PRP Records

Probable Primes Top 10000

(290751 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 ?
9251(2^297129+726)/289445Stefano Morozzi01/2020
92522^297122+9989443Lelio R Paula10/2012
9253(3^187435-5)/128689427Lelio R Paula01/2013
9254(28*10^89425+101)/389426Robert Price09/2020
9255(2^297037+3522)/289417Stefano Morozzi01/2020
9256(25*10^89413+161)/389414Robert Price01/2017
9257(89*10^89411-737)/989412Robert Price01/2022
925829080^1187+1187^2908089406Hans Havermann08/2020
92592^296990+187069989403Enzo Doria05/2016
92602^296972-101789398Lelio R Paula11/2013
9261(7*10^89383+167)/389384Robert Kinser10/2017
9262(85*10^89375-31)/989376Robert Price11/2015
92639*2^296870+789368Lelio R Paula08/2014
9264100^44683-99^4468389366Robert Price07/2013
92652^296810+7651989349Enzo Doria05/2016
9266(2747^25981-1)/274689342Serge Batalov08/2020
92678^98928+7^(98928+1)89341Robert Price06/2016
9269(3^187247+4)/102789337Lelio R Paula01/2013
926821832^12359+12359^2183289337Hans Havermann08/2020
9270(3^187235-2)/204589331Lelio R Paula01/2013
92712^296736-43214989327Paul Bourdelais05/2013
92722^296737-11251989327Enzo Doria06/2014
92732^296718-364589322Lelio R Paula11/2013
9274(2^296702+2338)/289316Stefano Morozzi01/2020
92752^296681-1622189310Enzo Doria04/2013
92762^296669-1651389307Enzo Doria04/2013
9277(2^296626+1282)/289294Stefano Morozzi01/2020
92782^296619-1635789292Enzo Doria04/2013
92792^296614-11005189290Enzo Doria04/2014
9280(2^296601+1730)/289286Stefano Morozzi01/2020
9281(3^187138+8)/8314789283Lelio R Paula01/2013
9282(2*10^89279+457)/989279Robert Price01/2017
9283(2^296568+1222)/289276Stefano Morozzi01/2020
9284(133*10^89273+17)/389275Robert Price11/2021
928515^75907-2889274Lelio R Paula11/2015
92862^296547-3789270Yves Minet01/2012
92872^296485+19189251Lelio R Paula10/2012
92882^296467-7589246Lelio R Paula10/2012
9289(2^296462+1674)/289244Stefano Morozzi01/2020
92902^296416-10953589231Enzo Doria04/2014
9291(23*2^296406+1)/389228Lelio R Paula01/2013
929266^49037-6589225Norbert Schneider11/2014
92932^296377-1624589219Enzo Doria04/2013
92942^296372-6487589217Lelio R Paula11/2013
92955*6^114648-789215Lelio R Paula10/2014
9296(2^296361+1262)/289214Stefano Morozzi01/2020
92973*10^89206+1389207Robert Price08/2017
92987*3^186960-489204Lelio R Paula08/2014
9299(28*10^89203+47)/389204Robert Price02/2021
93002^296290-11213389193Enzo Doria06/2014
93016^114620-1700389192Enzo Doria02/2013
9302(22*10^89190+179)/389191Robert Price02/2022
9303(4*10^89189+41)/989189Robert Price11/2014
93042^296261-16118189184Enzo Doria04/2013
9305(19*2^296269-1)/53062389182Lelio R Paula02/2014
93063^186903-1089176Robert Price09/2013
93077*10^89169-389170Dmitry Domanov11/2010
9308(2^296221-1017)/3589170Lelio R Paula01/2013
9309(43*10^89169+47)/989170Robert Price12/2017
9310(10^89160+29)/389160Serge Batalov12/2014
9311(28*10^89141-97)/389142Robert Price07/2016
93122^296116-73463989140Paul Bourdelais04/2013
