PRP Records

Probable Primes Top 10000

(193013 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 ?
400110^90227+5628190228Patrick De Geest06/2016
40042^299725+31590227Lelio R Paula11/2013
400210^90227-100000000190227Robert Price05/2016
400310^90227-6876390227Patrick De Geest06/2016
40055^129082+4890225Lelio R Paula03/2016
40062^299699+19590219Lelio R Paula10/2012
4007(55*10^90211-1)/990212Ray Chandler02/2012
40083^189053+28090202Lelio R Paula04/2016
40092^299639-18790201Lelio R Paula10/2012
40102^299631+18390198Lelio R Paula10/2012
4011(21*2^299611-1)/2990192Lelio R Paula02/2014
40122^299567+11390179Lelio R Paula10/2012
40132^299550+18990174Lelio R Paula10/2012
4014(2^299535+3)/2990168Lelio R Paula01/2013
4015(97*10^90155-1)/390157Serge Batalov12/2014
40163^188938+868090147Lelio R Paula04/2016
40176^115840-5590142Lelio R Paula05/2016
4018(5*10^90142-473)/990142Robert Price12/2017
40198*7^106659+590139Lelio R Paula10/2014
40202^299406-1665390131Enzo Doria05/2013
4021208049#+(216091#)/(208049#)90128Makoto Morimoto04/2016
4022(F(5)^128941-F(4)^128941)/F(3)90126Wayne Halsdorf03/2012
40236^115819-5390125Lelio R Paula05/2016
40246^115816-1685390123Enzo Doria02/2013
40256^115813-2390121Lelio R Paula05/2016
4026(22*10^90110+161)/390111Robert Price02/2017
4027(2^299330-509203)/6990106Lelio R Paula01/2013
4028(29*10^90096-17)/390097Erik Branger09/2014
40292^299247+187052990083Enzo Doria05/2016
40302^299229-279778390077Enzo Doria04/2016
40312^299220-1631790075Enzo Doria04/2013
403211^86491-135090072Enzo Doria12/2012
4033(31*10^90064-1)/390066Robert Price03/2017
4034L(430949)/861899/144038756153990045Serge Batalov07/2017
40352^299112+7395190042Enzo Doria04/2016
40368^99702+7^(99702-1)90040Robert Price02/2016
40375*10^90033+390034Dmitry Domanov11/2010
4038243^37738+37738^24390029Norbert Schneider01/2015
40392^299048-11329790023Enzo Doria07/2014
40403^188648+9290008Lelio R Paula12/2015
40415*2^298991+790006Lelio R Paula08/2014
4042(25*2^298997+1)/326790005Lelio R Paula01/2013
404310^90000+886990001Patrick De Geest12/2009
404510^89999+8293990000Dirk Augustin04/2007
404410^90000-14034390000Patrick De Geest12/2009
404610^89999-19489189999Patrick De Geest11/2009
404719^70365-7889980Lelio R Paula12/2015
4048NaturalLogarithmOf2(89973)89973Eric W. Weisstein10/2015
40492^298852-6487589964Lelio R Paula11/2013
405018^71659+3789952Lelio R Paula12/2015
4051(2908*29^61501-3)/789942Curtis Bright05/2015
405217^73067+2089906Lelio R Paula11/2015
40532^298637-9989899Lelio R Paula10/2012
40549^94188+3*8^94188-2*4^94188-3*2^9418889879Mike Oakes01/2011
40559*10^89858+1989859Robert Price05/2016
40562^298501+187006789858Enzo Doria05/2016
405711^86280-9889852Lelio R Paula11/2015
40582^298473-11005989850Enzo Doria04/2014
405919^70263-3289850Lelio R Paula12/2015
4060(299*10^89836-17)/389838Robert Price01/2017
40613^188286+1489836Robert Price09/2013
4062gcd(V(1091095),5*F(218219)*(F(218219)+1)+1)89822Serge Batalov04/2015
40632^298367+5890589818Lelio R Paula11/2013
40642^298319-10965789803Enzo Doria04/2014
40658*10^89800+8189801Robert Price05/2017
406618^71505-9189759Lelio R Paula12/2015
4067(7^106187+1)/889738Paul Bourdelais04/2008
40682^298079-10953189731Enzo Doria04/2014
4069(22699*2^298016+1)/38589714Lelio R Paula06/2014
4070156*(10^(4*22427)-1)/101-189709Robert Price05/2014
40712^298003-6694589708Lelio R Paula11/2013
4072(23*10^89705-83)/389706Robert Price09/2017
407317^72900-5489700Lelio R Paula11/2015
40743*2^297956+589695Lelio R Paula08/2014
407520^68938-1189691Lelio R Paula01/2016
407689*10^89687-789689Robert Price03/2017
40772^297923+7778389684Enzo Doria05/2016
407811^86107-2457600089672Enzo Doria02/2013
40792^297878-11191189671Enzo Doria05/2014
40807^106084+4089652Lelio R Paula10/2015
4081(86*10^89640-311)/989641Robert Price10/2017
