PRP Records

Probable Primes Top 10000

(252932 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 ?
45012^306200+118592176Lelio R Paula02/2016
45022^306153+1192162Lelio R Paula11/2012
4503(2^306141-7)/592157Lelio R Paula06/2013
4504(26*10^92152-23)/392153Robert Price08/2016
4505(2*10^92152+67)/392152Robert Price04/2017
45064*10^92099+3*7^9209992100Mike Oakes12/2010
4507115^44684+11492081Norbert Schneider07/2018
4508(2^305867-2^152934+1)/59207511/2006
45092^305851-10949592071Enzo Doria04/2014
451112^85300+3592055Lelio R Paula06/2016
4510((10^46026-1)*1000/9+739)*10^46026+(10^46026-1)/992055Hans Havermann05/2019
45123^192911+9292042Lelio R Paula04/2016
45132^305723-27627192032Enzo Doria07/2015
45142^305676+9392018Donovan Johnson06/2008
45153^192819+491999Lelio R Paula04/2013
4516(38*10^91997-83)/9991997Ray Chandler07/2011
45172^305539+7291191977Enzo Doria04/2016
4518Phi(212014,10)91960Makoto Kamada04/2019
4519(2^305427-5)/129799821391934Lelio R Paula06/2013
452085^47642+8491922Norbert Schneider10/2015
452110^91920+18765191921Patrick De Geest07/2013
452210^91920-3991920Robert Price05/2011
4523(22*10^91903+41)/991904Robert Price02/2015
45252^305275-2791897Lelio R Paula11/2012
45243^192607-772691897Enzo Doria05/2014
4526(7*10^91856-61)/991856Erik Branger12/2009
4527(89*10^91839-53)/991840Robert Price11/2015
45288*5^131351+791812Lelio R Paula10/2014
45293^192426-6891811Lelio R Paula04/2016
45302^304973+11791807Lelio R Paula11/2012
45312^304939-186372791796Enzo Doria03/2016
45322^304902+841591785Lelio R Paula02/2016
453318^73119+6191785Lelio R Paula06/2016
4534(78557*2^304740+1)/15991739Lelio R Paula06/2014
45352^304747+7135591738Lelio R Paula02/2016
45368*3^192251+591728Lelio R Paula08/2014
45372^304674-8791717Lelio R Paula11/2012
4538(28*10^91715+701)/991716Robert Price11/2017
4539(2^304698+9)/136280995391715Lelio R Paula06/2013
4540(5*10^91707-119)/391708Robert Price04/2016
45412^304633-11277191704Enzo Doria06/2014
45429*10^91693+2391694Robert Price11/2017
45432^304578-1671391688Enzo Doria05/2013
45446^117824-1871391685Enzo Doria03/2013
4545(17^74509-1)/1691679Paul Bourdelais03/2010
4546(2^304551-7)/891223191673Lelio R Paula06/2013
4547(2^304532-3)/301391670Lelio R Paula06/2013
45482^304507-1664591666Enzo Doria04/2013
4549(29*2^304489+1)/3191661Lelio R Paula09/2013
45502^304471-183612791655Enzo Doria04/2015
45512^304433+3276991644Lelio R Paula02/2016
45522^304410-1662591637Enzo Doria04/2013
4553183^40500-291630Lelio R Paula10/2017
4554(203*10^91613+1)/391615Robert Price09/2017
45554*5^131052+791603Lelio R Paula10/2014
45562^304278-400191597Yves Minet04/2017
45572^304272-186637791595Enzo Doria03/2016
45582^304268+1968391594Lelio R Paula02/2016
45592^304162-16191562Lelio R Paula11/2012
45605*7^108331+691552Lelio R Paula10/2014
45612^304082-278782191538Enzo Doria03/2016
45622^304015+6413391518David Broadhurst06/2002
4563(7*2^303963+1)/391503Lelio R Paula09/2013
4564(2^303945-9)/361791494Lelio R Paula06/2013
45652^303930+188052791493Enzo Doria10/2016
45663^191684-6891457Lelio R Paula04/2016
4567(21*2^303813-1)/16991456Lelio R Paula02/2014
456811^87797-12091432Enzo Doria07/2012
45692^303698-184723191423Enzo Doria07/2015
4570(38^28933-1)^2-291416Norbert Schneider06/2016
45712^303554+7729991379Enzo Doria05/2016
45722^303542+1270591376Lelio R Paula02/2016
457331^61269-291375Lelio R Paula09/2013
45742^303516-6487591368Lelio R Paula02/2016
4575(24737*2^303428+1)/391345Lelio R Paula06/2014
4576(21181*2^303357+1)/3236191320Lelio R Paula06/2014
45772^303344-278696991316Enzo Doria03/2016
45786^117346+6591313Lelio R Paula05/2016
45792^303321+85591309Lelio R Paula02/2016
458012^84606+4791306Lelio R Paula06/2016
45812^303288+187431191299Enzo Doria06/2016
4582197^39788-291293Lelio R Paula10/2017
458311^87663-171091292Enzo Doria12/2012