9313(2^296101+1250)/289135Stefano Morozzi01/2020
931422574^8883+8883^2257489135Hans Havermann08/2020
93156^114544-13389133Lelio R Paula12/2015
93162^296076-11329789128Enzo Doria07/2014
9317(11*2^296060-1)/21589122Lelio R Paula02/2014
93185*10^89118+8189119Robert Price08/2017
93192^296037-141189117Yves Minet01/2013
93202^296020-260480989111Enzo Doria05/2015
93212^296016+8189110Henri Lifchitz02/2007
93222^296010-1189108Lelio R Paula10/2012
93232^295998-11191189105Enzo Doria05/2014
9324(2^296014+47)/9399114989102Lelio R Paula01/2013
932529529^1040+1040^2952989090Hans Havermann08/2020
93262^295939-1662189087Enzo Doria04/2013
93272^295934-10969189086Enzo Doria04/2014
9328(2^295921+2246)/289081Stefano Morozzi01/2020
9329(185*10^89070-11)/389072Robert Price10/2020
9330(185*10^89063+7)/389065Robert Price02/2017
9331(8*10^89055-59)/389056Robert Price08/2021
93322^295831+14389055Lelio R Paula10/2012
933331^59713-3089054Theodore Burton02/2007
9334(7*2^295834-1)/2766389052Lelio R Paula02/2014
933579731!4-3289049Robert Price11/2019
9337123^42608+289047Lelio R Paula05/2013
93366^114433-114433^689047Norbert Schneider04/2017
93382^295800-45965989045Enzo Doria05/2015
9339(52*10^89037-1)/389039Robert Price02/2017
9340(2^295782+1870)/289039Stefano Morozzi01/2020
9341(6^114398-11)/589019Paul Bourdelais11/2011
934211^85470-585089008Enzo Doria02/2013
9343(2^295650+522)/289000Stefano Morozzi01/2020
9344(35*10^88998+37)/988999Robert Price05/2022
9345(27*2^295634+1)/468788993Lelio R Paula01/2013
9346(p(18424)#-4)/288985Robert Price09/2017
93472^295564-18988974Lelio R Paula10/2012
93482^295557+7309788972Enzo Doria04/2016
934911^85433-576088970Enzo Doria01/2013
935023074^7165+7165^2307488956Hans Havermann08/2020
9351(2^295479+3050)/288948Stefano Morozzi01/2020
93526*10^88938-9188939Robert Price11/2017
935315^75619-8888935Lelio R Paula11/2015
9354(2^295433+2234)/288934Stefano Morozzi01/2020
9355(15589^21211-1)/1558888930Serge Batalov08/2020
935623776^5499+5499^2377688929Hans Havermann08/2020
935721112^16291+16291^2111288923Hans Havermann08/2020
93582^295385-8588920Lelio R Paula10/2012
93592^295385-1633388920Enzo Doria04/2013
9360(89*10^88916-377)/988917Robert Price07/2021
936179617!4+3288909Robert Price09/2019
936222077^10640+10640^2207788903Hans Havermann08/2020
93632^295309+5988897Lelio R Paula10/2012
93642^295288-10979988891Enzo Doria04/2014
936510^88888+17037388889Stefano Morozzi07/2018
936610^88888+27139988889Stefano Morozzi07/2018
936710^88888+37539788889Stefano Morozzi07/2018
936810^88888+54882388889Stefano Morozzi07/2018
936910^88888+82086188889Stefano Morozzi07/2018
937010^88888+120634988889Stefano Morozzi07/2018
937110^88888+129204788889Stefano Morozzi07/2018
937210^88888+145602988889Stefano Morozzi07/2018
937310^88888-49028788888Patrick De Geest09/2018
93742^295245+6588878Lelio R Paula10/2012
93755*10^88874-3788875Robert Price11/2021
9377Padovan(727734)88874Eric W. Weisstein04/2011
