PRP Records

Probable Primes Top 10000

(252675 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
4751L(430949)/861899/144038756153990045Serge Batalov07/2017
47522^299112+7395190042Enzo Doria04/2016
47538^99702+7^(99702-1)90040Robert Price02/2016
475410^90038-968790038Patrick De Geest09/2018
47555*10^90033+390034Dmitry Domanov11/2010
475610^90030-146190030Patrick De Geest09/2018
4757243^37738+37738^24390029Norbert Schneider01/2015
475810^90025-870390025Patrick De Geest09/2018
47592^299048-11329790023Enzo Doria07/2014
476010^90015+84990016Patrick De Geest09/2018
476110^90010+681190011Patrick De Geest09/2018
476210^90010-18359790010Patrick De Geest11/2018
476310^90009+5832190010Patrick De Geest11/2018
476410^90008+84790009Patrick De Geest09/2018
476510^90009-35601390009Patrick De Geest11/2018
47673^188648+9290008Lelio R Paula12/2015
476610^90008-70604990008Patrick De Geest11/2018
47685*2^298991+790006Lelio R Paula08/2014
4769(25*2^298997+1)/326790005Lelio R Paula01/2013
477010^90000+886990001Patrick De Geest12/2009
477210^89999+8293990000Dirk Augustin04/2007
477110^90000-14034390000Patrick De Geest12/2009
477310^89999-19489189999Patrick De Geest11/2009
477419^70365-7889980Lelio R Paula12/2015
4775NaturalLogarithmOf2(89973)89973Eric W. Weisstein10/2015
47762^298852-6487589964Lelio R Paula11/2013
477718^71659+3789952Lelio R Paula12/2015
4778(2908*29^61501-3)/789942Curtis Bright05/2015
477917^73067+2089906Lelio R Paula11/2015
47802^298637-9989899Lelio R Paula10/2012
47819^94188+3*8^94188-2*4^94188-3*2^9418889879Mike Oakes01/2011
47829*10^89858+1989859Robert Price05/2016
47832^298501+187006789858Enzo Doria05/2016
478411^86280-9889852Lelio R Paula11/2015
47852^298473-11005989850Enzo Doria04/2014
478619^70263-3289850Lelio R Paula12/2015
4787(299*10^89836-17)/389838Robert Price01/2017
47883^188286+1489836Robert Price09/2013
4789gcd(V(1091095),5*F(218219)*(F(218219)+1)+1)89822Serge Batalov04/2015
47902^298367+5890589818Lelio R Paula11/2013
47912^298319-10965789803Enzo Doria04/2014
47928*10^89800+8189801Robert Price05/2017
479318^71505-9189759Lelio R Paula12/2015
4794(7^106187+1)/889738Paul Bourdelais04/2008
47952^298079-10953189731Enzo Doria04/2014
4796117^43380+11689718Norbert Schneider08/2018
4797(22699*2^298016+1)/38589714Lelio R Paula06/2014
4798156*(10^(4*22427)-1)/101-189709Robert Price05/2014
47992^298003-6694589708Lelio R Paula11/2013
4800(23*10^89705-83)/389706Robert Price09/2017
480117^72900-5489700Lelio R Paula11/2015
48023*2^297956+589695Lelio R Paula08/2014
480320^68938-1189691Lelio R Paula01/2016
480489*10^89687-789689Robert Price03/2017
48052^297923+7778389684Enzo Doria05/2016
480611^86107-2457600089672Enzo Doria02/2013
48072^297878-11191189671Enzo Doria05/2014
48087^106084+4089652Lelio R Paula10/2015
4809(86*10^89640-311)/989641Robert Price10/2017
48103*10^89608-5989609Robert Price10/2017
48113^187780-1103889594Enzo Doria05/2014
4812(13*2^297560-1)/4915178789568Lelio R Paula02/2014
48135^128141-3689567Lelio R Paula10/2015
48144*7^105951+989540Lelio R Paula10/2014
4815(7*10^89539-439)/989539Robert Price09/2017
48162^297397+17725789526Enzo Doria05/2016
48172^297346-1624189511Enzo Doria04/2013
4818(5*10^89510+79)/389511Robert Price11/2017
48204^148663-3^14866389505Jean-Louis Charton11/2005
48192^297328-86968810589505Lelio R Paula07/2016
48212^297325-45904389504Enzo Doria05/2015
48222^297310-11239189500Enzo Doria06/2014
48232^297296-11215789496Enzo Doria06/2014
482457^50966-289490Lelio R Paula08/2013
4825(266*10^89482+1)/389484Robert Price02/2016
4826(14*10^89480-101)/389481Robert Price04/2017
48272^297122+9989443Lelio R Paula10/2012
4828(3^187435-5)/128689427Lelio R Paula01/2013
4829(25*10^89413+161)/389414Robert Price01/2017
48302^296990+187069989403Enzo Doria05/2016
48312^296972-101789398Lelio R Paula11/2013
