PRP Records

Probable Primes Top 10000

(271067 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 ?
6251(2^298408+450)/289830Stefano Morozzi01/2020
6252gcd(V(1091095),5*F(218219)*(F(218219)+1)+1)89822Serge Batalov04/2015
62532^298367+5890589818Lelio R Paula11/2013
625421966^12269+12269^2196689815Hans Havermann08/2020
6255(2^298333+3126)/289807Stefano Morozzi01/2020
62562^298319-10965789803Enzo Doria04/2014
62578*10^89800+8189801Robert Price05/2017
625821354^16037+16037^2135489797Hans Havermann08/2020
6259(2^298249+714)/289782Stefano Morozzi01/2020
626021227^16954+16954^2122789775Hans Havermann08/2020
6261(733^31333-1)/73289770Serge Batalov08/2020
626418^71505-9189759Lelio R Paula12/2015
6262(2^298171+1586)/289759Stefano Morozzi01/2020
6263(4788^24391-1)/478789759Serge Batalov08/2020
6265(2^298161+3530)/289756Stefano Morozzi01/2020
6266(7^106187+1)/889738Paul Bourdelais04/2008
62672^298079-10953189731Enzo Doria04/2014
6268(9255^22621-1)/925489720Serge Batalov08/2020
6269117^43380+11689718Norbert Schneider08/2018
6270(22699*2^298016+1)/38589714Lelio R Paula06/2014
6271156*(10^(4*22427)-1)/101-189709Robert Price05/2014
62722^298003-6694589708Lelio R Paula11/2013
6273(23*10^89705-83)/389706Robert Price09/2017
627417^72900-5489700Lelio R Paula11/2015
6275(2^297968+2482)/289698Stefano Morozzi01/2020
62763*2^297956+589695Lelio R Paula08/2014
6277(2^297952+3558)/289693Stefano Morozzi01/2020
6278(3992^24907-1)/399189692Serge Batalov08/2020
627920^68938-1189691Lelio R Paula01/2016
628089*10^89687-789689Robert Price03/2017
6281(6882^23371-1)/688189688Serge Batalov08/2020
6282(297847^16384+1)/289686Richard Fischer08/2019
62832^297923+7778389684Enzo Doria05/2016
6284(2^297893+1694)/289675Stefano Morozzi01/2020
628511^86107-2457600089672Enzo Doria02/2013
62862^297878-11191189671Enzo Doria05/2014
628720823^20236+20236^2082389667Hans Havermann08/2020
628825708^3075+3075^2570889666Hans Havermann08/2020
628921002^18585+18585^2100289661Hans Havermann08/2020
6290(2^297830+3670)/289656Stefano Morozzi01/2020
62917^106084+4089652Lelio R Paula10/2015
6292(2^297815+618)/289651Stefano Morozzi01/2020
629321223^16752+16752^2122389648Hans Havermann08/2020
6295(86*10^89640-311)/989641Robert Price10/2017
6294(2^297781+2094)/289641Stefano Morozzi01/2020
6296(2^297741+3326)/289629Stefano Morozzi01/2020
6297(2^297724+3606)/289624Stefano Morozzi01/2020
62983*10^89608-5989609Robert Price10/2017
6299(2^297650+3250)/289602Stefano Morozzi01/2020
63003^187780-1103889594Enzo Doria05/2014
6301(13*2^297560-1)/4915178789568Lelio R Paula02/2014
63025^128141-3689567Lelio R Paula10/2015
63034*7^105951+989540Lelio R Paula10/2014
6304(7*10^89539-439)/989539Robert Price09/2017
6305(9772^22441-1)/977189536Serge Batalov08/2020
630622823^8374+8374^2282389534Hans Havermann08/2020
6307(2^297401+2954)/289527Stefano Morozzi01/2020
6308(2^297403+1670)/289527Stefano Morozzi01/2020
63092^297397+17725789526Enzo Doria05/2016
63112^297346-1624189511Enzo Doria04/2013
