PRP Records

Probable Primes Top 10000

(252402 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 ?
425110^92178-17550992178Patrick De Geest07/2013
42522^306200+118592176Lelio R Paula02/2016
42532^306153+1192162Lelio R Paula11/2012
4254(2^306141-7)/592157Lelio R Paula06/2013
4255(26*10^92152-23)/392153Robert Price08/2016
4256(2*10^92152+67)/392152Robert Price04/2017
42574*10^92099+3*7^9209992100Mike Oakes12/2010
4258115^44684+11492081Norbert Schneider07/2018
4259(2^305867-2^152934+1)/59207511/2006
42602^305851-10949592071Enzo Doria04/2014
426112^85300+3592055Lelio R Paula06/2016
42623^192911+9292042Lelio R Paula04/2016
42632^305723-27627192032Enzo Doria07/2015
42642^305676+9392018Donovan Johnson06/2008
42653^192819+491999Lelio R Paula04/2013
4266(38*10^91997-83)/9991997Ray Chandler07/2011
42672^305539+7291191977Enzo Doria04/2016
4268(2^305427-5)/129799821391934Lelio R Paula06/2013
426985^47642+8491922Norbert Schneider10/2015
427010^91920+18765191921Patrick De Geest07/2013
427110^91920-3991920Robert Price05/2011
4272(22*10^91903+41)/991904Robert Price02/2015
42742^305275-2791897Lelio R Paula11/2012
42733^192607-772691897Enzo Doria05/2014
4275(7*10^91856-61)/991856Erik Branger12/2009
4276(89*10^91839-53)/991840Robert Price11/2015
42778*5^131351+791812Lelio R Paula10/2014
42783^192426-6891811Lelio R Paula04/2016
42792^304973+11791807Lelio R Paula11/2012
42802^304939-186372791796Enzo Doria03/2016
42812^304902+841591785Lelio R Paula02/2016
428218^73119+6191785Lelio R Paula06/2016
4283(78557*2^304740+1)/15991739Lelio R Paula06/2014
42842^304747+7135591738Lelio R Paula02/2016
42858*3^192251+591728Lelio R Paula08/2014
42862^304674-8791717Lelio R Paula11/2012
4287(28*10^91715+701)/991716Robert Price11/2017
4288(2^304698+9)/136280995391715Lelio R Paula06/2013
4289(5*10^91707-119)/391708Robert Price04/2016
42902^304633-11277191704Enzo Doria06/2014
42919*10^91693+2391694Robert Price11/2017
42922^304578-1671391688Enzo Doria05/2013
42936^117824-1871391685Enzo Doria03/2013
4294(17^74509-1)/1691679Paul Bourdelais03/2010
4295(2^304551-7)/891223191673Lelio R Paula06/2013
4296(2^304532-3)/301391670Lelio R Paula06/2013
42972^304507-1664591666Enzo Doria04/2013
4298(29*2^304489+1)/3191661Lelio R Paula09/2013
42992^304471-183612791655Enzo Doria04/2015
43002^304433+3276991644Lelio R Paula02/2016
43012^304410-1662591637Enzo Doria04/2013
4302183^40500-291630Lelio R Paula10/2017
4303(203*10^91613+1)/391615Robert Price09/2017
43044*5^131052+791603Lelio R Paula10/2014
43052^304278-400191597Yves Minet04/2017
43062^304272-186637791595Enzo Doria03/2016
43072^304268+1968391594Lelio R Paula02/2016
43082^304162-16191562Lelio R Paula11/2012
43095*7^108331+691552Lelio R Paula10/2014
43102^304082-278782191538Enzo Doria03/2016
43112^304015+6413391518David Broadhurst06/2002
4312(7*2^303963+1)/391503Lelio R Paula09/2013
4313(2^303945-9)/361791494Lelio R Paula06/2013
43142^303930+188052791493Enzo Doria10/2016
43153^191684-6891457Lelio R Paula04/2016
4316(21*2^303813-1)/16991456Lelio R Paula02/2014
431711^87797-12091432Enzo Doria07/2012
43182^303698-184723191423Enzo Doria07/2015
4319(38^28933-1)^2-291416Norbert Schneider06/2016
43202^303554+7729991379Enzo Doria05/2016
43212^303542+1270591376Lelio R Paula02/2016
432231^61269-291375Lelio R Paula09/2013
43232^303516-6487591368Lelio R Paula02/2016
4324(24737*2^303428+1)/391345Lelio R Paula06/2014
4325(21181*2^303357+1)/3236191320Lelio R Paula06/2014
43262^303344-278696991316Enzo Doria03/2016
43276^117346+6591313Lelio R Paula05/2016
43282^303321+85591309Lelio R Paula02/2016
432912^84606+4791306Lelio R Paula06/2016
43302^303288+187431191299Enzo Doria06/2016
4331197^39788-291293Lelio R Paula10/2017
433211^87663-171091292Enzo Doria12/2012
43332^303224+253391280Henri Lifchitz05/2005
