PRP Records

Probable Primes Top 10000

(193407 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 ?
37512^308809+3796792961Phil Moore03/2008
3752(3^194825+5)/1165692952Lelio R Paula04/2013
3753(2^308679+5)/157392919Lelio R Paula06/2013
37542^308650+51392913Lelio R Paula02/2016
37555*7^109936+692908Lelio R Paula10/2014
37562*10^92897+8992898Robert Price07/2016
375712^86073-2992889Lelio R Paula06/2016
37582^308566-11792888Lelio R Paula11/2012
3759(17*10^92869-11)/392870Robert Price07/2015
37602^308459+7543192856Enzo Doria04/2016
37612^308426-186637792846Enzo Doria03/2016
3762(96^46831-1)/9592830Paul Bourdelais09/2017
37632^308349-11211192823Enzo Doria06/2014
37649*10^92821+1992822Robert Price05/2016
37652^308337-7592819Lelio R Paula11/2012
37664*3^194508+792805Lelio R Paula08/2014
376722*25^66379-11392796Curtis Bright05/2015
376811^89101-108092790Enzo Doria12/2012
37692^308236-186785992789Enzo Doria04/2016
377012^85963+2592770Lelio R Paula06/2016
37717^109750-6692750Lelio R Paula04/2016
37729*10^92742+1192743Robert Kinser01/2017
3773(21*2^308046-1)/885792729Lelio R Paula02/2014
37742^307997-11065592717Enzo Doria05/2014
3775L(443609)92709Renaud Lifchitz11/2003
377610^92691+992692Robert Price03/2011
377710^92691-25229192691Patrick De Geest08/2013
37782^307879-252192681Yves Minet07/2014
3779(2^307780-7)/1995966992644Lelio R Paula06/2013
378014^80831+4792643Lelio R Paula06/2016
378115^78744+9292611Lelio R Paula07/2016
378265^51083-6492610Norbert Schneider11/2014
37836^118996-1694392597Enzo Doria02/2013
3784(16*10^92591+41)/392592Robert Price10/2017
3785(3^194014-7)/292568Lelio R Paula04/2013
3786(63^51439+1)/6492555Paul Bourdelais08/2017
3787(26*10^92546-77)/392547Robert Price02/2017
37883^193954+34092540Lelio R Paula04/2016
37892^307407-307407^292539Henri Lifchitz05/2005
3790(17*10^92513-11)/392514Robert Price07/2015
37912^307318-421192512Yves Minet06/2011
37922^307280+19392501Lelio R Paula11/2012
379320^71075-3392471Lelio R Paula05/2016
37942^307126-7879592455Lelio R Paula02/2016
37952^307125-4978992454Henri Lifchitz08/2005
37962^307099+2392447Lelio R Paula11/2012
37977*10^92414-6992415Robert Price01/2017
3798(9787*2^306975-1)/212915592407Lelio R Paula04/2015
37992^306915+187337392391Enzo Doria06/2016
38002^306908+1291592389Lelio R Paula02/2016
380119^72244-8092383Lelio R Paula06/2016
38032^306849+7592371Lelio R Paula11/2012
3802(397*10^92369+53)/992371Robert Price11/2017
38042^306813-86968810592360Lelio R Paula08/2016
38052^306672-10905992318Enzo Doria04/2014
38066^118604-1706392292Enzo Doria02/2013
3807(31*2^306487-1)/229192260Lelio R Paula02/2014
38082^306467-183561192256Enzo Doria04/2015
38092^306433+7642792246Enzo Doria05/2016
38102^306430-11331392245Enzo Doria07/2014
3811(23*10^92244-59)/992245Robert Price03/2017
3812(47*2^306398+1)/138480392231Lelio R Paula04/2015
3813(25*10^92186+59)/392187Robert Price05/2016
38142^306213-28618392180Enzo Doria06/2015
381510^92178+6192179Robert Price04/2011
381610^92178-17550992178Patrick De Geest07/2013
38172^306200+118592176Lelio R Paula02/2016
38182^306153+1192162Lelio R Paula11/2012
3819(2^306141-7)/592157Lelio R Paula06/2013
3820(26*10^92152-23)/392153Robert Price08/2016
3821(2*10^92152+67)/392152Robert Price04/2017
38224*10^92099+3*7^9209992100Mike Oakes12/2010
3823(2^305867-2^152934+1)/59207511/2006
38242^305851-10949592071Enzo Doria04/2014
382512^85300+3592055Lelio R Paula06/2016
38263^192911+9292042Lelio R Paula04/2016
38272^305723-27627192032Enzo Doria07/2015
38282^305676+9392018Donovan Johnson06/2008
38293^192819+491999Lelio R Paula04/2013
3830(38*10^91997-83)/9991997Ray Chandler07/2011
38312^305539+7291191977Enzo Doria04/2016
3832(2^305427-5)/129799821391934Lelio R Paula06/2013
383385^47642+8491922Norbert Schneider10/2015