4832(7*10^89383+167)/389384Robert Kinser10/2017
4833(85*10^89375-31)/989376Robert Price11/2015
48349*2^296870+789368Lelio R Paula08/2014
4835100^44683-99^4468389366Robert Price07/2013
48362^296810+7651989349Enzo Doria05/2016
48378^98928+7^(98928+1)89341Robert Price06/2016
4838(3^187247+4)/102789337Lelio R Paula01/2013
4839(3^187235-2)/204589331Lelio R Paula01/2013
48412^296736-43214989327Paul Bourdelais05/2013
48402^296737-11251989327Enzo Doria06/2014
48422^296718-364589322Lelio R Paula11/2013
48432^296681-1622189310Enzo Doria04/2013
48442^296669-1651389307Enzo Doria04/2013
48452^296619-1635789292Enzo Doria04/2013
48462^296614-11005189290Enzo Doria04/2014
4847(3^187138+8)/8314789283Lelio R Paula01/2013
4848(2*10^89279+457)/989279Robert Price01/2017
484915^75907-2889274Lelio R Paula11/2015
48502^296547-3789270Yves Minet01/2012
48512^296485+19189251Lelio R Paula10/2012
48522^296467-7589246Lelio R Paula10/2012
48532^296416-10953589231Enzo Doria04/2014
4854(23*2^296406+1)/389228Lelio R Paula01/2013
485566^49037-6589225Norbert Schneider11/2014
48562^296377-1624589219Enzo Doria04/2013
48572^296372-6487589217Lelio R Paula11/2013
48585*6^114648-789215Lelio R Paula10/2014
48593*10^89206+1389207Robert Price08/2017
48607*3^186960-489204Lelio R Paula08/2014
48612^296290-11213389193Enzo Doria06/2014
48626^114620-1700389192Enzo Doria02/2013
4863(4*10^89189+41)/989189Robert Price11/2014
48642^296261-16118189184Enzo Doria04/2013
4865(19*2^296269-1)/53062389182Lelio R Paula02/2014
48663^186903-1089176Robert Price09/2013
48687*10^89169-389170Dmitry Domanov11/2010
4869(2^296221-1017)/3589170Lelio R Paula01/2013
4867(43*10^89169+47)/989170Robert Price12/2017
4870(10^89160+29)/389160Serge Batalov12/2014
4871(28*10^89141-97)/389142Robert Price07/2016
48722^296116-73463989140Paul Bourdelais04/2013
48736^114544-13389133Lelio R Paula12/2015
48742^296076-11329789128Enzo Doria07/2014
4875(11*2^296060-1)/21589122Lelio R Paula02/2014
48765*10^89118+8189119Robert Price08/2017
48772^296037-141189117Yves Minet01/2013
48782^296020-260480989111Enzo Doria05/2015
48792^296016+8189110Henri Lifchitz02/2007
48802^296010-1189108Lelio R Paula10/2012
48812^295998-11191189105Enzo Doria05/2014
4882(2^296014+47)/9399114989102Lelio R Paula01/2013
48832^295939-1662189087Enzo Doria04/2013
48842^295934-10969189086Enzo Doria04/2014
4885(185*10^89063+7)/389065Robert Price02/2017
48862^295831+14389055Lelio R Paula10/2012
488731^59713-3089054Theodore Burton02/2007
4888(7*2^295834-1)/2766389052Lelio R Paula02/2014
4890123^42608+289047Lelio R Paula05/2013
48896^114433-114433^689047Norbert Schneider04/2017
48912^295800-45965989045Enzo Doria05/2015
4892(52*10^89037-1)/389039Robert Price02/2017
4893(6^114398-11)/589019Paul Bourdelais11/2011
489411^85470-585089008Enzo Doria02/2013
4895(27*2^295634+1)/468788993Lelio R Paula01/2013
4896(p(18424)#-4)/288985Robert Price09/2017
48972^295564-18988974Lelio R Paula10/2012
48982^295557+7309788972Enzo Doria04/2016
489911^85433-576088970Enzo Doria01/2013
49006*10^88938-9188939Robert Price11/2017
490115^75619-8888935Lelio R Paula11/2015
49022^295385-8588920Lelio R Paula10/2012
49032^295385-1633388920Enzo Doria04/2013
49042^295309+5988897Lelio R Paula10/2012
49052^295288-10979988891Enzo Doria04/2014
490610^88888+17037388889Stefano Morozzi07/2018
490710^88888+27139988889Stefano Morozzi07/2018
490810^88888+37539788889Stefano Morozzi07/2018
490910^88888+54882388889Stefano Morozzi07/2018
491010^88888+82086188889Stefano Morozzi07/2018
491110^88888+120634988889Stefano Morozzi07/2018
491210^88888+129204788889Stefano Morozzi07/2018
491310^88888+145602988889Stefano Morozzi07/2018
491410^88888-49028788888Patrick De Geest09/2018
49152^295245+6588878Lelio R Paula10/2012
4916Padovan(727734)88874Eric W. Weisstein04/2011
491718^70793-1788865Lelio R Paula11/2015
49186^114196-1757388862Enzo Doria02/2013