43346^117302+14391279Lelio R Paula05/2016
43353^191306-11288091277Enzo Doria07/2014
43362^303207+1291591275Lelio R Paula02/2016
43372^303191-11125991270Enzo Doria05/2014
433810^91230+9^(91230+1)91231Robert Price08/2016
433910^91230+792191231Patrick De Geest11/2016
434010^91230-91114191230Patrick De Geest11/2016
43416^117232-1742391225Enzo Doria02/2013
43427*10^91215+391216Erik Branger11/2009
434397*10^91205-391207Robert Price01/2017
43442^302979-16118191206Enzo Doria04/2013
43452^302949+8191197Henri Lifchitz02/2007
43464*6^117192-591194Lelio R Paula10/2014
43472^302918+9991188Lelio R Paula11/2012
43482^302797+186958791151Enzo Doria05/2016
4349265^37614+37614^26591148Norbert Schneider01/2015
43507^107852+8291146Lelio R Paula04/2016
4351(38*10^91144-11)/991145Robert Price05/2015
4352(55*10^91142+377)/991143Robert Price10/2017
4353249^38030+38030^24991128Norbert Schneider01/2015
43546^117094-21104991117Mike Oakes05/2011
43552^302602-186718191093Enzo Doria03/2016
4356(1017*2^302592-1)/5391091Lelio R Paula04/2015
435715^77445-1691083Lelio R Paula07/2016
43582^302505+8191064Henri Lifchitz02/2007
43592^302496-11234991061Enzo Doria06/2014
436017^73999-7291052Lelio R Paula07/2016
4361(16*10^91032+41)/391033Robert Price10/2017
43622^302332+57729457591012Lelio R Paula08/2016
43632^302274+7420990994Enzo Doria04/2016
4364(311^36497-1)/31090976Eric Chen09/2017
4365(3^190668+2)/8990970Lelio R Paula04/2013
43662^302188+9019590968Lelio R Paula02/2016
4367(53*10^90965-71)/990966Robert Price09/2015
43682^302113+7410590946Enzo Doria04/2016
43692^302102-655590942Lelio R Paula02/2016
4371156*(10^(4*22731)-1)/101-190925Robert Price05/2014
43703^190568+3890925Lelio R Paula04/2016
43722^302009-1644990914Enzo Doria04/2013
4373(17*2^301951-1)/16590896Lelio R Paula02/2014
43743^190497+7490891Lelio R Paula04/2016
4375(24737*2^301896+1)/39990882Lelio R Paula06/2014
437618^72397+8990878Lelio R Paula06/2016
43776^116769-4790864Lelio R Paula05/2016
43782^301712-46590825Lelio R Paula02/2016
43792^301693-6990819Lelio R Paula11/2012
43802^301683-301683^290816Henri Lifchitz05/2005
438110^90800-645390800Patrick De Geest11/2018
438211^87187-171090796Enzo Doria12/2012
43835*10^90793+2190794Robert Price01/2017
4384(22*10^90792-13)/990793Robert Price03/2015
43852^301591-161590788Lelio R Paula02/2016
4386(52^52901+1)/5390777Paul Bourdelais08/2017
43872^301546-10903790775Enzo Doria04/2014
438810^90772+402990773Patrick De Geest11/2018
438910^90770-43190770Patrick De Geest11/2018
439014^79195-390768Lelio R Paula06/2016
439110^90766+87790767Patrick De Geest11/2018
43922^301517-186169390766Enzo Doria11/2015
439310^90765-479790765Patrick De Geest11/2018
439410^90757+757390758Patrick De Geest11/2018
439510^90756-872790756Patrick De Geest11/2018
439610^90749+82390750Patrick De Geest11/2018
43982^301460-17390749Lelio R Paula11/2012
439710^90748+421390749Patrick De Geest11/2018
439910^90747-927990747Patrick De Geest11/2018
4400(85*10^90745-103)/990746Robert Price10/2017
440110^90726+407790727Patrick De Geest11/2018
440210^90721+18190722Patrick De Geest11/2018
44032^301312-8990704Lelio R Paula11/2012
440410^90696+634990697Patrick De Geest11/2018
44052^301285-12990696Lelio R Paula11/2012
44062^301282-10999190695Enzo Doria04/2014
440710^90690+887790691Patrick De Geest11/2018
440810^90683-257790683Patrick De Geest11/2018
44092^301228-185426990679Enzo Doria09/2015
4410(151*10^90669-1)/390671Robert Price04/2017
4411(32*10^90669+13)/990670Robert Price04/2015
441210^90669+979390670Patrick De Geest11/2018
441310^90665-308790665Patrick De Geest11/2018
441410^90662-951990662Patrick De Geest11/2018
441510^90661+237390662Patrick De Geest11/2018
44163*5^129698+890656Lelio R Paula10/2014
4417F(433781)90655Henri Lifchitz09/2003
441819^70891+8290653Lelio R Paula06/2016