383410^91920+18765191921Patrick De Geest07/2013
383510^91920-3991920Robert Price05/2011
3836(22*10^91903+41)/991904Robert Price02/2015
38382^305275-2791897Lelio R Paula11/2012
38373^192607-772691897Enzo Doria05/2014
3839(7*10^91856-61)/991856Erik Branger12/2009
3840(89*10^91839-53)/991840Robert Price11/2015
38418*5^131351+791812Lelio R Paula10/2014
38423^192426-6891811Lelio R Paula04/2016
38432^304973+11791807Lelio R Paula11/2012
38442^304939-186372791796Enzo Doria03/2016
38452^304902+841591785Lelio R Paula02/2016
384618^73119+6191785Lelio R Paula06/2016
3847(78557*2^304740+1)/15991739Lelio R Paula06/2014
38482^304747+7135591738Lelio R Paula02/2016
38498*3^192251+591728Lelio R Paula08/2014
38502^304674-8791717Lelio R Paula11/2012
3851(28*10^91715+701)/991716Robert Price11/2017
3852(2^304698+9)/136280995391715Lelio R Paula06/2013
3853(5*10^91707-119)/391708Robert Price04/2016
38542^304633-11277191704Enzo Doria06/2014
38559*10^91693+2391694Robert Price11/2017
38562^304578-1671391688Enzo Doria05/2013
38576^117824-1871391685Enzo Doria03/2013
3858(17^74509-1)/1691679Paul Bourdelais03/2010
3859(2^304551-7)/891223191673Lelio R Paula06/2013
3860(2^304532-3)/301391670Lelio R Paula06/2013
38612^304507-1664591666Enzo Doria04/2013
3862(29*2^304489+1)/3191661Lelio R Paula09/2013
38632^304471-183612791655Enzo Doria04/2015
38642^304433+3276991644Lelio R Paula02/2016
38652^304410-1662591637Enzo Doria04/2013
3866183^40500-291630Lelio R Paula10/2017
3867(203*10^91613+1)/391615Robert Price09/2017
38684*5^131052+791603Lelio R Paula10/2014
38692^304278-400191597Yves Minet04/2017
38702^304272-186637791595Enzo Doria03/2016
38712^304268+1968391594Lelio R Paula02/2016
38722^304162-16191562Lelio R Paula11/2012
38735*7^108331+691552Lelio R Paula10/2014
38742^304082-278782191538Enzo Doria03/2016
38752^304015+6413391518David Broadhurst06/2002
3876(7*2^303963+1)/391503Lelio R Paula09/2013
3877(2^303945-9)/361791494Lelio R Paula06/2013
38782^303930+188052791493Enzo Doria10/2016
38793^191684-6891457Lelio R Paula04/2016
3880(21*2^303813-1)/16991456Lelio R Paula02/2014
388111^87797-12091432Enzo Doria07/2012
38822^303698-184723191423Enzo Doria07/2015
3883(38^28933-1)^2-291416Norbert Schneider06/2016
38842^303554+7729991379Enzo Doria05/2016
38852^303542+1270591376Lelio R Paula02/2016
388631^61269-291375Lelio R Paula09/2013
38872^303516-6487591368Lelio R Paula02/2016
3888(24737*2^303428+1)/391345Lelio R Paula06/2014
3889(21181*2^303357+1)/3236191320Lelio R Paula06/2014
38902^303344-278696991316Enzo Doria03/2016
38916^117346+6591313Lelio R Paula05/2016
38922^303321+85591309Lelio R Paula02/2016
389312^84606+4791306Lelio R Paula06/2016
38942^303288+187431191299Enzo Doria06/2016
3895197^39788-291293Lelio R Paula10/2017
389611^87663-171091292Enzo Doria12/2012
38972^303224+253391280Henri Lifchitz05/2005
38986^117302+14391279Lelio R Paula05/2016
38993^191306-11288091277Enzo Doria07/2014
39002^303207+1291591275Lelio R Paula02/2016
39012^303191-11125991270Enzo Doria05/2014
390210^91230+9^(91230+1)91231Robert Price08/2016
390310^91230+792191231Patrick De Geest11/2016
390410^91230-91114191230Patrick De Geest11/2016
39056^117232-1742391225Enzo Doria02/2013
39067*10^91215+391216Erik Branger11/2009
390797*10^91205-391207Robert Price01/2017
39082^302979-16118191206Enzo Doria04/2013
39092^302949+8191197Henri Lifchitz02/2007
39104*6^117192-591194Lelio R Paula10/2014
39112^302918+9991188Lelio R Paula11/2012
39122^302797+186958791151Enzo Doria05/2016
3913265^37614+37614^26591148Norbert Schneider01/2015
39147^107852+8291146Lelio R Paula04/2016
3915(38*10^91144-11)/991145Robert Price05/2015
3916(55*10^91142+377)/991143Robert Price10/2017
3917249^38030+38030^24991128Norbert Schneider01/2015