45842^303224+253391280Henri Lifchitz05/2005
45856^117302+14391279Lelio R Paula05/2016
45863^191306-11288091277Enzo Doria07/2014
45872^303207+1291591275Lelio R Paula02/2016
45882^303191-11125991270Enzo Doria05/2014
458910^91230+9^(91230+1)91231Robert Price08/2016
459010^91230+792191231Patrick De Geest11/2016
459110^91230-91114191230Patrick De Geest11/2016
459210^91229-247191229Patrick De Geest01/2019
459310^91225+527191226Patrick De Geest01/2019
45946^117232-1742391225Enzo Doria02/2013
45957*10^91215+391216Erik Branger11/2009
459610^91215-453991215Patrick De Geest01/2019
459710^91210+242191211Patrick De Geest01/2019
459810^91210-173791210Patrick De Geest01/2019
459997*10^91205-391207Robert Price01/2017
46002^302979-16118191206Enzo Doria04/2013
46012^302949+8191197Henri Lifchitz02/2007
46024*6^117192-591194Lelio R Paula10/2014
460310^91194-866391194Patrick De Geest01/2019
46042^302918+9991188Lelio R Paula11/2012
460510^91186-776391186Patrick De Geest01/2019
460610^91181-136791181Patrick De Geest01/2019
460710^91178-471991178Patrick De Geest01/2019
460810^91165+304391166Patrick De Geest01/2019
460910^91156+386191157Patrick De Geest01/2019
46102^302797+186958791151Enzo Doria05/2016
4611265^37614+37614^26591148Norbert Schneider01/2015
46127^107852+8291146Lelio R Paula04/2016
4613(38*10^91144-11)/991145Robert Price05/2015
4614(55*10^91142+377)/991143Robert Price10/2017
461510^91128+996191129Patrick De Geest01/2019
4616249^38030+38030^24991128Norbert Schneider01/2015
46176^117094-21104991117Mike Oakes05/2011
46182^302602-186718191093Enzo Doria03/2016
461910^91092-910791092Patrick De Geest01/2019
4620(1017*2^302592-1)/5391091Lelio R Paula04/2015
462115^77445-1691083Lelio R Paula07/2016
46222^302505+8191064Henri Lifchitz02/2007
46232^302496-11234991061Enzo Doria06/2014
462417^73999-7291052Lelio R Paula07/2016
462510^91047+933191048Patrick De Geest01/2019
462610^91044+207791045Patrick De Geest01/2019
462710^91041+934991042Patrick De Geest01/2019
462810^91041-782391041Patrick De Geest01/2019
462910^91040+407791041Patrick De Geest01/2019
463010^91037+276991038Patrick De Geest01/2019
4631(16*10^91032+41)/391033Robert Price10/2017
463210^91023-647191023Patrick De Geest01/2019
463310^91018+787391019Patrick De Geest01/2019
463410^91016-797391016Patrick De Geest01/2019
46352^302332+57729457591012Lelio R Paula08/2016
463610^91004+907391005Patrick De Geest01/2019
463710^91003-390391003Patrick De Geest01/2019
46382^302274+7420990994Enzo Doria04/2016
463910^90991-627990991Patrick De Geest01/2019
464010^90983+139390984Patrick De Geest01/2019
4641(311^36497-1)/31090976Eric Chen09/2017
4642(3^190668+2)/8990970Lelio R Paula04/2013
46432^302188+9019590968Lelio R Paula02/2016
4644(53*10^90965-71)/990966Robert Price09/2015
464510^90965-683390965Patrick De Geest01/2019
464610^90963-365990963Patrick De Geest01/2019
464710^90962+765790963Patrick De Geest01/2019
464810^90959+879190960Patrick De Geest01/2019
464910^90948+986790949Patrick De Geest01/2019
46502^302113+7410590946Enzo Doria04/2016
46512^302102-655590942Lelio R Paula02/2016
465210^90930-362390930Patrick De Geest01/2019
4654156*(10^(4*22731)-1)/101-190925Robert Price05/2014
46533^190568+3890925Lelio R Paula04/2016
465510^90917-669390917Patrick De Geest01/2019
46562^302009-1644990914Enzo Doria04/2013
465710^90908+318190909Patrick De Geest01/2019
465810^90904-516990904Patrick De Geest01/2019
465910^90902+261390903Patrick De Geest01/2019
4660(17*2^301951-1)/16590896Lelio R Paula02/2014
46613^190497+7490891Lelio R Paula04/2016
4662(24737*2^301896+1)/39990882Lelio R Paula06/2014
466310^90880+570790881Patrick De Geest01/2019
466418^72397+8990878Lelio R Paula06/2016
4665134^42719-13390868Norbert Schneider03/2019
46666^116769-4790864Lelio R Paula05/2016
466710^90858-830190858Patrick De Geest01/2019