4419(29*2^301124-1)/1390648Lelio R Paula02/2014
442010^90636-310190636Patrick De Geest11/2018
44217*3^189953-890632Lelio R Paula08/2014
442210^90626-113190626Patrick De Geest11/2018
442311^87022-180090625Enzo Doria12/2012
442410^90623+86190624Patrick De Geest11/2018
4425(2^301042+47)/1203696990616Lelio R Paula06/2013
44262^301004-278693990612Enzo Doria03/2016
442710^90611-973790611Patrick De Geest11/2018
442810^90609+682390610Patrick De Geest11/2018
44292^300980-2790605Lelio R Paula11/2012
44302*10^90597-790598Dmitry Domanov11/2010
4431197^39485+290597Lelio R Paula06/2013
44327^107198+4890593Lelio R Paula04/2016
4433(86*10^90588+121)/990589Robert Price03/2017
44342^300923+5390587Lelio R Paula11/2012
44352^300874+790573Lelio R Paula10/2012
443610^90567+948990568Patrick De Geest11/2018
44375^129568-5690565Lelio R Paula04/2016
44382^300847-11283190564Enzo Doria06/2014
443910^90562-298190562Patrick De Geest11/2018
444010^90549+381190550Patrick De Geest11/2018
444110^90532+816990533Patrick De Geest11/2018
444210^90531+983190532Patrick De Geest11/2018
44432^300718+25525590526Lelio R Paula02/2016
444410^90516-678390516Patrick De Geest11/2018
444510^90511-697790511Patrick De Geest11/2018
44462^300637+9590501Lelio R Paula11/2012
44477^107087-2490500Lelio R Paula04/2016
444810^90499-582390499Patrick De Geest11/2018
4450(10^90499+3^90499)/1390498Robert Price01/2013
444913^81241+9090498Lelio R Paula06/2016
445110^90480+513190481Patrick De Geest11/2018
44526^116273-8590478Lelio R Paula05/2016
445310^90473+313990474Patrick De Geest11/2018
445410^90470+231990471Patrick De Geest11/2018
44556^116256-1757390465Enzo Doria02/2013
44562^300502+5461590461Lelio R Paula02/2016
4457(13*2^300487+1)/4590456Lelio R Paula09/2013
445810^90453-396990453Patrick De Geest11/2018
445910^90440+135990441Patrick De Geest11/2018
4460(3^189545-8)/590436Lelio R Paula01/2013
4461(7*2^300406-1)/390432Lelio R Paula02/2014
446210^90430+333990431Patrick De Geest11/2018
446310^90414-154790414Patrick De Geest11/2018
446410^90404-642990404Patrick De Geest11/2018
446510^90401+207790402Patrick De Geest11/2018
44664*5^129332+390400Lelio R Paula10/2014
446710^90397-32390397Patrick De Geest11/2018
44682^300249-1624590384Enzo Doria04/2013
4469(7*10^90371-313)/990371Robert Price11/2016
447010^90363-355790363Patrick De Geest11/2018
44722*6^116118+790358Lelio R Paula10/2014
447110^90358-497990358Patrick De Geest11/2018
447310^90356-719790356Patrick De Geest11/2018
447410^90353-108990353Patrick De Geest11/2018
4475(24737*2^300101+1)/2590343Lelio R Paula06/2014
44764*10^90334-2190335Robert Price04/2016
447710^90322-955190322Patrick De Geest11/2018
447810^90316+999190317Patrick De Geest11/2018
44802^300019-11033590315Enzo Doria05/2014
447910^90315-856190315Patrick De Geest11/2018
44812^299949-100590294Lelio R Paula11/2013
448210^90279-155190279Patrick De Geest09/2018
44832^299868-10961390270Enzo Doria04/2014
448410^90259-944390259Patrick De Geest09/2018
448510^90252-810390252Patrick De Geest09/2018
44865*2^299799-390250Lelio R Paula08/2014
448713^81008-290239Lelio R Paula09/2013
448864^49957-63^4995790232Robert Price07/2013
448910^90227+5628190228Patrick De Geest06/2016
44922^299725+31590227Lelio R Paula11/2013
449010^90227-100000000190227Robert Price05/2016
449110^90227-6876390227Patrick De Geest06/2016
44935^129082+4890225Lelio R Paula03/2016
44942^299699+19590219Lelio R Paula10/2012
4495(55*10^90211-1)/990212Ray Chandler02/2012
449610^90209+897190210Patrick De Geest09/2018
449710^90208-224790208Patrick De Geest09/2018
4498116^43693-11590203Norbert Schneider08/2018
449910^90202+355390203Patrick De Geest09/2018
45003^189053+28090202Lelio R Paula04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 17 2018 20:37 (Time in France)

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