price09/2020
9601(2^297037+3522)/289417Stefano Morozzi01/2020
9602(25*10^89413+161)/389414Robert Price01/2017
9603(89*10^89411-737)/989412Robert Price01/2022
960429080^1187+1187^2908089406Hans Havermann08/2020
96052^296990+187069989403Enzo Doria05/2016
96062^296972-101789398Lelio R Paula11/2013
9607(7*10^89383+167)/389384Robert Kinser10/2017
9608(85*10^89375-31)/989376Robert Price11/2015
96099*2^296870+789368Lelio R Paula08/2014
9610100^44683-99^4468389366Robert Price07/2013
96112^296810+7651989349Enzo Doria05/2016
9612(2747^25981-1)/274689342Serge Batalov08/2020
96138^98928+7^(98928+1)89341Robert Price06/2016
9615(3^187247+4)/102789337Lelio R Paula01/2013
961421832^12359+12359^2183289337Hans Havermann08/2020
9616(3^187235-2)/204589331Lelio R Paula01/2013
96172^296736-43214989327Paul Bourdelais05/2013
96182^296737-11251989327Enzo Doria06/2014
96192^296718-364589322Lelio R Paula11/2013
9620(2^296702+2338)/289316Stefano Morozzi01/2020
96212^296681-1622189310Enzo Doria04/2013
96222^296669-1651389307Enzo Doria04/2013
9623(2^296626+1282)/289294Stefano Morozzi01/2020
96242^296619-1635789292Enzo Doria04/2013
96252^296614-11005189290Enzo Doria04/2014
9626(2^296601+1730)/289286Stefano Morozzi01/2020
9627(3^187138+8)/8314789283Lelio R Paula01/2013
9628(2*10^89279+457)/989279Robert Price01/2017
9629(2^296568+1222)/289276Stefano Morozzi01/2020
9630(133*10^89273+17)/389275Robert Price11/2021
963115^75907-2889274Lelio R Paula11/2015
96322^296547-3789270Yves Minet01/2012
96332^296485+19189251Lelio R Paula10/2012
96342^296467-7589246Lelio R Paula10/2012
9635(2^296462+1674)/289244Stefano Morozzi01/2020
96362^296416-10953589231Enzo Doria04/2014
9637(23*2^296406+1)/389228Lelio R Paula01/2013
963866^49037-6589225Norbert Schneider11/2014
96392^296377-1624589219Enzo Doria04/2013
96402^296372-6487589217Lelio R Paula11/2013
96415*6^114648-789215Lelio R Paula10/2014
9642(2^296361+1262)/289214Stefano Morozzi01/2020
96433*10^89206+1389207Robert Price08/2017
96447*3^186960-489204Lelio R Paula08/2014
9645(28*10^89203+47)/389204Robert Price02/2021
96462^296290-11213389193Enzo Doria06/2014
96476^114620-1700389192Enzo Doria02/2013
9648(22*10^89190+179)/389191Robert Price02/2022
9649(4*10^89189+41)/989189Robert Price11/2014
96502^296261-16118189184Enzo Doria04/2013
9651(19*2^296269-1)/53062389182Lelio R Paula02/2014
96523^186903-1089176Robert Price09/2013
96537*10^89169-389170Dmitry Domanov11/2010
9654(2^296221-1017)/3589170Lelio R Paula01/2013
9655(43*10^89169+47)/989170Robert Price12/2017
9656(10^89160+29)/389160Serge Batalov12/2014
9657(28*10^89141-97)/389142Robert Price07/2016
96582^296116-73463989140Paul Bourdelais04/2013
9659(2^296101+1250)/289135Stefano Morozzi01/2020
966022574^8883+8883^2257489135Hans Havermann08/2020
96616^114544-13389133Lelio R Paula12/2015
96622^296076-11329789128Enzo Doria07/2014
9663(11*2^296060-1)/21589122Lelio R Paula02/2014
96645*10^89118+8189119Robert Price08/2017
96652^296037-141189117Yves Minet01/2013
96662^296020-260480989111Enzo Doria05/2015
96672^296016+8189110Henri Lifchitz02/2007
96682^296010-1189108Lelio R Paula10/2012
96692^295998-11191189105Enzo Doria05/2014
9670(2^296014+47)/9399114989102Lelio R Paula01/2013
967129529^1040+1040^2952989090Hans Havermann08/2020
96722^295939-1662189087Enzo Doria04/2013
96732^295934-10969189086Enzo Doria04/2014
9674(2^295921+2246)/289081Stefano Morozzi01/2020
9675(185*10^89070-11)/389072Robert Price10/2020
9676(185*10^89063+7)/389065Robert Price02/2017
9677(8*10^89055-59)/389056Robert Price08/2021