466810^90849-472190849Patrick De Geest01/2019
46692^301712-46590825Lelio R Paula02/2016
46702^301693-6990819Lelio R Paula11/2012
46712^301683-301683^290816Henri Lifchitz05/2005
467210^90807+727990808Patrick De Geest01/2019
467310^90800-645390800Patrick De Geest11/2018
467411^87187-171090796Enzo Doria12/2012
46755*10^90793+2190794Robert Price01/2017
4676(22*10^90792-13)/990793Robert Price03/2015
46772^301591-161590788Lelio R Paula02/2016
4678(52^52901+1)/5390777Paul Bourdelais08/2017
46792^301546-10903790775Enzo Doria04/2014
468010^90772+402990773Patrick De Geest11/2018
468110^90770-43190770Patrick De Geest11/2018
468214^79195-390768Lelio R Paula06/2016
468310^90766+87790767Patrick De Geest11/2018
46842^301517-186169390766Enzo Doria11/2015
468510^90765-479790765Patrick De Geest11/2018
468610^90757+757390758Patrick De Geest11/2018
468710^90756-872790756Patrick De Geest11/2018
468810^90749+82390750Patrick De Geest11/2018
46902^301460-17390749Lelio R Paula11/2012
468910^90748+421390749Patrick De Geest11/2018
469110^90747-927990747Patrick De Geest11/2018
4692(85*10^90745-103)/990746Robert Price10/2017
469310^90726+407790727Patrick De Geest11/2018
469410^90721+18190722Patrick De Geest11/2018
46952^301312-8990704Lelio R Paula11/2012
469610^90696+634990697Patrick De Geest11/2018
46972^301285-12990696Lelio R Paula11/2012
46982^301282-10999190695Enzo Doria04/2014
469910^90690+887790691Patrick De Geest11/2018
470010^90683-257790683Patrick De Geest11/2018
47012^301228-185426990679Enzo Doria09/2015
4702(151*10^90669-1)/390671Robert Price04/2017
4703(32*10^90669+13)/990670Robert Price04/2015
470410^90669+979390670Patrick De Geest11/2018
470510^90665-308790665Patrick De Geest11/2018
470610^90662-951990662Patrick De Geest11/2018
470710^90661+237390662Patrick De Geest11/2018
47083*5^129698+890656Lelio R Paula10/2014
4709F(433781)90655Henri Lifchitz09/2003
471019^70891+8290653Lelio R Paula06/2016
4711(29*2^301124-1)/1390648Lelio R Paula02/2014
471210^90636-310190636Patrick De Geest11/2018
47137*3^189953-890632Lelio R Paula08/2014
471410^90626-113190626Patrick De Geest11/2018
471511^87022-180090625Enzo Doria12/2012
471610^90623+86190624Patrick De Geest11/2018
4717(2^301042+47)/1203696990616Lelio R Paula06/2013
47182^301004-278693990612Enzo Doria03/2016
471910^90611-973790611Patrick De Geest11/2018
472010^90609+682390610Patrick De Geest11/2018
47212^300980-2790605Lelio R Paula11/2012
47222*10^90597-790598Dmitry Domanov11/2010
4723197^39485+290597Lelio R Paula06/2013
47247^107198+4890593Lelio R Paula04/2016
4725(86*10^90588+121)/990589Robert Price03/2017
47262^300923+5390587Lelio R Paula11/2012
47272^300874+790573Lelio R Paula10/2012
472810^90567+948990568Patrick De Geest11/2018
47295^129568-5690565Lelio R Paula04/2016
47302^300847-11283190564Enzo Doria06/2014
473110^90562-298190562Patrick De Geest11/2018
473210^90549+381190550Patrick De Geest11/2018
47332^300790-454190547Yves Minet03/2019
473410^90532+816990533Patrick De Geest11/2018
473510^90531+983190532Patrick De Geest11/2018
47362^300718+25525590526Lelio R Paula02/2016
473710^90516-678390516Patrick De Geest11/2018
473810^90511-697790511Patrick De Geest11/2018
47392^300637+9590501Lelio R Paula11/2012
47407^107087-2490500Lelio R Paula04/2016
474110^90499-582390499Patrick De Geest11/2018
4743(10^90499+3^90499)/1390498Robert Price01/2013
474213^81241+9090498Lelio R Paula06/2016
474410^90480+513190481Patrick De Geest11/2018
47456^116273-8590478Lelio R Paula05/2016
474610^90473+313990474Patrick De Geest11/2018
474710^90470+231990471Patrick De Geest11/2018
47486^116256-1757390465Enzo Doria02/2013
47492^300502+5461590461Lelio R Paula02/2016
4750(13*2^300487+1)/4590456Lelio R Paula09/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2019 07:14 (Time in France)

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