PRP Records

Probable Primes Top 10000

(224926 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 ?
4251(21181*2^303357+1)/3236191320Lelio R Paula06/2014
42522^303344-278696991316Enzo Doria03/2016
42536^117346+6591313Lelio R Paula05/2016
42542^303321+85591309Lelio R Paula02/2016
425512^84606+4791306Lelio R Paula06/2016
42562^303288+187431191299Enzo Doria06/2016
4257197^39788-291293Lelio R Paula10/2017
425811^87663-171091292Enzo Doria12/2012
42592^303224+253391280Henri Lifchitz05/2005
42606^117302+14391279Lelio R Paula05/2016
42613^191306-11288091277Enzo Doria07/2014
42622^303207+1291591275Lelio R Paula02/2016
42632^303191-11125991270Enzo Doria05/2014
426410^91230+9^(91230+1)91231Robert Price08/2016
426510^91230+792191231Patrick De Geest11/2016
426610^91230-91114191230Patrick De Geest11/2016
42676^117232-1742391225Enzo Doria02/2013
42687*10^91215+391216Erik Branger11/2009
426997*10^91205-391207Robert Price01/2017
42702^302979-16118191206Enzo Doria04/2013
42712^302949+8191197Henri Lifchitz02/2007
42724*6^117192-591194Lelio R Paula10/2014
42732^302918+9991188Lelio R Paula11/2012
42742^302797+186958791151Enzo Doria05/2016
4275265^37614+37614^26591148Norbert Schneider01/2015
42767^107852+8291146Lelio R Paula04/2016
4277(38*10^91144-11)/991145Robert Price05/2015
4278(55*10^91142+377)/991143Robert Price10/2017
4279249^38030+38030^24991128Norbert Schneider01/2015
42806^117094-21104991117Mike Oakes05/2011
42812^302602-186718191093Enzo Doria03/2016
4282(1017*2^302592-1)/5391091Lelio R Paula04/2015
428315^77445-1691083Lelio R Paula07/2016
42842^302505+8191064Henri Lifchitz02/2007
42852^302496-11234991061Enzo Doria06/2014
428617^73999-7291052Lelio R Paula07/2016
4287(16*10^91032+41)/391033Robert Price10/2017
42882^302332+57729457591012Lelio R Paula08/2016
42892^302274+7420990994Enzo Doria04/2016
4290(311^36497-1)/31090976Eric Chen09/2017
4291(3^190668+2)/8990970Lelio R Paula04/2013
42922^302188+9019590968Lelio R Paula02/2016
4293(53*10^90965-71)/990966Robert Price09/2015
42942^302113+7410590946Enzo Doria04/2016
42952^302102-655590942Lelio R Paula02/2016
4297156*(10^(4*22731)-1)/101-190925Robert Price05/2014
42963^190568+3890925Lelio R Paula04/2016
42982^302009-1644990914Enzo Doria04/2013
4299(17*2^301951-1)/16590896Lelio R Paula02/2014
43003^190497+7490891Lelio R Paula04/2016
4301(24737*2^301896+1)/39990882Lelio R Paula06/2014
430218^72397+8990878Lelio R Paula06/2016
43036^116769-4790864Lelio R Paula05/2016
43042^301712-46590825Lelio R Paula02/2016
43052^301693-6990819Lelio R Paula11/2012
43062^301683-301683^290816Henri Lifchitz05/2005
430711^87187-171090796Enzo Doria12/2012
43085*10^90793+2190794Robert Price01/2017
4309(22*10^90792-13)/990793Robert Price03/2015
43102^301591-161590788Lelio R Paula02/2016
4311(52^52901+1)/5390777Paul Bourdelais08/2017
43122^301546-10903790775Enzo Doria04/2014
431314^79195-390768Lelio R Paula06/2016
43142^301517-186169390766Enzo Doria11/2015
43152^301460-17390749Lelio R Paula11/2012
4316(85*10^90745-103)/990746Robert Price10/2017
43172^301312-8990704Lelio R Paula11/2012
43182^301285-12990696Lelio R Paula11/2012
43192^301282-10999190695Enzo Doria04/2014
43202^301228-185426990679Enzo Doria09/2015
4321(151*10^90669-1)/390671Robert Price04/2017
4322(32*10^90669+13)/990670Robert Price04/2015
43233*5^129698+890656Lelio R Paula10/2014
4324F(433781)90655Henri Lifchitz09/2003
432519^70891+8290653Lelio R Paula06/2016
4326(29*2^301124-1)/1390648Lelio R Paula02/2014
43277*3^189953-890632Lelio R Paula08/2014
432811^87022-180090625Enzo Doria12/2012
4329(2^301042+47)/1203696990616Lelio R Paula06/2013
43302^301004-278693990612Enzo Doria03/2016
43312^300980-2790605Lelio R Paula11/2012
43322*10^90597-790598Dmitry Domanov11/2010
4333197^39485+290597Lelio R Paula06/2013
43347^107198+4890593Lelio R Paula04/2016
