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 ?
45012^299639-18790201Lelio R Paula10/2012
450210^90199-289190199Patrick De Geest09/2018
45032^299631+18390198Lelio R Paula10/2012
450410^90196-968390196Patrick De Geest09/2018
450510^90193-980990193Patrick De Geest09/2018
4506(21*2^299611-1)/2990192Lelio R Paula02/2014
45072^299567+11390179Lelio R Paula10/2012
45082^299550+18990174Lelio R Paula10/2012
450910^90170-674990170Patrick De Geest09/2018
4510(2^299535+3)/2990168Lelio R Paula01/2013
451110^90160-561390160Patrick De Geest09/2018
4512(97*10^90155-1)/390157Serge Batalov12/2014
45133^188938+868090147Lelio R Paula04/2016
451410^90146-202790146Patrick De Geest09/2018
45166^115840-5590142Lelio R Paula05/2016
4515(5*10^90142-473)/990142Robert Price12/2017
45178*7^106659+590139Lelio R Paula10/2014
45182^299406-1665390131Enzo Doria05/2013
4520208049#+(216091#)/(208049#)90128Makoto Morimoto04/2016
451910^90128-838790128Patrick De Geest09/2018
4521(F(5)^128941-F(4)^128941)/F(3)90126Wayne Halsdorf03/2012
45226^115819-5390125Lelio R Paula05/2016
452310^90123+631390124Patrick De Geest09/2018
45246^115816-1685390123Enzo Doria02/2013
45256^115813-2390121Lelio R Paula05/2016
4526(22*10^90110+161)/390111Robert Price02/2017
4527(2^299330-509203)/6990106Lelio R Paula01/2013
452810^90105-76790105Patrick De Geest09/2018
452910^90104-770390104Patrick De Geest09/2018
453010^90103+915990104Patrick De Geest09/2018
453110^90101-320790101Patrick De Geest09/2018
4532(29*10^90096-17)/390097Erik Branger09/2014
453310^90089-357390089Patrick De Geest09/2018
45342^299247+187052990083Enzo Doria05/2016
453510^90079+160990080Patrick De Geest09/2018
45362^299229-279778390077Enzo Doria04/2016
45372^299220-1631790075Enzo Doria04/2013
453811^86491-135090072Enzo Doria12/2012
453910^90071-123390071Patrick De Geest09/2018
454010^90069-784190069Patrick De Geest09/2018
4541(31*10^90064-1)/390066Robert Price03/2017
454210^90060-83990060Patrick De Geest09/2018
454310^90052+236190053Patrick De Geest09/2018
454410^90047+61990048Patrick De Geest09/2018
4545L(430949)/861899/144038756153990045Serge Batalov07/2017
45462^299112+7395190042Enzo Doria04/2016
45478^99702+7^(99702-1)90040Robert Price02/2016
454810^90038-968790038Patrick De Geest09/2018
45495*10^90033+390034Dmitry Domanov11/2010
455010^90030-146190030Patrick De Geest09/2018
4551243^37738+37738^24390029Norbert Schneider01/2015
455210^90025-870390025Patrick De Geest09/2018
45532^299048-11329790023Enzo Doria07/2014
455410^90015+84990016Patrick De Geest09/2018
455510^90010+681190011Patrick De Geest09/2018
455610^90010-18359790010Patrick De Geest11/2018
455710^90009+5832190010Patrick De Geest11/2018
455810^90008+84790009Patrick De Geest09/2018
455910^90009-35601390009Patrick De Geest11/2018
45613^188648+9290008Lelio R Paula12/2015
456010^90008-70604990008Patrick De Geest11/2018
45625*2^298991+790006Lelio R Paula08/2014
4563(25*2^298997+1)/326790005Lelio R Paula01/2013
456410^90000+886990001Patrick De Geest12/2009
456610^89999+8293990000Dirk Augustin04/2007
456510^90000-14034390000Patrick De Geest12/2009
456710^89999-19489189999Patrick De Geest11/2009
456819^70365-7889980Lelio R Paula12/2015
4569NaturalLogarithmOf2(89973)89973Eric W. Weisstein10/2015
45702^298852-6487589964Lelio R Paula11/2013
457118^71659+3789952Lelio R Paula12/2015
4572(2908*29^61501-3)/789942Curtis Bright05/2015
457317^73067+2089906Lelio R Paula11/2015
45742^298637-9989899Lelio R Paula10/2012
45759^94188+3*8^94188-2*4^94188-3*2^9418889879Mike Oakes01/2011
45769*10^89858+1989859Robert Price05/2016
45772^298501+187006789858Enzo Doria05/2016
457811^86280-9889852Lelio R Paula11/2015
45792^298473-11005989850Enzo Doria04/2014
458019^70263-3289850Lelio R Paula12/2015
4581(299*10^89836-17)/389838Robert Price01/2017
45823^188286+1489836Robert Price09/2013