6310(5*10^89510+79)/389511Robert Price11/2017
63124^148663-3^14866389505Jean-Louis Charton11/2005
63132^297328-86968810589505Lelio R Paula07/2016
63142^297325-45904389504Enzo Doria05/2015
63152^297310-11239189500Enzo Doria06/2014
63162^297296-11215789496Enzo Doria06/2014
631757^50966-289490Lelio R Paula08/2013
6318(266*10^89482+1)/389484Robert Price02/2016
6319(14*10^89480-101)/389481Robert Price04/2017
63202618^26175+26175^261889466Norbert Schneider01/2020
6321(2^297150+3922)/289451Stefano Morozzi01/2020
6322(2^297141+1842)/289449Stefano Morozzi01/2020
6323(2^297140+1458)/289448Stefano Morozzi01/2020
6324(2^297129+726)/289445Stefano Morozzi01/2020
63252^297122+9989443Lelio R Paula10/2012
6326(3^187435-5)/128689427Lelio R Paula01/2013
6327(28*10^89425+101)/389426Robert Price09/2020
6328(2^297037+3522)/289417Stefano Morozzi01/2020
6329(25*10^89413+161)/389414Robert Price01/2017
633029080^1187+1187^2908089406Hans Havermann08/2020
63312^296990+187069989403Enzo Doria05/2016
63322^296972-101789398Lelio R Paula11/2013
6333(7*10^89383+167)/389384Robert Kinser10/2017
6334(85*10^89375-31)/989376Robert Price11/2015
63359*2^296870+789368Lelio R Paula08/2014
6336100^44683-99^4468389366Robert Price07/2013
63372^296810+7651989349Enzo Doria05/2016
6338(2747^25981-1)/274689342Serge Batalov08/2020
63398^98928+7^(98928+1)89341Robert Price06/2016
6341(3^187247+4)/102789337Lelio R Paula01/2013
634021832^12359+12359^2183289337Hans Havermann08/2020
6342(3^187235-2)/204589331Lelio R Paula01/2013
63432^296736-43214989327Paul Bourdelais05/2013
63442^296737-11251989327Enzo Doria06/2014
63452^296718-364589322Lelio R Paula11/2013
6346(2^296702+2338)/289316Stefano Morozzi01/2020
63472^296681-1622189310Enzo Doria04/2013
63482^296669-1651389307Enzo Doria04/2013
6349(2^296626+1282)/289294Stefano Morozzi01/2020
63502^296619-1635789292Enzo Doria04/2013
63512^296614-11005189290Enzo Doria04/2014
6352(2^296601+1730)/289286Stefano Morozzi01/2020
6353(3^187138+8)/8314789283Lelio R Paula01/2013
6354(2*10^89279+457)/989279Robert Price01/2017
6355(2^296568+1222)/289276Stefano Morozzi01/2020
635615^75907-2889274Lelio R Paula11/2015
63572^296547-3789270Yves Minet01/2012
63582^296485+19189251Lelio R Paula10/2012
63592^296467-7589246Lelio R Paula10/2012
6360(2^296462+1674)/289244Stefano Morozzi01/2020
63612^296416-10953589231Enzo Doria04/2014
6362(23*2^296406+1)/389228Lelio R Paula01/2013
636366^49037-6589225Norbert Schneider11/2014
63642^296377-1624589219Enzo Doria04/2013
63652^296372-6487589217Lelio R Paula11/2013
63665*6^114648-789215Lelio R Paula10/2014
6367(2^296361+1262)/289214Stefano Morozzi01/2020
63683*10^89206+1389207Robert Price08/2017
63697*3^186960-489204Lelio R Paula08/2014
63702^296290-11213389193Enzo Doria06/2014
63716^114620-1700389192Enzo Doria02/2013
6372(4*10^89189+41)/989189Robert Price11/2014
63732^296261-16118189184Enzo Doria04/2013
6374(19*2^296269-1)/53062389182Lelio R Paula02/2014
