PRP Records

Probable Primes Top 10000

(259919 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 ?
5251FAB2(300001,29405)90310Robert Price05/2019
5252(2^299965+2774)/290299Stefano Morozzi01/2020
52532^299949-100590294Lelio R Paula11/2013
5254(2^299947+2054)/290293Stefano Morozzi01/2020
525510^90279+6245790280Patrick De Geest07/2019
525610^90279-155190279Patrick De Geest09/2018
5257(2^299892+1986)/290277Stefano Morozzi01/2020
5258(2^299893+3866)/290277Stefano Morozzi01/2020
52592^299868-10961390270Enzo Doria04/2014
526010^90259+35929990260Patrick De Geest07/2019
526110^90259-944390259Patrick De Geest09/2018
5262(2^299831+3786)/290258Stefano Morozzi01/2020
526310^90252+10287390253Patrick De Geest07/2019
526410^90252-810390252Patrick De Geest09/2018
52665*2^299799-390250Lelio R Paula08/2014
5265(2^299803+3326)/290250Stefano Morozzi01/2020
526713^81008-290239Lelio R Paula09/2013
526880697!4-25690234Robert Price11/2019
527064^49957-63^4995790232Robert Price07/2013
5269(2^299745+2994)/290232Stefano Morozzi01/2020
527110^90227+5628190228Patrick De Geest06/2016
52742^299725+31590227Lelio R Paula11/2013
527210^90227-100000000190227Robert Price05/2016
527310^90227-6876390227Patrick De Geest06/2016
52755^129082+4890225Lelio R Paula03/2016
52762^299699+19590219Lelio R Paula10/2012
5277(55*10^90211-1)/990212Ray Chandler02/2012
527810^90209+897190210Patrick De Geest09/2018
527910^90209-72479790209Patrick De Geest07/2019
528010^90208+18953190209Patrick De Geest07/2019
528110^90208-224790208Patrick De Geest09/2018
5282116^43693-11590203Norbert Schneider08/2018
528310^90202+355390203Patrick De Geest09/2018
52843^189053+28090202Lelio R Paula04/2016
528510^90202-6779390202Patrick De Geest07/2019
52862^299639-18790201Lelio R Paula10/2012
528710^90199+25403190200Patrick De Geest07/2019
528810^90199-289190199Patrick De Geest09/2018
52892^299631+18390198Lelio R Paula10/2012
529010^90196+18753990197Patrick De Geest07/2019
529110^90196-968390196Patrick De Geest09/2018
529210^90193+10497390194Patrick De Geest07/2019
529310^90193-980990193Patrick De Geest09/2018
5294(21*2^299611-1)/2990192Lelio R Paula02/2014
52952^299567+11390179Lelio R Paula10/2012
52962^299550+18990174Lelio R Paula10/2012
529710^90170+37606390171Patrick De Geest07/2019
529810^90170-674990170Patrick De Geest09/2018
5299(2^299535+3)/2990168Lelio R Paula01/2013
5300(2^299521+13)/1590164Stefano Morozzi03/2020
530110^90160+27194790161Patrick De Geest07/2019
530210^90160-561390160Patrick De Geest09/2018
5303(97*10^90155-1)/390157Serge Batalov12/2014
53053^188938+868090147Lelio R Paula04/2016
530410^90146+16020990147Patrick De Geest07/2019
530610^90146-202790146Patrick De Geest09/2018
53076^115840-5590142Lelio R Paula05/2016
5308(5*10^90142-473)/990142Robert Price12/2017
53098*7^106659+590139Lelio R Paula10/2014
53122^299406-1665390131Enzo Doria05/2013
5310(317057^16384+1)/290131Richard Fischer10/2019
5311(2^299409+834)/290131Stefano Morozzi01/2020
531310^90128+28867390129Patrick De Geest07/2019
5315208049#+(216091#)/(208049#)90128Makoto Morimoto04/2016
531410^90128-838790128Patrick De Geest09/2018
5316(F(5)^128941-F(4)^128941)/F(3)90126Wayne Halsdorf03/2012
53176^115819-5390125Lelio R Paula05/2016
531810^90123+631390124Patrick De Geest09/2018
53206^115816-1685390123Enzo Doria02/2013
531910^90123-2261790123Patrick De Geest07/2019
53216^115813-2390121Lelio R Paula05/2016
5322(22*10^90110+161)/390111Robert Price02/2017
5324(2^299330-509203)/6990106Lelio R Paula01/2013
532310^90105+91575990106Patrick De Geest07/2019
532610^90105-76790105Patrick De Geest09/2018
532510^90104+4818990105Patrick De Geest07/2019
532710^90104-770390104Patrick De Geest09/2018
532810^90103+915990104Patrick De Geest09/2018
532910^90103-20845790103Patrick De Geest07/2019
533010^90102+7301190103Patrick De Geest07/2019
533110^90102-60243390102Patrick De Geest07/2019
533210^90101+122553790102Patrick De Geest07/2019
533310^90101-320790101Patrick De Geest09/2018
