PRP Records

Probable Primes Top 10000

(252538 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 ?
42513*10^93179-9793180Robert Price08/2017
42525*7^110252-493175Lelio R Paula11/2014
42532^309380-2793133Lelio R Paula11/2012
425423*10^93116-793118Robert Price03/2016
4255(29*10^93082+1)/393083Robert Price11/2015
4256(58*10^93062-13)/993063Robert Price09/2015
42572^309131+186938393058Enzo Doria05/2016
42582^309066-9393039Lelio R Paula11/2012
42592^309063-11326993038Enzo Doria07/2014
42603^194965+1693022Robert Price10/2013
42612^308979+186914393012Enzo Doria05/2016
42625^133064+5493008Lelio R Paula04/2016
4263(2^308905-509203)/11992988Lelio R Paula06/2013
4264(94*10^92981-49)/9992981Ray Chandler07/2011
4265(2*10^92976-17)/392976Robert Price08/2014
42662^308809+3796792961Phil Moore03/2008
4267(3^194825+5)/1165692952Lelio R Paula04/2013
4268(2^308679+5)/157392919Lelio R Paula06/2013
42692^308650+51392913Lelio R Paula02/2016
42705*7^109936+692908Lelio R Paula10/2014
42712*10^92897+8992898Robert Price07/2016
427212^86073-2992889Lelio R Paula06/2016
42732^308566-11792888Lelio R Paula11/2012
4274(17*10^92869-11)/392870Robert Price07/2015
42752^308459+7543192856Enzo Doria04/2016
42762^308426-186637792846Enzo Doria03/2016
4277(96^46831-1)/9592830Paul Bourdelais09/2017
42782^308349-11211192823Enzo Doria06/2014
42799*10^92821+1992822Robert Price05/2016
42802^308337-7592819Lelio R Paula11/2012
42814*3^194508+792805Lelio R Paula08/2014
428222*25^66379-11392796Curtis Bright05/2015
428311^89101-108092790Enzo Doria12/2012
42842^308236-186785992789Enzo Doria04/2016
428512^85963+2592770Lelio R Paula06/2016
42867^109750-6692750Lelio R Paula04/2016
42879*10^92742+1192743Robert Kinser01/2017
4288(21*2^308046-1)/885792729Lelio R Paula02/2014
42892^307997-11065592717Enzo Doria05/2014
4290L(443609)92709Renaud Lifchitz11/2003
429110^92691+992692Robert Price03/2011
429210^92691-25229192691Patrick De Geest08/2013
42932^307879-252192681Yves Minet07/2014
4294(2^307780-7)/1995966992644Lelio R Paula06/2013
429514^80831+4792643Lelio R Paula06/2016
429615^78744+9292611Lelio R Paula07/2016
429765^51083-6492610Norbert Schneider11/2014
42986^118996-1694392597Enzo Doria02/2013
4299(16*10^92591+41)/392592Robert Price10/2017
4300(3^194014-7)/292568Lelio R Paula04/2013
4301(63^51439+1)/6492555Paul Bourdelais08/2017
4302(26*10^92546-77)/392547Robert Price02/2017
43033^193954+34092540Lelio R Paula04/2016
43042^307407-307407^292539Henri Lifchitz05/2005
4305(17*10^92513-11)/392514Robert Price07/2015
43062^307318-421192512Yves Minet06/2011
43072^307280+19392501Lelio R Paula11/2012
430820^71075-3392471Lelio R Paula05/2016
43092^307126-7879592455Lelio R Paula02/2016
43102^307125-4978992454Henri Lifchitz08/2005
43112^307099+2392447Lelio R Paula11/2012
4312129^43798+12892440Norbert Schneider01/2019
43137*10^92414-6992415Robert Price01/2017
4314(9787*2^306975-1)/212915592407Lelio R Paula04/2015
43152^306915+187337392391Enzo Doria06/2016
43162^306908+1291592389Lelio R Paula02/2016
431719^72244-8092383Lelio R Paula06/2016
43192^306849+7592371Lelio R Paula11/2012
4318(397*10^92369+53)/992371Robert Price11/2017
43202^306813-86968810592360Lelio R Paula08/2016
43212^306672-10905992318Enzo Doria04/2014
43226^118604-1706392292Enzo Doria02/2013
4323(31*2^306487-1)/229192260Lelio R Paula02/2014
43242^306467-183561192256Enzo Doria04/2015
43252^306433+7642792246Enzo Doria05/2016
43272^306430-11331392245Enzo Doria07/2014
4326(23*10^92244-59)/992245Robert Price03/2017
4328(47*2^306398+1)/138480392231Lelio R Paula04/2015
4329(25*10^92186+59)/392187Robert Price05/2016
43302^306213-28618392180Enzo Doria06/2015
433110^92178+6192179Robert Price04/2011
433210^92178-17550992178Patrick De Geest07/2013
43332^306200+118592176Lelio R Paula02/2016
43342^306153+1192162Lelio R Paula11/2012