4583gcd(V(1091095),5*F(218219)*(F(218219)+1)+1)89822Serge Batalov04/2015
45842^298367+5890589818Lelio R Paula11/2013
45852^298319-10965789803Enzo Doria04/2014
45868*10^89800+8189801Robert Price05/2017
458718^71505-9189759Lelio R Paula12/2015
4588(7^106187+1)/889738Paul Bourdelais04/2008
45892^298079-10953189731Enzo Doria04/2014
4590117^43380+11689718Norbert Schneider08/2018
4591(22699*2^298016+1)/38589714Lelio R Paula06/2014
4592156*(10^(4*22427)-1)/101-189709Robert Price05/2014
45932^298003-6694589708Lelio R Paula11/2013
4594(23*10^89705-83)/389706Robert Price09/2017
459517^72900-5489700Lelio R Paula11/2015
45963*2^297956+589695Lelio R Paula08/2014
459720^68938-1189691Lelio R Paula01/2016
459889*10^89687-789689Robert Price03/2017
45992^297923+7778389684Enzo Doria05/2016
460011^86107-2457600089672Enzo Doria02/2013
46012^297878-11191189671Enzo Doria05/2014
46027^106084+4089652Lelio R Paula10/2015
4603(86*10^89640-311)/989641Robert Price10/2017
46043*10^89608-5989609Robert Price10/2017
46053^187780-1103889594Enzo Doria05/2014
4606(13*2^297560-1)/4915178789568Lelio R Paula02/2014
46075^128141-3689567Lelio R Paula10/2015
46084*7^105951+989540Lelio R Paula10/2014
4609(7*10^89539-439)/989539Robert Price09/2017
46102^297397+17725789526Enzo Doria05/2016
46112^297346-1624189511Enzo Doria04/2013
4612(5*10^89510+79)/389511Robert Price11/2017
46144^148663-3^14866389505Jean-Louis Charton11/2005
46132^297328-86968810589505Lelio R Paula07/2016
46152^297325-45904389504Enzo Doria05/2015
46162^297310-11239189500Enzo Doria06/2014
46172^297296-11215789496Enzo Doria06/2014
461857^50966-289490Lelio R Paula08/2013
4619(266*10^89482+1)/389484Robert Price02/2016
4620(14*10^89480-101)/389481Robert Price04/2017
46212^297122+9989443Lelio R Paula10/2012
4622(3^187435-5)/128689427Lelio R Paula01/2013
4623(25*10^89413+161)/389414Robert Price01/2017
46242^296990+187069989403Enzo Doria05/2016
46252^296972-101789398Lelio R Paula11/2013
4626(7*10^89383+167)/389384Robert Kinser10/2017
4627(85*10^89375-31)/989376Robert Price11/2015
46289*2^296870+789368Lelio R Paula08/2014
4629100^44683-99^4468389366Robert Price07/2013
46302^296810+7651989349Enzo Doria05/2016
46318^98928+7^(98928+1)89341Robert Price06/2016
4632(3^187247+4)/102789337Lelio R Paula01/2013
4633(3^187235-2)/204589331Lelio R Paula01/2013
46352^296736-43214989327Paul Bourdelais05/2013
46342^296737-11251989327Enzo Doria06/2014
46362^296718-364589322Lelio R Paula11/2013
46372^296681-1622189310Enzo Doria04/2013
46382^296669-1651389307Enzo Doria04/2013
46392^296619-1635789292Enzo Doria04/2013
46402^296614-11005189290Enzo Doria04/2014
4641(3^187138+8)/8314789283Lelio R Paula01/2013
4642(2*10^89279+457)/989279Robert Price01/2017
464315^75907-2889274Lelio R Paula11/2015
46442^296547-3789270Yves Minet01/2012
46452^296485+19189251Lelio R Paula10/2012
46462^296467-7589246Lelio R Paula10/2012
46472^296416-10953589231Enzo Doria04/2014
4648(23*2^296406+1)/389228Lelio R Paula01/2013
464966^49037-6589225Norbert Schneider11/2014
46502^296377-1624589219Enzo Doria04/2013
46512^296372-6487589217Lelio R Paula11/2013
46525*6^114648-789215Lelio R Paula10/2014
46533*10^89206+1389207Robert Price08/2017
46547*3^186960-489204Lelio R Paula08/2014
46552^296290-11213389193Enzo Doria06/2014
46566^114620-1700389192Enzo Doria02/2013
4657(4*10^89189+41)/989189Robert Price11/2014
46582^296261-16118189184Enzo Doria04/2013
4659(19*2^296269-1)/53062389182Lelio R Paula02/2014
46603^186903-1089176Robert Price09/2013
46617*10^89169-389170Dmitry Domanov11/2010
4663(2^296221-1017)/3589170Lelio R Paula01/2013
4662(43*10^89169+47)/989170Robert Price12/2017
4664(10^89160+29)/389160Serge Batalov12/2014
4665(28*10^89141-97)/389142Robert Price07/2016
46662^296116-73463989140Paul Bourdelais04/2013
46676^114544-13389133Lelio R Paula12/2015
46682^296076-11329789128Enzo Doria07/2014