5334(29*10^90096-17)/390097Erik Branger09/2014
533510^90089+14318190090Patrick De Geest07/2019
533610^90089-357390089Patrick De Geest09/2018
53372^299247+187052990083Enzo Doria05/2016
533810^90079+160990080Patrick De Geest09/2018
533910^90079-23004390079Patrick De Geest07/2019
53402^299229-279778390077Enzo Doria04/2016
53412^299220-1631790075Enzo Doria04/2013
534211^86491-135090072Enzo Doria12/2012
534310^90071+5233390072Patrick De Geest07/2019
534410^90071-123390071Patrick De Geest09/2018
5345(314401^16384+1)/290071Richard Fischer10/2019
534610^90069+15852790070Patrick De Geest07/2019
534710^90069-784190069Patrick De Geest09/2018
5348(31*10^90064-1)/390066Robert Price03/2017
534910^90060+14943190061Patrick De Geest07/2019
535010^90060-83990060Patrick De Geest09/2018
535110^90052+236190053Patrick De Geest09/2018
535210^90052-9092990052Patrick De Geest07/2019
535310^90047+61990048Patrick De Geest09/2018
535410^90047-15107190047Patrick De Geest07/2019
5355L(430949)/861899/144038756153990045Serge Batalov07/2017
53562^299112+7395190042Enzo Doria04/2016
53578^99702+7^(99702-1)90040Robert Price02/2016
535810^90038+15780390039Patrick De Geest07/2019
535910^90038-968790038Patrick De Geest09/2018
53605*10^90033+390034Dmitry Domanov11/2010
536110^90030+22581390031Patrick De Geest07/2019
536210^90030-146190030Patrick De Geest09/2018
5363243^37738+37738^24390029Norbert Schneider01/2015
536410^90025+7056990026Patrick De Geest07/2019
536510^90025-870390025Patrick De Geest09/2018
53662^299048-11329790023Enzo Doria07/2014
536710^90015+84990016Patrick De Geest09/2018
536810^90015-22838790015Patrick De Geest07/2019
536910^90010+681190011Patrick De Geest09/2018
537010^90010-18359790010Patrick De Geest11/2018
537110^90009+5832190010Patrick De Geest11/2018
537210^90008+84790009Patrick De Geest09/2018
537310^90009-35601390009Patrick De Geest11/2018
53753^188648+9290008Lelio R Paula12/2015
537410^90008-70604990008Patrick De Geest11/2018
53765*2^298991+790006Lelio R Paula08/2014
5377(25*2^298997+1)/326790005Lelio R Paula01/2013
537810^90000+886990001Patrick De Geest12/2009
538010^89999+8293990000Dirk Augustin04/2007
537910^90000-14034390000Patrick De Geest12/2009
538110^89999-19489189999Patrick De Geest11/2009
5382(2^298918+1798)/289983Stefano Morozzi01/2020
538319^70365-7889980Lelio R Paula12/2015
5384NaturalLogarithmOf2(89973)89973Eric W. Weisstein10/2015
53852^298852-6487589964Lelio R Paula11/2013
5386(2^298825+1010)/289955Stefano Morozzi01/2020
538718^71659+3789952Lelio R Paula12/2015
5388(2908*29^61501-3)/789942Curtis Bright05/2015
5389(2^298769+1202)/289939Stefano Morozzi01/2020
539017^73067+2089906Lelio R Paula11/2015
53912^298637-9989899Lelio R Paula10/2012
53929^94188+3*8^94188-2*4^94188-3*2^9418889879Mike Oakes01/2011
5393(2^298558+3654)/289875Stefano Morozzi01/2020
53949*10^89858+1989859Robert Price05/2016
53952^298501+187006789858Enzo Doria05/2016
539611^86280-9889852Lelio R Paula11/2015
53972^298473-11005989850Enzo Doria04/2014
539819^70263-3289850Lelio R Paula12/2015
5399(299*10^89836-17)/389838Robert Price01/2017
54003^188286+1489836Robert Price09/2013
5401(2^298408+450)/289830Stefano Morozzi01/2020
5402gcd(V(1091095),5*F(218219)*(F(218219)+1)+1)89822Serge Batalov04/2015
54032^298367+5890589818Lelio R Paula11/2013
5404(2^298333+3126)/289807Stefano Morozzi01/2020
54052^298319-10965789803Enzo Doria04/2014
54068*10^89800+8189801Robert Price05/2017
5407(2^298249+714)/289782Stefano Morozzi01/2020
540918^71505-9189759Lelio R Paula12/2015
5408(2^298171+1586)/289759Stefano Morozzi01/2020
5410(2^298161+3530)/289756Stefano Morozzi01/2020
5411(7^106187+1)/889738Paul Bourdelais04/2008
54122^298079-10953189731Enzo Doria04/2014
5413117^43380+11689718Norbert Schneider08/2018
5414(22699*2^298016+1)/38589714Lelio R Paula06/2014
5415156*(10^(4*22427)-1)/101-189709Robert Price05/2014
54162^298003-6694589708Lelio R Paula11/2013
5417(23*10^89705-83)/389706Robert Price09/2017