96782^295831+14389055Lelio R Paula10/2012
967931^59713-3089054Theodore Burton02/2007
9680(7*2^295834-1)/2766389052Lelio R Paula02/2014
968179731!4-3289049Robert Price11/2019
9683123^42608+289047Lelio R Paula05/2013
96826^114433-114433^689047Norbert Schneider04/2017
96842^295800-45965989045Enzo Doria05/2015
9685(52*10^89037-1)/389039Robert Price02/2017
9686(2^295782+1870)/289039Stefano Morozzi01/2020
9687(6^114398-11)/589019Paul Bourdelais11/2011
968811^85470-585089008Enzo Doria02/2013
9689(2^295650+522)/289000Stefano Morozzi01/2020
9690(35*10^88998+37)/988999Robert Price05/2022
9691(27*2^295634+1)/468788993Lelio R Paula01/2013
9692(p(18424)#-4)/288985Robert Price09/2017
96932^295564-18988974Lelio R Paula10/2012
96942^295557+7309788972Enzo Doria04/2016
969511^85433-576088970Enzo Doria01/2013
969623074^7165+7165^2307488956Hans Havermann08/2020
9697(2^295479+3050)/288948Stefano Morozzi01/2020
96986*10^88938-9188939Robert Price11/2017
969915^75619-8888935Lelio R Paula11/2015
9700(2^295433+2234)/288934Stefano Morozzi01/2020
9701(15589^21211-1)/1558888930Serge Batalov08/2020
970223776^5499+5499^2377688929Hans Havermann08/2020
970321112^16291+16291^2111288923Hans Havermann08/2020
97042^295385-8588920Lelio R Paula10/2012
97052^295385-1633388920Enzo Doria04/2013
9706(89*10^88916-377)/988917Robert Price07/2021
970779617!4+3288909Robert Price09/2019
970822077^10640+10640^2207788903Hans Havermann08/2020
97092^295309+5988897Lelio R Paula10/2012
97102^295288-10979988891Enzo Doria04/2014
971110^88888+17037388889Stefano Morozzi07/2018
971210^88888+27139988889Stefano Morozzi07/2018
971310^88888+37539788889Stefano Morozzi07/2018
971410^88888+54882388889Stefano Morozzi07/2018
971510^88888+82086188889Stefano Morozzi07/2018
971610^88888+120634988889Stefano Morozzi07/2018
971710^88888+129204788889Stefano Morozzi07/2018
971810^88888+145602988889Stefano Morozzi07/2018
971910^88888-49028788888Patrick De Geest09/2018
97202^295245+6588878Lelio R Paula10/2012
97215*10^88874-3788875Robert Price11/2021
9723Padovan(727734)88874Eric W. Weisstein04/2011
9722(2^295231+1554)/288874Stefano Morozzi01/2020
972479585!4-3288870Robert Price11/2019
972518^70793-1788865Lelio R Paula11/2015
97266^114196-1757388862Enzo Doria02/2013
9727302^35829+35829^30288857Norbert Schneider12/2014
97283^186223+1688851Robert Price10/2013
97293*2^295139+788847Lelio R Paula08/2014
97303^186212-11300888846Enzo Doria07/2014
97312*10^88844+2388845Robert Price12/2020
973223415^6224+6224^2341588839Hans Havermann08/2020
973387^45803-8688836Norbert Schneider11/2015
97342^295094-11027388833Enzo Doria05/2014
97352^295080+186915188828Enzo Doria05/2016
9736(2^295061+2174)/288822Stefano Morozzi01/2020
97372^295027-11340788812Enzo Doria07/2014
9738(2*10^88808-71)/388808Robert Price01/2017
9739(2^295009+2102)/288807Stefano Morozzi01/2020
974013^79722-8088806Lelio R Paula11/2015
974121112^16077+16077^2111288802Hans Havermann08/2020
97423^186103+10488794Lelio R Paula12/2015
9743(3*2^294971+1)/2556588792Lelio R Paula01/2013
9744(4025^24631-1)/402488786Serge Batalov08/2020
97452^294937-11500388785Enzo Doria06/2015
9746(2^294923+3134)/288781Stefano Morozzi01/2020
9747(15326^21211-1)/1532588773Serge Batalov08/2020
97482551^26056+26056^255188766Norbert Schneider01/2020
97492^294868-10970988765Enzo Doria04/2014
97502^294864-298588763Yves Minet09/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 22 2022 18:03 (Time in France)

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