4335(2^306141-7)/592157Lelio R Paula06/2013
4336(26*10^92152-23)/392153Robert Price08/2016
4337(2*10^92152+67)/392152Robert Price04/2017
43384*10^92099+3*7^9209992100Mike Oakes12/2010
4339115^44684+11492081Norbert Schneider07/2018
4340(2^305867-2^152934+1)/59207511/2006
43412^305851-10949592071Enzo Doria04/2014
434212^85300+3592055Lelio R Paula06/2016
43433^192911+9292042Lelio R Paula04/2016
43442^305723-27627192032Enzo Doria07/2015
43452^305676+9392018Donovan Johnson06/2008
43463^192819+491999Lelio R Paula04/2013
4347(38*10^91997-83)/9991997Ray Chandler07/2011
43482^305539+7291191977Enzo Doria04/2016
4349(2^305427-5)/129799821391934Lelio R Paula06/2013
435085^47642+8491922Norbert Schneider10/2015
435110^91920+18765191921Patrick De Geest07/2013
435210^91920-3991920Robert Price05/2011
4353(22*10^91903+41)/991904Robert Price02/2015
43552^305275-2791897Lelio R Paula11/2012
43543^192607-772691897Enzo Doria05/2014
4356(7*10^91856-61)/991856Erik Branger12/2009
4357(89*10^91839-53)/991840Robert Price11/2015
43588*5^131351+791812Lelio R Paula10/2014
43593^192426-6891811Lelio R Paula04/2016
43602^304973+11791807Lelio R Paula11/2012
43612^304939-186372791796Enzo Doria03/2016
43622^304902+841591785Lelio R Paula02/2016
436318^73119+6191785Lelio R Paula06/2016
4364(78557*2^304740+1)/15991739Lelio R Paula06/2014
43652^304747+7135591738Lelio R Paula02/2016
43668*3^192251+591728Lelio R Paula08/2014
43672^304674-8791717Lelio R Paula11/2012
4368(28*10^91715+701)/991716Robert Price11/2017
4369(2^304698+9)/136280995391715Lelio R Paula06/2013
4370(5*10^91707-119)/391708Robert Price04/2016
43712^304633-11277191704Enzo Doria06/2014
43729*10^91693+2391694Robert Price11/2017
43732^304578-1671391688Enzo Doria05/2013
43746^117824-1871391685Enzo Doria03/2013
4375(17^74509-1)/1691679Paul Bourdelais03/2010
4376(2^304551-7)/891223191673Lelio R Paula06/2013
4377(2^304532-3)/301391670Lelio R Paula06/2013
43782^304507-1664591666Enzo Doria04/2013
4379(29*2^304489+1)/3191661Lelio R Paula09/2013
43802^304471-183612791655Enzo Doria04/2015
43812^304433+3276991644Lelio R Paula02/2016
43822^304410-1662591637Enzo Doria04/2013
4383183^40500-291630Lelio R Paula10/2017
4384(203*10^91613+1)/391615Robert Price09/2017
43854*5^131052+791603Lelio R Paula10/2014
43862^304278-400191597Yves Minet04/2017
43872^304272-186637791595Enzo Doria03/2016
43882^304268+1968391594Lelio R Paula02/2016
43892^304162-16191562Lelio R Paula11/2012
43905*7^108331+691552Lelio R Paula10/2014
43912^304082-278782191538Enzo Doria03/2016
43922^304015+6413391518David Broadhurst06/2002
4393(7*2^303963+1)/391503Lelio R Paula09/2013
4394(2^303945-9)/361791494Lelio R Paula06/2013
43952^303930+188052791493Enzo Doria10/2016
43963^191684-6891457Lelio R Paula04/2016
4397(21*2^303813-1)/16991456Lelio R Paula02/2014
439811^87797-12091432Enzo Doria07/2012
43992^303698-184723191423Enzo Doria07/2015
4400(38^28933-1)^2-291416Norbert Schneider06/2016
44012^303554+7729991379Enzo Doria05/2016
44022^303542+1270591376Lelio R Paula02/2016
440331^61269-291375Lelio R Paula09/2013
44042^303516-6487591368Lelio R Paula02/2016
4405(24737*2^303428+1)/391345Lelio R Paula06/2014
4406(21181*2^303357+1)/3236191320Lelio R Paula06/2014
44072^303344-278696991316Enzo Doria03/2016
44086^117346+6591313Lelio R Paula05/2016
44092^303321+85591309Lelio R Paula02/2016
441012^84606+4791306Lelio R Paula06/2016
44112^303288+187431191299Enzo Doria06/2016
4412197^39788-291293Lelio R Paula10/2017
441311^87663-171091292Enzo Doria12/2012
44142^303224+253391280Henri Lifchitz05/2005
44156^117302+14391279Lelio R Paula05/2016
44163^191306-11288091277Enzo Doria07/2014
44172^303207+1291591275Lelio R Paula02/2016
44182^303191-11125991270Enzo Doria05/2014
441910^91230+9^(91230+1)91231Robert Price08/2016
442010^91230+792191231Patrick De Geest11/2016