4669(11*2^296060-1)/21589122Lelio R Paula02/2014
46705*10^89118+8189119Robert Price08/2017
46712^296037-141189117Yves Minet01/2013
46722^296020-260480989111Enzo Doria05/2015
46732^296016+8189110Henri Lifchitz02/2007
46742^296010-1189108Lelio R Paula10/2012
46752^295998-11191189105Enzo Doria05/2014
4676(2^296014+47)/9399114989102Lelio R Paula01/2013
46772^295939-1662189087Enzo Doria04/2013
46782^295934-10969189086Enzo Doria04/2014
4679(185*10^89063+7)/389065Robert Price02/2017
46802^295831+14389055Lelio R Paula10/2012
468131^59713-3089054Theodore Burton02/2007
4682(7*2^295834-1)/2766389052Lelio R Paula02/2014
4683123^42608+289047Lelio R Paula05/2013
46846^114433-114433^689047Norbert Schneider04/2017
46852^295800-45965989045Enzo Doria05/2015
4686(52*10^89037-1)/389039Robert Price02/2017
4687(6^114398-11)/589019Paul Bourdelais11/2011
468811^85470-585089008Enzo Doria02/2013
4689(27*2^295634+1)/468788993Lelio R Paula01/2013
4690(p(18424)#-4)/288985Robert Price09/2017
46912^295564-18988974Lelio R Paula10/2012
46922^295557+7309788972Enzo Doria04/2016
469311^85433-576088970Enzo Doria01/2013
46946*10^88938-9188939Robert Price11/2017
469515^75619-8888935Lelio R Paula11/2015
46962^295385-8588920Lelio R Paula10/2012
46972^295385-1633388920Enzo Doria04/2013
46982^295309+5988897Lelio R Paula10/2012
46992^295288-10979988891Enzo Doria04/2014
470010^88888+17037388889Stefano Morozzi07/2018
470110^88888+27139988889Stefano Morozzi07/2018
470210^88888+37539788889Stefano Morozzi07/2018
470310^88888+54882388889Stefano Morozzi07/2018
470410^88888+82086188889Stefano Morozzi07/2018
470510^88888+120634988889Stefano Morozzi07/2018
470610^88888+129204788889Stefano Morozzi07/2018
470710^88888+145602988889Stefano Morozzi07/2018
470810^88888-49028788888Patrick De Geest09/2018
47092^295245+6588878Lelio R Paula10/2012
4710Padovan(727734)88874Eric W. Weisstein04/2011
471118^70793-1788865Lelio R Paula11/2015
47126^114196-1757388862Enzo Doria02/2013
4713302^35829+35829^30288857Norbert Schneider12/2014
47143^186223+1688851Robert Price10/2013
47153*2^295139+788847Lelio R Paula08/2014
47163^186212-11300888846Enzo Doria07/2014
471787^45803-8688836Norbert Schneider11/2015
47182^295094-11027388833Enzo Doria05/2014
47192^295080+186915188828Enzo Doria05/2016
47202^295027-11340788812Enzo Doria07/2014
4721(2*10^88808-71)/388808Robert Price01/2017
472213^79722-8088806Lelio R Paula11/2015
47233^186103+10488794Lelio R Paula12/2015
4724(3*2^294971+1)/2556588792Lelio R Paula01/2013
47252^294937-11500388785Enzo Doria06/2015
47262^294868-10970988765Enzo Doria04/2014
47272^294864-298588763Yves Minet09/2014
4728(17*10^88761-41)/388762Robert Price09/2017
47292^294754+1501588730Lelio R Paula10/2013
4730(3^185951-7)/2088720Lelio R Paula01/2013
4731(2^294661+5)/44369338388694Lelio R Paula01/2013
4732(10^88680+11)/388680Robert Price11/2014
47332*7^104928-988675Lelio R Paula10/2014
473411^85150+1288675Lelio R Paula11/2015
47358*6^113951+588673Lelio R Paula10/2014
47376^113940-1856388663Enzo Doria03/2013
473638^56123-56123^3888663Norbert Schneider02/2017
47382^294492-6588651Lelio R Paula10/2012
473920^68120-5388627Lelio R Paula01/2016
4740122^42477-12188623Norbert Schneider10/2018
47412^294391-11325788621Enzo Doria07/2014
47425^126784-1547688619Enzo Doria02/2013
47432^294327+988602Lelio R Paula10/2012
47442^294320+1891588600Lelio R Paula10/2013
4745(98*10^88595-89)/9988595Ray Chandler07/2011
4746(17*2^294262-1)/1388582Lelio R Paula02/2014
4747(2*10^88545+7)/988545Erik Branger03/2011
47482^294137-13388545Lelio R Paula10/2012
4749(2^294092-1017)/117188528Lelio R Paula01/2013
47504^147036+147036^4+188525Robert Price04/2014


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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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