9376(2^295231+1554)/288874Stefano Morozzi01/2020
937879585!4-3288870Robert Price11/2019
937918^70793-1788865Lelio R Paula11/2015
93806^114196-1757388862Enzo Doria02/2013
9381302^35829+35829^30288857Norbert Schneider12/2014
93823^186223+1688851Robert Price10/2013
93833*2^295139+788847Lelio R Paula08/2014
93843^186212-11300888846Enzo Doria07/2014
93852*10^88844+2388845Robert Price12/2020
938623415^6224+6224^2341588839Hans Havermann08/2020
938787^45803-8688836Norbert Schneider11/2015
93882^295094-11027388833Enzo Doria05/2014
93892^295080+186915188828Enzo Doria05/2016
9390(2^295061+2174)/288822Stefano Morozzi01/2020
93912^295027-11340788812Enzo Doria07/2014
9392(2*10^88808-71)/388808Robert Price01/2017
9393(2^295009+2102)/288807Stefano Morozzi01/2020
939413^79722-8088806Lelio R Paula11/2015
939521112^16077+16077^2111288802Hans Havermann08/2020
93963^186103+10488794Lelio R Paula12/2015
9397(3*2^294971+1)/2556588792Lelio R Paula01/2013
9398(4025^24631-1)/402488786Serge Batalov08/2020
93992^294937-11500388785Enzo Doria06/2015
9400(2^294923+3134)/288781Stefano Morozzi01/2020
9401(15326^21211-1)/1532588773Serge Batalov08/2020
94022551^26056+26056^255188766Norbert Schneider01/2020
94032^294868-10970988765Enzo Doria04/2014
94042^294864-298588763Yves Minet09/2014
9405(17*10^88761-41)/388762Robert Price09/2017
9406(2^294834+2854)/288754Stefano Morozzi01/2020
9407(2^294823+2466)/288751Stefano Morozzi01/2020
9408(2^294764+642)/288733Stefano Morozzi01/2020
94092^294754+1501588730Lelio R Paula10/2013
9410(3^185951-7)/2088720Lelio R Paula01/2013
9411(2^294688+3186)/288710Stefano Morozzi01/2020
9412(2^294673+3906)/288706Stefano Morozzi01/2020
9413(2^294661+5)/44369338388694Lelio R Paula01/2013
9414(2^294631+2514)/288693Stefano Morozzi01/2020
9415(10^88680+11)/388680Robert Price11/2014
94162*7^104928-988675Lelio R Paula10/2014
941711^85150+1288675Lelio R Paula11/2015
94188*6^113951+588673Lelio R Paula10/2014
9419(2^294549+3110)/288668Stefano Morozzi01/2020
94206*10^88665-7988666Robert Price03/2022
94216^113940-1856388663Enzo Doria03/2013
942238^56123-56123^3888663Norbert Schneider02/2017
94232^294492-6588651Lelio R Paula10/2012
9424(2^294481+2822)/288648Stefano Morozzi01/2020
942523874^5165+5165^2387488646Hans Havermann08/2020
9426(2^294469+1466)/288644Stefano Morozzi01/2020
94277*10^88634-2788635Dylan Delgado08/2019
942820^68120-5388627Lelio R Paula01/2016
9429122^42477-12188623Norbert Schneider10/2018
94302^294391-11325788621Enzo Doria07/2014
94315^126784-1547688619Enzo Doria02/2013
9432(2^294335+554)/288604Stefano Morozzi01/2020
94332^294327+988602Lelio R Paula10/2012
94342^294320+1891588600Lelio R Paula10/2013
9435(98*10^88595-89)/9988595Ray Chandler07/2011
9436(5*10^88595+103)/988595Robert Price04/2022
943720723^18834+18834^2072388590Hans Havermann08/2020
9438(68*10^88586-329)/988587Robert Price03/2021
9439(2^294268+1402)/288584Stefano Morozzi01/2020
9440(17*2^294262-1)/1388582Lelio R Paula02/2014