4919302^35829+35829^30288857Norbert Schneider12/2014
49203^186223+1688851Robert Price10/2013
49213*2^295139+788847Lelio R Paula08/2014
49223^186212-11300888846Enzo Doria07/2014
492387^45803-8688836Norbert Schneider11/2015
49242^295094-11027388833Enzo Doria05/2014
49252^295080+186915188828Enzo Doria05/2016
49262^295027-11340788812Enzo Doria07/2014
4927(2*10^88808-71)/388808Robert Price01/2017
492813^79722-8088806Lelio R Paula11/2015
49293^186103+10488794Lelio R Paula12/2015
4930(3*2^294971+1)/2556588792Lelio R Paula01/2013
49312^294937-11500388785Enzo Doria06/2015
49322^294868-10970988765Enzo Doria04/2014
49332^294864-298588763Yves Minet09/2014
4934(17*10^88761-41)/388762Robert Price09/2017
49352^294754+1501588730Lelio R Paula10/2013
4936(3^185951-7)/2088720Lelio R Paula01/2013
4937(2^294661+5)/44369338388694Lelio R Paula01/2013
4938(10^88680+11)/388680Robert Price11/2014
49392*7^104928-988675Lelio R Paula10/2014
494011^85150+1288675Lelio R Paula11/2015
49418*6^113951+588673Lelio R Paula10/2014
49436^113940-1856388663Enzo Doria03/2013
494238^56123-56123^3888663Norbert Schneider02/2017
49442^294492-6588651Lelio R Paula10/2012
494520^68120-5388627Lelio R Paula01/2016
4946122^42477-12188623Norbert Schneider10/2018
49472^294391-11325788621Enzo Doria07/2014
49485^126784-1547688619Enzo Doria02/2013
49492^294327+988602Lelio R Paula10/2012
49502^294320+1891588600Lelio R Paula10/2013
4951(98*10^88595-89)/9988595Ray Chandler07/2011
4952(17*2^294262-1)/1388582Lelio R Paula02/2014
4954(2*10^88545+7)/988545Erik Branger03/2011
49532^294137-13388545Lelio R Paula10/2012
4955(2^294092-1017)/117188528Lelio R Paula01/2013
49564^147036+147036^4+188525Robert Price04/2014
4957(14^77213-5^77213)/988496Robert Price04/2013
49582^293965+279337788493Enzo Doria03/2016
495911^84971-15088489Enzo Doria08/2012
496048^52626-4788478Norbert Schneider08/2018
4961(2^293956-1017)/3985137669667788476Lelio R Paula01/2013
496211^84958-219088475Enzo Doria12/2012
49632^293880-11134788467Enzo Doria05/2014
4964(106*10^88459-1)/388461Serge Batalov12/2014
496510^88457+27873388458Patrick De Geest07/2017
496610^88457-40188457Robert Price06/2017
496711^84908-168088423Enzo Doria12/2012
49682^293679-11207588407Enzo Doria06/2014
49696^113608-6588405Lelio R Paula12/2015
49702^293624+8287588390Lelio R Paula10/2013
49712^293612-11233788387Enzo Doria06/2014
4972758^30693+30693^75888386Norbert Schneider05/2017
4973gcd(V(1062695),5*F(212539)*(F(212539)-1)+1)88383Serge Batalov04/2015
49745*10^88377+7788378Robert Price06/2016
4975(5*2^293526+1)/30388359Lelio R Paula01/2013
49762^293461-278584388341Enzo Doria03/2016
49772^293416-103788328Yves Minet11/2012
4978(2^293384-7)/388317Lelio R Paula01/2013
4979(3^185092-5)/488311Lelio R Paula01/2013
4980(5*10^88303-173)/388304Robert Price11/2017
498114^77039-5788297Lelio R Paula11/2015
49823*10^88293-5988294Robert Price10/2017
49835^126303+4288283Lelio R Paula10/2015
498419^69025-1888266Theodore Burton01/2006
49855*10^88261-388262Dmitry Domanov11/2010
49868^97731-7^(97731-1)88260Robert Price04/2016
49875*10^88254+5988255Robert Price09/2016
49884*3^184968-788253Lelio R Paula08/2014
49897^104426+8888251Lelio R Paula10/2015
49902^293142+9988245Lelio R Paula10/2012
499111^84736-213088244Enzo Doria12/2012
4992(10^110315+1)/(10^22063+1)/582481268216764857846028164188225Makoto Kamada04/2019
49932^293068-8988223Lelio R Paula10/2012
49942^293014-10965588207Enzo Doria04/2014
49958*7^104371-388205Lelio R Paula10/2014
49962^292995-214588201Lelio R Paula10/2013
49975*10^88182+7788183Robert Price06/2016
49992^292929+4387788181Donovan Johnson04/2005
49986^113321+13188181Lelio R Paula12/2015
50002^292904-58394988173Paul Bourdelais04/2013


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 20 2019 09:21 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!