40823*10^89608-5989609Robert Price10/2017
40833^187780-1103889594Enzo Doria05/2014
4084(13*2^297560-1)/4915178789568Lelio R Paula02/2014
40855^128141-3689567Lelio R Paula10/2015
40864*7^105951+989540Lelio R Paula10/2014
4087(7*10^89539-439)/989539Robert Price09/2017
40882^297397+17725789526Enzo Doria05/2016
40892^297346-1624189511Enzo Doria04/2013
4090(5*10^89510+79)/389511Robert Price11/2017
40924^148663-3^14866389505Jean-Louis Charton11/2005
40912^297328-86968810589505Lelio R Paula07/2016
40932^297325-45904389504Enzo Doria05/2015
40942^297310-11239189500Enzo Doria06/2014
40952^297296-11215789496Enzo Doria06/2014
409657^50966-289490Lelio R Paula08/2013
4097(266*10^89482+1)/389484Robert Price02/2016
4098(14*10^89480-101)/389481Robert Price04/2017
40992^297122+9989443Lelio R Paula10/2012
4100(3^187435-5)/128689427Lelio R Paula01/2013
4101(25*10^89413+161)/389414Robert Price01/2017
41022^296990+187069989403Enzo Doria05/2016
41032^296972-101789398Lelio R Paula11/2013
4104(7*10^89383+167)/389384Robert Kinser10/2017
4105(85*10^89375-31)/989376Robert Price11/2015
41069*2^296870+789368Lelio R Paula08/2014
4107100^44683-99^4468389366Robert Price07/2013
41082^296810+7651989349Enzo Doria05/2016
41098^98928+7^(98928+1)89341Robert Price06/2016
4110(3^187247+4)/102789337Lelio R Paula01/2013
4111(3^187235-2)/204589331Lelio R Paula01/2013
41132^296736-43214989327Paul Bourdelais05/2013
41122^296737-11251989327Enzo Doria06/2014
41142^296718-364589322Lelio R Paula11/2013
41152^296681-1622189310Enzo Doria04/2013
41162^296669-1651389307Enzo Doria04/2013
41172^296619-1635789292Enzo Doria04/2013
41182^296614-11005189290Enzo Doria04/2014
4119(3^187138+8)/8314789283Lelio R Paula01/2013
4120(2*10^89279+457)/989279Robert Price01/2017
412115^75907-2889274Lelio R Paula11/2015
41222^296547-3789270Yves Minet01/2012
41232^296485+19189251Lelio R Paula10/2012
41242^296467-7589246Lelio R Paula10/2012
41252^296416-10953589231Enzo Doria04/2014
4126(23*2^296406+1)/389228Lelio R Paula01/2013
412766^49037-6589225Norbert Schneider11/2014
41282^296377-1624589219Enzo Doria04/2013
41292^296372-6487589217Lelio R Paula11/2013
41305*6^114648-789215Lelio R Paula10/2014
41313*10^89206+1389207Robert Price08/2017
41327*3^186960-489204Lelio R Paula08/2014
41332^296290-11213389193Enzo Doria06/2014
41346^114620-1700389192Enzo Doria02/2013
4135(4*10^89189+41)/989189Robert Price11/2014
41362^296261-16118189184Enzo Doria04/2013
4137(19*2^296269-1)/53062389182Lelio R Paula02/2014
41383^186903-1089176Robert Price09/2013
41417*10^89169-389170Dmitry Domanov11/2010
4139(2^296221-1017)/3589170Lelio R Paula01/2013
4140(43*10^89169+47)/989170Robert Price12/2017
4142(10^89160+29)/389160Serge Batalov12/2014
4143(28*10^89141-97)/389142Robert Price07/2016
41442^296116-73463989140Paul Bourdelais04/2013
41456^114544-13389133Lelio R Paula12/2015
41462^296076-11329789128Enzo Doria07/2014
4147(11*2^296060-1)/21589122Lelio R Paula02/2014
41485*10^89118+8189119Robert Price08/2017
41492^296037-141189117Yves Minet01/2013
41502^296020-260480989111Enzo Doria05/2015
41512^296016+8189110Henri Lifchitz02/2007
41522^296010-1189108Lelio R Paula10/2012
41532^295998-11191189105Enzo Doria05/2014
4154(2^296014+47)/9399114989102Lelio R Paula01/2013
41552^295939-1662189087Enzo Doria04/2013
41562^295934-10969189086Enzo Doria04/2014
4157(185*10^89063+7)/389065Robert Price02/2017
41582^295831+14389055Lelio R Paula10/2012
415931^59713-3089054Theodore Burton02/2007
4160(7*2^295834-1)/2766389052Lelio R Paula02/2014
4161123^42608+289047Lelio R Paula05/2013
41626^114433-114433^689047Norbert Schneider04/2017
41632^295800-45965989045Enzo Doria05/2015
4164(52*10^89037-1)/389039Robert Price02/2017
4165(6^114398-11)/589019Paul Bourdelais11/2011
416611^85470-585089008Enzo Doria02/2013
4167(27*2^295634+1)/468788993Lelio R Paula01/2013