442110^91230-91114191230Patrick De Geest11/2016
442210^91229-247191229Patrick De Geest01/2019
442310^91225+527191226Patrick De Geest01/2019
44246^117232-1742391225Enzo Doria02/2013
44257*10^91215+391216Erik Branger11/2009
442610^91215-453991215Patrick De Geest01/2019
442710^91210+242191211Patrick De Geest01/2019
442810^91210-173791210Patrick De Geest01/2019
442997*10^91205-391207Robert Price01/2017
44302^302979-16118191206Enzo Doria04/2013
44312^302949+8191197Henri Lifchitz02/2007
44334*6^117192-591194Lelio R Paula10/2014
443210^91194-866391194Patrick De Geest01/2019
44342^302918+9991188Lelio R Paula11/2012
443510^91186-776391186Patrick De Geest01/2019
443610^91181-136791181Patrick De Geest01/2019
443710^91178-471991178Patrick De Geest01/2019
443810^91165+304391166Patrick De Geest01/2019
443910^91156+386191157Patrick De Geest01/2019
44402^302797+186958791151Enzo Doria05/2016
4441265^37614+37614^26591148Norbert Schneider01/2015
44427^107852+8291146Lelio R Paula04/2016
4443(38*10^91144-11)/991145Robert Price05/2015
4444(55*10^91142+377)/991143Robert Price10/2017
444510^91128+996191129Patrick De Geest01/2019
4446249^38030+38030^24991128Norbert Schneider01/2015
44476^117094-21104991117Mike Oakes05/2011
44482^302602-186718191093Enzo Doria03/2016
444910^91092-910791092Patrick De Geest01/2019
4450(1017*2^302592-1)/5391091Lelio R Paula04/2015
445115^77445-1691083Lelio R Paula07/2016
44522^302505+8191064Henri Lifchitz02/2007
44532^302496-11234991061Enzo Doria06/2014
445417^73999-7291052Lelio R Paula07/2016
445510^91047+933191048Patrick De Geest01/2019
445610^91044+207791045Patrick De Geest01/2019
445710^91041+934991042Patrick De Geest01/2019
445810^91041-782391041Patrick De Geest01/2019
445910^91040+407791041Patrick De Geest01/2019
446010^91037+276991038Patrick De Geest01/2019
4461(16*10^91032+41)/391033Robert Price10/2017
446210^91023-647191023Patrick De Geest01/2019
446310^91018+787391019Patrick De Geest01/2019
446410^91016-797391016Patrick De Geest01/2019
44652^302332+57729457591012Lelio R Paula08/2016
446610^91004+907391005Patrick De Geest01/2019
446710^91003-390391003Patrick De Geest01/2019
44682^302274+7420990994Enzo Doria04/2016
446910^90991-627990991Patrick De Geest01/2019
447010^90983+139390984Patrick De Geest01/2019
4471(311^36497-1)/31090976Eric Chen09/2017
4472(3^190668+2)/8990970Lelio R Paula04/2013
44732^302188+9019590968Lelio R Paula02/2016
4474(53*10^90965-71)/990966Robert Price09/2015
447510^90965-683390965Patrick De Geest01/2019
447610^90963-365990963Patrick De Geest01/2019
447710^90962+765790963Patrick De Geest01/2019
447810^90959+879190960Patrick De Geest01/2019
447910^90948+986790949Patrick De Geest01/2019
44802^302113+7410590946Enzo Doria04/2016
44812^302102-655590942Lelio R Paula02/2016
448210^90930-362390930Patrick De Geest01/2019
4483156*(10^(4*22731)-1)/101-190925Robert Price05/2014
44843^190568+3890925Lelio R Paula04/2016
448510^90917-669390917Patrick De Geest01/2019
44862^302009-1644990914Enzo Doria04/2013
448710^90908+318190909Patrick De Geest01/2019
448810^90904-516990904Patrick De Geest01/2019
448910^90902+261390903Patrick De Geest01/2019
4490(17*2^301951-1)/16590896Lelio R Paula02/2014
44913^190497+7490891Lelio R Paula04/2016
4492(24737*2^301896+1)/39990882Lelio R Paula06/2014
449310^90880+570790881Patrick De Geest01/2019
449418^72397+8990878Lelio R Paula06/2016
44956^116769-4790864Lelio R Paula05/2016
449610^90858-830190858Patrick De Geest01/2019
449710^90849-472190849Patrick De Geest01/2019
44982^301712-46590825Lelio R Paula02/2016
44992^301693-6990819Lelio R Paula11/2012
45002^301683-301683^290816Henri Lifchitz05/2005


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 14 2019 10:37 (Time in France)

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