39186^117094-21104991117Mike Oakes05/2011
39192^302602-186718191093Enzo Doria03/2016
3920(1017*2^302592-1)/5391091Lelio R Paula04/2015
392115^77445-1691083Lelio R Paula07/2016
39222^302505+8191064Henri Lifchitz02/2007
39232^302496-11234991061Enzo Doria06/2014
392417^73999-7291052Lelio R Paula07/2016
3925(16*10^91032+41)/391033Robert Price10/2017
39262^302332+57729457591012Lelio R Paula08/2016
39272^302274+7420990994Enzo Doria04/2016
3928(311^36497-1)/31090976Eric Chen09/2017
3929(3^190668+2)/8990970Lelio R Paula04/2013
39302^302188+9019590968Lelio R Paula02/2016
3931(53*10^90965-71)/990966Robert Price09/2015
39322^302113+7410590946Enzo Doria04/2016
39332^302102-655590942Lelio R Paula02/2016
3934156*(10^(4*22731)-1)/101-190925Robert Price05/2014
39353^190568+3890925Lelio R Paula04/2016
39362^302009-1644990914Enzo Doria04/2013
3937(17*2^301951-1)/16590896Lelio R Paula02/2014
39383^190497+7490891Lelio R Paula04/2016
3939(24737*2^301896+1)/39990882Lelio R Paula06/2014
394018^72397+8990878Lelio R Paula06/2016
39416^116769-4790864Lelio R Paula05/2016
39422^301712-46590825Lelio R Paula02/2016
39432^301693-6990819Lelio R Paula11/2012
39442^301683-301683^290816Henri Lifchitz05/2005
394511^87187-171090796Enzo Doria12/2012
39465*10^90793+2190794Robert Price01/2017
3947(22*10^90792-13)/990793Robert Price03/2015
39482^301591-161590788Lelio R Paula02/2016
3949(52^52901+1)/5390777Paul Bourdelais08/2017
39502^301546-10903790775Enzo Doria04/2014
395114^79195-390768Lelio R Paula06/2016
39522^301517-186169390766Enzo Doria11/2015
39532^301460-17390749Lelio R Paula11/2012
3954(85*10^90745-103)/990746Robert Price10/2017
39552^301312-8990704Lelio R Paula11/2012
39562^301285-12990696Lelio R Paula11/2012
39572^301282-10999190695Enzo Doria04/2014
39582^301228-185426990679Enzo Doria09/2015
3959(151*10^90669-1)/390671Robert Price04/2017
3960(32*10^90669+13)/990670Robert Price04/2015
39613*5^129698+890656Lelio R Paula10/2014
3962F(433781)90655Henri Lifchitz09/2003
396319^70891+8290653Lelio R Paula06/2016
3964(29*2^301124-1)/1390648Lelio R Paula02/2014
39657*3^189953-890632Lelio R Paula08/2014
396611^87022-180090625Enzo Doria12/2012
3967(2^301042+47)/1203696990616Lelio R Paula06/2013
39682^301004-278693990612Enzo Doria03/2016
39692^300980-2790605Lelio R Paula11/2012
39702*10^90597-790598Dmitry Domanov11/2010
3971197^39485+290597Lelio R Paula06/2013
39727^107198+4890593Lelio R Paula04/2016
3973(86*10^90588+121)/990589Robert Price03/2017
39742^300923+5390587Lelio R Paula11/2012
39752^300874+790573Lelio R Paula10/2012
39765^129568-5690565Lelio R Paula04/2016
39772^300847-11283190564Enzo Doria06/2014
39782^300718+25525590526Lelio R Paula02/2016
39792^300637+9590501Lelio R Paula11/2012
39807^107087-2490500Lelio R Paula04/2016
3981(10^90499+3^90499)/1390498Robert Price01/2013
398213^81241+9090498Lelio R Paula06/2016
39836^116273-8590478Lelio R Paula05/2016
39846^116256-1757390465Enzo Doria02/2013
39852^300502+5461590461Lelio R Paula02/2016
3986(13*2^300487+1)/4590456Lelio R Paula09/2013
3987(3^189545-8)/590436Lelio R Paula01/2013
3988(7*2^300406-1)/390432Lelio R Paula02/2014
39894*5^129332+390400Lelio R Paula10/2014
39902^300249-1624590384Enzo Doria04/2013
3991(7*10^90371-313)/990371Robert Price11/2016
39922*6^116118+790358Lelio R Paula10/2014
3993(24737*2^300101+1)/2590343Lelio R Paula06/2014
39944*10^90334-2190335Robert Price04/2016
39952^300019-11033590315Enzo Doria05/2014
39962^299949-100590294Lelio R Paula11/2013
39972^299868-10961390270Enzo Doria04/2014
39985*2^299799-390250Lelio R Paula08/2014
399913^81008-290239Lelio R Paula09/2013
400064^49957-63^4995790232Robert Price07/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 12 2017 10:35 (Time in France)

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