63753^186903-1089176Robert Price09/2013
63767*10^89169-389170Dmitry Domanov11/2010
6377(2^296221-1017)/3589170Lelio R Paula01/2013
6378(43*10^89169+47)/989170Robert Price12/2017
6379(10^89160+29)/389160Serge Batalov12/2014
6380(28*10^89141-97)/389142Robert Price07/2016
63812^296116-73463989140Paul Bourdelais04/2013
6382(2^296101+1250)/289135Stefano Morozzi01/2020
638322574^8883+8883^2257489135Hans Havermann08/2020
63846^114544-13389133Lelio R Paula12/2015
63852^296076-11329789128Enzo Doria07/2014
6386(11*2^296060-1)/21589122Lelio R Paula02/2014
63875*10^89118+8189119Robert Price08/2017
63882^296037-141189117Yves Minet01/2013
63892^296020-260480989111Enzo Doria05/2015
63902^296016+8189110Henri Lifchitz02/2007
63912^296010-1189108Lelio R Paula10/2012
63922^295998-11191189105Enzo Doria05/2014
6393(2^296014+47)/9399114989102Lelio R Paula01/2013
639429529^1040+1040^2952989090Hans Havermann08/2020
63952^295939-1662189087Enzo Doria04/2013
63962^295934-10969189086Enzo Doria04/2014
6397(2^295921+2246)/289081Stefano Morozzi01/2020
6398(185*10^89063+7)/389065Robert Price02/2017
63992^295831+14389055Lelio R Paula10/2012
640031^59713-3089054Theodore Burton02/2007
6401(7*2^295834-1)/2766389052Lelio R Paula02/2014
640279731!4-3289049Robert Price11/2019
6404123^42608+289047Lelio R Paula05/2013
64036^114433-114433^689047Norbert Schneider04/2017
64052^295800-45965989045Enzo Doria05/2015
6406(52*10^89037-1)/389039Robert Price02/2017
6407(2^295782+1870)/289039Stefano Morozzi01/2020
6408(6^114398-11)/589019Paul Bourdelais11/2011
640911^85470-585089008Enzo Doria02/2013
6410(2^295650+522)/289000Stefano Morozzi01/2020
6411(27*2^295634+1)/468788993Lelio R Paula01/2013
6412(p(18424)#-4)/288985Robert Price09/2017
64132^295564-18988974Lelio R Paula10/2012
64142^295557+7309788972Enzo Doria04/2016
641511^85433-576088970Enzo Doria01/2013
641623074^7165+7165^2307488956Hans Havermann08/2020
6417(2^295479+3050)/288948Stefano Morozzi01/2020
64186*10^88938-9188939Robert Price11/2017
641915^75619-8888935Lelio R Paula11/2015
6420(2^295433+2234)/288934Stefano Morozzi01/2020
6421(15589^21211-1)/1558888930Serge Batalov08/2020
642223776^5499+5499^2377688929Hans Havermann08/2020
642321112^16291+16291^2111288923Hans Havermann08/2020
64242^295385-8588920Lelio R Paula10/2012
64252^295385-1633388920Enzo Doria04/2013
642679617!4+3288909Robert Price09/2019
642722077^10640+10640^2207788903Hans Havermann08/2020
64282^295309+5988897Lelio R Paula10/2012
64292^295288-10979988891Enzo Doria04/2014
643010^88888+17037388889Stefano Morozzi07/2018
643110^88888+27139988889Stefano Morozzi07/2018
643210^88888+37539788889Stefano Morozzi07/2018
643310^88888+54882388889Stefano Morozzi07/2018
643410^88888+82086188889Stefano Morozzi07/2018
643510^88888+120634988889Stefano Morozzi07/2018
643610^88888+129204788889Stefano Morozzi07/2018
643710^88888+145602988889Stefano Morozzi07/2018
643810^88888-49028788888Patrick De Geest09/2018
64392^295245+6588878Lelio R Paula10/2012