4335(86*10^90588+121)/990589Robert Price03/2017
43362^300923+5390587Lelio R Paula11/2012
43372^300874+790573Lelio R Paula10/2012
43385^129568-5690565Lelio R Paula04/2016
43392^300847-11283190564Enzo Doria06/2014
43402^300718+25525590526Lelio R Paula02/2016
43412^300637+9590501Lelio R Paula11/2012
43427^107087-2490500Lelio R Paula04/2016
4343(10^90499+3^90499)/1390498Robert Price01/2013
434413^81241+9090498Lelio R Paula06/2016
43456^116273-8590478Lelio R Paula05/2016
43466^116256-1757390465Enzo Doria02/2013
43472^300502+5461590461Lelio R Paula02/2016
4348(13*2^300487+1)/4590456Lelio R Paula09/2013
4349(3^189545-8)/590436Lelio R Paula01/2013
4350(7*2^300406-1)/390432Lelio R Paula02/2014
43514*5^129332+390400Lelio R Paula10/2014
43522^300249-1624590384Enzo Doria04/2013
4353(7*10^90371-313)/990371Robert Price11/2016
43542*6^116118+790358Lelio R Paula10/2014
4355(24737*2^300101+1)/2590343Lelio R Paula06/2014
43564*10^90334-2190335Robert Price04/2016
43572^300019-11033590315Enzo Doria05/2014
43582^299949-100590294Lelio R Paula11/2013
435910^90279-155190279Patrick De Geest09/2018
43602^299868-10961390270Enzo Doria04/2014
436110^90259-944390259Patrick De Geest09/2018
436210^90252-810390252Patrick De Geest09/2018
43635*2^299799-390250Lelio R Paula08/2014
436413^81008-290239Lelio R Paula09/2013
436564^49957-63^4995790232Robert Price07/2013
436610^90227+5628190228Patrick De Geest06/2016
43692^299725+31590227Lelio R Paula11/2013
436710^90227-100000000190227Robert Price05/2016
436810^90227-6876390227Patrick De Geest06/2016
43705^129082+4890225Lelio R Paula03/2016
43712^299699+19590219Lelio R Paula10/2012
4372(55*10^90211-1)/990212Ray Chandler02/2012
437310^90209+897190210Patrick De Geest09/2018
437410^90208-224790208Patrick De Geest09/2018
4375116^43693-11590203Norbert Schneider08/2018
437610^90202+355390203Patrick De Geest09/2018
43773^189053+28090202Lelio R Paula04/2016
43782^299639-18790201Lelio R Paula10/2012
437910^90199-289190199Patrick De Geest09/2018
43802^299631+18390198Lelio R Paula10/2012
438110^90196-968390196Patrick De Geest09/2018
438210^90193-980990193Patrick De Geest09/2018
4383(21*2^299611-1)/2990192Lelio R Paula02/2014
43842^299567+11390179Lelio R Paula10/2012
43852^299550+18990174Lelio R Paula10/2012
438610^90170-674990170Patrick De Geest09/2018
4387(2^299535+3)/2990168Lelio R Paula01/2013
438810^90160-561390160Patrick De Geest09/2018
4389(97*10^90155-1)/390157Serge Batalov12/2014
43903^188938+868090147Lelio R Paula04/2016
439110^90146-202790146Patrick De Geest09/2018
43936^115840-5590142Lelio R Paula05/2016
4392(5*10^90142-473)/990142Robert Price12/2017
43948*7^106659+590139Lelio R Paula10/2014
43952^299406-1665390131Enzo Doria05/2013
4397208049#+(216091#)/(208049#)90128Makoto Morimoto04/2016
439610^90128-838790128Patrick De Geest09/2018
4398(F(5)^128941-F(4)^128941)/F(3)90126Wayne Halsdorf03/2012
43996^115819-5390125Lelio R Paula05/2016
440010^90123+631390124Patrick De Geest09/2018
44016^115816-1685390123Enzo Doria02/2013
44026^115813-2390121Lelio R Paula05/2016
4403(22*10^90110+161)/390111Robert Price02/2017
4404(2^299330-509203)/6990106Lelio R Paula01/2013
440510^90105-76790105Patrick De Geest09/2018
440610^90104-770390104Patrick De Geest09/2018
440710^90103+915990104Patrick De Geest09/2018
440810^90101-320790101Patrick De Geest09/2018
4409(29*10^90096-17)/390097Erik Branger09/2014
441010^90089-357390089Patrick De Geest09/2018
44112^299247+187052990083Enzo Doria05/2016
441210^90079+160990080Patrick De Geest09/2018
44132^299229-279778390077Enzo Doria04/2016
44142^299220-1631790075Enzo Doria04/2013
441511^86491-135090072Enzo Doria12/2012
441610^90071-123390071Patrick De Geest09/2018
441710^90069-784190069Patrick De Geest09/2018
4418(31*10^90064-1)/390066Robert Price03/2017
441910^90060-83990060Patrick De Geest09/2018