94416*10^88571+7788572Robert Price06/2020
94422^294224-93307588571Paul Bourdelais04/2021
9443(2^294145+1346)/288547Stefano Morozzi01/2020
9444(2*10^88545+7)/988545Erik Branger03/2011
94452^294137-13388545Lelio R Paula10/2012
9446(2^294109+3494)/288536Stefano Morozzi01/2020
944723515^5818+5818^2351588529Hans Havermann08/2020
9448(2^294092-1017)/117188528Lelio R Paula01/2013
94494^147036+147036^4+188525Robert Price04/2014
945022541^8458+8458^2254188525Hans Havermann08/2020
9451(14^77213-5^77213)/988496Robert Price04/2013
94522^293965+279337788493Enzo Doria03/2016
9453(2^293956+3306)/288490Stefano Morozzi01/2020
945411^84971-15088489Enzo Doria08/2012
9455(2^293944+1066)/288486Stefano Morozzi01/2020
94569*10^88485+9188486Robert Price10/2020
945748^52626-4788478Norbert Schneider08/2018
9458(2^293956-1017)/3985137669667788476Lelio R Paula01/2013
945911^84958-219088475Enzo Doria12/2012
9460(2^293902+3070)/288474Stefano Morozzi01/2020
9461(35*10^88471-89)/988472Robert Price02/2022
94622^293880-11134788467Enzo Doria05/2014
9463(106*10^88459-1)/388461Serge Batalov12/2014
946410^88457+27873388458Patrick De Geest07/2017
946510^88457-40188457Robert Price06/2017
9466(2^293834+3018)/288453Stefano Morozzi01/2020
9467(2^293747+1626)/288427Stefano Morozzi01/2020
946822080^10109+10109^2208088424Hans Havermann08/2020
946911^84908-168088423Enzo Doria12/2012
9470(2^293703+3486)/288414Stefano Morozzi01/2020
94712^293679-11207588407Enzo Doria06/2014
94726^113608-6588405Lelio R Paula12/2015
94732^293624+8287588390Lelio R Paula10/2013
9474(2^293618+918)/288388Stefano Morozzi01/2020
94752^293612-11233788387Enzo Doria06/2014
9476758^30693+30693^75888386Norbert Schneider05/2017
9477gcd(V(1062695),5*F(212539)*(F(212539)-1)+1)88383Serge Batalov04/2015
94785*10^88377+7788378Robert Price06/2016
9479(2^293584+1558)/288378Stefano Morozzi01/2020
9480(5*2^293526+1)/30388359Lelio R Paula01/2013
948120918^16743+16743^2091888355Hans Havermann08/2020
9482(2^293499+2390)/288352Stefano Morozzi01/2020
948320727^18292+18292^2072788344Hans Havermann08/2020
94852^293461-278584388341Enzo Doria03/2016
9484(31*10^88340+257)/988341Robert Price12/2021
94872^293416-103788328Yves Minet11/2012
94866*10^88327+4388328Robert Price07/2020
9488(58*10^88321-49)/988322Robert Price05/2022
948925109^3292+3292^2510988320Hans Havermann08/2020
9490(2^293384-7)/388317Lelio R Paula01/2013
9491(3^185092-5)/488311Lelio R Paula01/2013
9492(5*10^88303-173)/388304Robert Price11/2017
949314^77039-5788297Lelio R Paula11/2015
94943*10^88293-5988294Robert Price10/2017
94955^126303+4288283Lelio R Paula10/2015
9496(88*10^88269+83)/988270Robert Price03/2022
949819^69025-1888266Theodore Burton01/2006
9497140^41128+13988266Norbert Schneider04/2019
94995*10^88261-388262Dmitry Domanov11/2010
9500(2^293195+2238)/288261Stefano Morozzi01/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 23 2022 21:24 (Time in France)

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