6440Padovan(727734)88874Eric W. Weisstein04/2011
6441(2^295231+1554)/288874Stefano Morozzi01/2020
644279585!4-3288870Robert Price11/2019
644318^70793-1788865Lelio R Paula11/2015
64446^114196-1757388862Enzo Doria02/2013
6445302^35829+35829^30288857Norbert Schneider12/2014
64463^186223+1688851Robert Price10/2013
64473*2^295139+788847Lelio R Paula08/2014
64483^186212-11300888846Enzo Doria07/2014
644923415^6224+6224^2341588839Hans Havermann08/2020
645087^45803-8688836Norbert Schneider11/2015
64512^295094-11027388833Enzo Doria05/2014
64522^295080+186915188828Enzo Doria05/2016
6453(2^295061+2174)/288822Stefano Morozzi01/2020
64542^295027-11340788812Enzo Doria07/2014
6455(2*10^88808-71)/388808Robert Price01/2017
6456(2^295009+2102)/288807Stefano Morozzi01/2020
645713^79722-8088806Lelio R Paula11/2015
645821112^16077+16077^2111288802Hans Havermann08/2020
64593^186103+10488794Lelio R Paula12/2015
6460(3*2^294971+1)/2556588792Lelio R Paula01/2013
6461(4025^24631-1)/402488786Serge Batalov08/2020
64622^294937-11500388785Enzo Doria06/2015
6463(2^294923+3134)/288781Stefano Morozzi01/2020
6464(15326^21211-1)/1532588773Serge Batalov08/2020
64652551^26056+26056^255188766Norbert Schneider01/2020
64662^294868-10970988765Enzo Doria04/2014
64672^294864-298588763Yves Minet09/2014
6468(17*10^88761-41)/388762Robert Price09/2017
6469(2^294834+2854)/288754Stefano Morozzi01/2020
6470(2^294823+2466)/288751Stefano Morozzi01/2020
6471(2^294764+642)/288733Stefano Morozzi01/2020
64722^294754+1501588730Lelio R Paula10/2013
6473(3^185951-7)/2088720Lelio R Paula01/2013
6474(2^294688+3186)/288710Stefano Morozzi01/2020
6475(2^294673+3906)/288706Stefano Morozzi01/2020
6476(2^294661+5)/44369338388694Lelio R Paula01/2013
6477(2^294631+2514)/288693Stefano Morozzi01/2020
6478(10^88680+11)/388680Robert Price11/2014
64792*7^104928-988675Lelio R Paula10/2014
648011^85150+1288675Lelio R Paula11/2015
64818*6^113951+588673Lelio R Paula10/2014
6482(2^294549+3110)/288668Stefano Morozzi01/2020
64846^113940-1856388663Enzo Doria03/2013
648338^56123-56123^3888663Norbert Schneider02/2017
64852^294492-6588651Lelio R Paula10/2012
6486(2^294481+2822)/288648Stefano Morozzi01/2020
648723874^5165+5165^2387488646Hans Havermann08/2020
6488(2^294469+1466)/288644Stefano Morozzi01/2020
64897*10^88634-2788635Dylan Delgado08/2019
649020^68120-5388627Lelio R Paula01/2016
6491122^42477-12188623Norbert Schneider10/2018
64922^294391-11325788621Enzo Doria07/2014
64935^126784-1547688619Enzo Doria02/2013
6494(2^294335+554)/288604Stefano Morozzi01/2020
64952^294327+988602Lelio R Paula10/2012
64962^294320+1891588600Lelio R Paula10/2013
6497(98*10^88595-89)/9988595Ray Chandler07/2011
649820723^18834+18834^2072388590Hans Havermann08/2020
6499(2^294268+1402)/288584Stefano Morozzi01/2020
6500(17*2^294262-1)/1388582Lelio R Paula02/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 30 2020 10:03 (Time in France)

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