541817^72900-5489700Lelio R Paula11/2015
5419(2^297968+2482)/289698Stefano Morozzi01/2020
54203*2^297956+589695Lelio R Paula08/2014
5421(2^297952+3558)/289693Stefano Morozzi01/2020
542220^68938-1189691Lelio R Paula01/2016
542389*10^89687-789689Robert Price03/2017
5424(297847^16384+1)/289686Richard Fischer08/2019
54252^297923+7778389684Enzo Doria05/2016
5426(2^297893+1694)/289675Stefano Morozzi01/2020
542711^86107-2457600089672Enzo Doria02/2013
54282^297878-11191189671Enzo Doria05/2014
5429(2^297830+3670)/289656Stefano Morozzi01/2020
54307^106084+4089652Lelio R Paula10/2015
5431(2^297815+618)/289651Stefano Morozzi01/2020
5433(86*10^89640-311)/989641Robert Price10/2017
5432(2^297781+2094)/289641Stefano Morozzi01/2020
5434(2^297741+3326)/289629Stefano Morozzi01/2020
5435(2^297724+3606)/289624Stefano Morozzi01/2020
54363*10^89608-5989609Robert Price10/2017
5437(2^297650+3250)/289602Stefano Morozzi01/2020
54383^187780-1103889594Enzo Doria05/2014
5439(13*2^297560-1)/4915178789568Lelio R Paula02/2014
54405^128141-3689567Lelio R Paula10/2015
54414*7^105951+989540Lelio R Paula10/2014
5442(7*10^89539-439)/989539Robert Price09/2017
5443(2^297401+2954)/289527Stefano Morozzi01/2020
5444(2^297403+1670)/289527Stefano Morozzi01/2020
54452^297397+17725789526Enzo Doria05/2016
54472^297346-1624189511Enzo Doria04/2013
5446(5*10^89510+79)/389511Robert Price11/2017
54484^148663-3^14866389505Jean-Louis Charton11/2005
54492^297328-86968810589505Lelio R Paula07/2016
54502^297325-45904389504Enzo Doria05/2015
54512^297310-11239189500Enzo Doria06/2014
54522^297296-11215789496Enzo Doria06/2014
545357^50966-289490Lelio R Paula08/2013
5454(266*10^89482+1)/389484Robert Price02/2016
5455(14*10^89480-101)/389481Robert Price04/2017
54562618^26175+26175^261889466Norbert Schneider01/2020
5457(2^297150+3922)/289451Stefano Morozzi01/2020
5458(2^297141+1842)/289449Stefano Morozzi01/2020
5459(2^297140+1458)/289448Stefano Morozzi01/2020
5460(2^297129+726)/289445Stefano Morozzi01/2020
54612^297122+9989443Lelio R Paula10/2012
5462(3^187435-5)/128689427Lelio R Paula01/2013
5463(2^297037+3522)/289417Stefano Morozzi01/2020
5464(25*10^89413+161)/389414Robert Price01/2017
54652^296990+187069989403Enzo Doria05/2016
54662^296972-101789398Lelio R Paula11/2013
5467(7*10^89383+167)/389384Robert Kinser10/2017
5468(85*10^89375-31)/989376Robert Price11/2015
54699*2^296870+789368Lelio R Paula08/2014
5470100^44683-99^4468389366Robert Price07/2013
54712^296810+7651989349Enzo Doria05/2016
54728^98928+7^(98928+1)89341Robert Price06/2016
5473(3^187247+4)/102789337Lelio R Paula01/2013
5474(3^187235-2)/204589331Lelio R Paula01/2013
54752^296736-43214989327Paul Bourdelais05/2013
54762^296737-11251989327Enzo Doria06/2014
54772^296718-364589322Lelio R Paula11/2013
5478(2^296702+2338)/289316Stefano Morozzi01/2020
54792^296681-1622189310Enzo Doria04/2013
54802^296669-1651389307Enzo Doria04/2013
5481(2^296626+1282)/289294Stefano Morozzi01/2020
54822^296619-1635789292Enzo Doria04/2013
54832^296614-11005189290Enzo Doria04/2014
5484(2^296601+1730)/289286Stefano Morozzi01/2020
5485(3^187138+8)/8314789283Lelio R Paula01/2013
5486(2*10^89279+457)/989279Robert Price01/2017
5487(2^296568+1222)/289276Stefano Morozzi01/2020
548815^75907-2889274Lelio R Paula11/2015
54892^296547-3789270Yves Minet01/2012
54902^296485+19189251Lelio R Paula10/2012
54912^296467-7589246Lelio R Paula10/2012
5492(2^296462+1674)/289244Stefano Morozzi01/2020
54932^296416-10953589231Enzo Doria04/2014
5494(23*2^296406+1)/389228Lelio R Paula01/2013
549566^49037-6589225Norbert Schneider11/2014
54962^296377-1624589219Enzo Doria04/2013
54972^296372-6487589217Lelio R Paula11/2013
54985*6^114648-789215Lelio R Paula10/2014
5499(2^296361+1262)/289214Stefano Morozzi01/2020
55003*10^89206+1389207Robert Price08/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 29 2020 17:41 (Time in France)

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