442010^90052+236190053Patrick De Geest09/2018
442110^90047+61990048Patrick De Geest09/2018
4422L(430949)/861899/144038756153990045Serge Batalov07/2017
44232^299112+7395190042Enzo Doria04/2016
44248^99702+7^(99702-1)90040Robert Price02/2016
442510^90038-968790038Patrick De Geest09/2018
44265*10^90033+390034Dmitry Domanov11/2010
442710^90030-146190030Patrick De Geest09/2018
4428243^37738+37738^24390029Norbert Schneider01/2015
442910^90025-870390025Patrick De Geest09/2018
44302^299048-11329790023Enzo Doria07/2014
443110^90015+84990016Patrick De Geest09/2018
443210^90010+681190011Patrick De Geest09/2018
443310^90008+84790009Patrick De Geest09/2018
44343^188648+9290008Lelio R Paula12/2015
44355*2^298991+790006Lelio R Paula08/2014
4436(25*2^298997+1)/326790005Lelio R Paula01/2013
443710^90000+886990001Patrick De Geest12/2009
443910^89999+8293990000Dirk Augustin04/2007
443810^90000-14034390000Patrick De Geest12/2009
444010^89999-19489189999Patrick De Geest11/2009
444119^70365-7889980Lelio R Paula12/2015
4442NaturalLogarithmOf2(89973)89973Eric W. Weisstein10/2015
44432^298852-6487589964Lelio R Paula11/2013
444418^71659+3789952Lelio R Paula12/2015
4445(2908*29^61501-3)/789942Curtis Bright05/2015
444617^73067+2089906Lelio R Paula11/2015
44472^298637-9989899Lelio R Paula10/2012
44489^94188+3*8^94188-2*4^94188-3*2^9418889879Mike Oakes01/2011
44499*10^89858+1989859Robert Price05/2016
44502^298501+187006789858Enzo Doria05/2016
445111^86280-9889852Lelio R Paula11/2015
44522^298473-11005989850Enzo Doria04/2014
445319^70263-3289850Lelio R Paula12/2015
4454(299*10^89836-17)/389838Robert Price01/2017
44553^188286+1489836Robert Price09/2013
4456gcd(V(1091095),5*F(218219)*(F(218219)+1)+1)89822Serge Batalov04/2015
44572^298367+5890589818Lelio R Paula11/2013
44582^298319-10965789803Enzo Doria04/2014
44598*10^89800+8189801Robert Price05/2017
446018^71505-9189759Lelio R Paula12/2015
4461(7^106187+1)/889738Paul Bourdelais04/2008
44622^298079-10953189731Enzo Doria04/2014
4463117^43380+11689718Norbert Schneider08/2018
4464(22699*2^298016+1)/38589714Lelio R Paula06/2014
4465156*(10^(4*22427)-1)/101-189709Robert Price05/2014
44662^298003-6694589708Lelio R Paula11/2013
4467(23*10^89705-83)/389706Robert Price09/2017
446817^72900-5489700Lelio R Paula11/2015
44693*2^297956+589695Lelio R Paula08/2014
447020^68938-1189691Lelio R Paula01/2016
447189*10^89687-789689Robert Price03/2017
44722^297923+7778389684Enzo Doria05/2016
447311^86107-2457600089672Enzo Doria02/2013
44742^297878-11191189671Enzo Doria05/2014
44757^106084+4089652Lelio R Paula10/2015
4476(86*10^89640-311)/989641Robert Price10/2017
44773*10^89608-5989609Robert Price10/2017
44783^187780-1103889594Enzo Doria05/2014
4479(13*2^297560-1)/4915178789568Lelio R Paula02/2014
44805^128141-3689567Lelio R Paula10/2015
44814*7^105951+989540Lelio R Paula10/2014
4482(7*10^89539-439)/989539Robert Price09/2017
44832^297397+17725789526Enzo Doria05/2016
44842^297346-1624189511Enzo Doria04/2013
4485(5*10^89510+79)/389511Robert Price11/2017
44874^148663-3^14866389505Jean-Louis Charton11/2005
44862^297328-86968810589505Lelio R Paula07/2016
44882^297325-45904389504Enzo Doria05/2015
44892^297310-11239189500Enzo Doria06/2014
44902^297296-11215789496Enzo Doria06/2014
449157^50966-289490Lelio R Paula08/2013
4492(266*10^89482+1)/389484Robert Price02/2016
4493(14*10^89480-101)/389481Robert Price04/2017
44942^297122+9989443Lelio R Paula10/2012
4495(3^187435-5)/128689427Lelio R Paula01/2013
4496(25*10^89413+161)/389414Robert Price01/2017
44972^296990+187069989403Enzo Doria05/2016
44982^296972-101789398Lelio R Paula11/2013
4499(7*10^89383+167)/389384Robert Kinser10/2017
4500(85*10^89375-31)/989376Robert Price11/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 18 2018 22:22 (Time in France)

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