4168(p(18424)#-4)/288985Robert Price09/2017
41692^295564-18988974Lelio R Paula10/2012
41702^295557+7309788972Enzo Doria04/2016
417111^85433-576088970Enzo Doria01/2013
41726*10^88938-9188939Robert Price11/2017
417315^75619-8888935Lelio R Paula11/2015
41742^295385-8588920Lelio R Paula10/2012
41752^295385-1633388920Enzo Doria04/2013
41762^295309+5988897Lelio R Paula10/2012
41772^295288-10979988891Enzo Doria04/2014
41782^295245+6588878Lelio R Paula10/2012
4179Padovan(727734)88874Eric W. Weisstein04/2011
418018^70793-1788865Lelio R Paula11/2015
41816^114196-1757388862Enzo Doria02/2013
4182302^35829+35829^30288857Norbert Schneider12/2014
41833^186223+1688851Robert Price10/2013
41843*2^295139+788847Lelio R Paula08/2014
41853^186212-11300888846Enzo Doria07/2014
418687^45803-8688836Norbert Schneider11/2015
41872^295094-11027388833Enzo Doria05/2014
41882^295080+186915188828Enzo Doria05/2016
41892^295027-11340788812Enzo Doria07/2014
4190(2*10^88808-71)/388808Robert Price01/2017
419113^79722-8088806Lelio R Paula11/2015
41923^186103+10488794Lelio R Paula12/2015
4193(3*2^294971+1)/2556588792Lelio R Paula01/2013
41942^294937-11500388785Enzo Doria06/2015
41952^294868-10970988765Enzo Doria04/2014
41962^294864-298588763Yves Minet09/2014
4197(17*10^88761-41)/388762Robert Price09/2017
41982^294754+1501588730Lelio R Paula10/2013
4199(3^185951-7)/2088720Lelio R Paula01/2013
4200(2^294661+5)/44369338388694Lelio R Paula01/2013
4201(10^88680+11)/388680Robert Price11/2014
42022*7^104928-988675Lelio R Paula10/2014
420311^85150+1288675Lelio R Paula11/2015
42048*6^113951+588673Lelio R Paula10/2014
42056^113940-1856388663Enzo Doria03/2013
420638^56123-56123^3888663Norbert Schneider02/2017
42072^294492-6588651Lelio R Paula10/2012
420820^68120-5388627Lelio R Paula01/2016
42092^294391-11325788621Enzo Doria07/2014
42105^126784-1547688619Enzo Doria02/2013
42112^294327+988602Lelio R Paula10/2012
42122^294320+1891588600Lelio R Paula10/2013
4213(98*10^88595-89)/9988595Ray Chandler07/2011
4214(17*2^294262-1)/1388582Lelio R Paula02/2014
4215(2*10^88545+7)/988545Erik Branger03/2011
42162^294137-13388545Lelio R Paula10/2012
4217(2^294092-1017)/117188528Lelio R Paula01/2013
42184^147036+147036^4+188525Robert Price04/2014
4219(14^77213-5^77213)/988496Robert Price04/2013
42202^293965+279337788493Enzo Doria03/2016
422111^84971-15088489Enzo Doria08/2012
4222(2^293956-1017)/3985137669667788476Lelio R Paula01/2013
422311^84958-219088475Enzo Doria12/2012
42242^293880-11134788467Enzo Doria05/2014
4225(106*10^88459-1)/388461Serge Batalov12/2014
422610^88457+27873388458Patrick De Geest07/2017
422710^88457-40188457Robert Price06/2017
422811^84908-168088423Enzo Doria12/2012
42292^293679-11207588407Enzo Doria06/2014
42306^113608-6588405Lelio R Paula12/2015
42312^293624+8287588390Lelio R Paula10/2013
42322^293612-11233788387Enzo Doria06/2014
4233758^30693+30693^75888386Norbert Schneider05/2017
4234gcd(V(1062695),5*F(212539)*(F(212539)-1)+1)88383Serge Batalov04/2015
42355*10^88377+7788378Robert Price06/2016
4236(5*2^293526+1)/30388359Lelio R Paula01/2013
42372^293461-278584388341Enzo Doria03/2016
42382^293416-103788328Yves Minet11/2012
4239(2^293384-7)/388317Lelio R Paula01/2013
4240(3^185092-5)/488311Lelio R Paula01/2013
4241(5*10^88303-173)/388304Robert Price11/2017
424214^77039-5788297Lelio R Paula11/2015
42433*10^88293-5988294Robert Price10/2017
42445^126303+4288283Lelio R Paula10/2015
424519^69025-1888266Theodore Burton01/2006
42465*10^88261-388262Dmitry Domanov11/2010
42478^97731-7^(97731-1)88260Robert Price04/2016
42485*10^88254+5988255Robert Price09/2016
42494*3^184968-788253Lelio R Paula08/2014
42507^104426+8888251Lelio R Paula10/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 09 2017 09:21 (Time in France)

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