PRP Records

Probable Primes Top 10000

(247113 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 ?
4501(2^299535+3)/2990168Lelio R Paula01/2013
450210^90160-561390160Patrick De Geest09/2018
4503(97*10^90155-1)/390157Serge Batalov12/2014
45043^188938+868090147Lelio R Paula04/2016
450510^90146-202790146Patrick De Geest09/2018
45076^115840-5590142Lelio R Paula05/2016
4506(5*10^90142-473)/990142Robert Price12/2017
45088*7^106659+590139Lelio R Paula10/2014
45092^299406-1665390131Enzo Doria05/2013
4511208049#+(216091#)/(208049#)90128Makoto Morimoto04/2016
451010^90128-838790128Patrick De Geest09/2018
4512(F(5)^128941-F(4)^128941)/F(3)90126Wayne Halsdorf03/2012
45136^115819-5390125Lelio R Paula05/2016
451410^90123+631390124Patrick De Geest09/2018
45156^115816-1685390123Enzo Doria02/2013
45166^115813-2390121Lelio R Paula05/2016
4517(22*10^90110+161)/390111Robert Price02/2017
4518(2^299330-509203)/6990106Lelio R Paula01/2013
451910^90105-76790105Patrick De Geest09/2018
452010^90104-770390104Patrick De Geest09/2018
452110^90103+915990104Patrick De Geest09/2018
452210^90101-320790101Patrick De Geest09/2018
4523(29*10^90096-17)/390097Erik Branger09/2014
452410^90089-357390089Patrick De Geest09/2018
45252^299247+187052990083Enzo Doria05/2016
452610^90079+160990080Patrick De Geest09/2018
45272^299229-279778390077Enzo Doria04/2016
45282^299220-1631790075Enzo Doria04/2013
452911^86491-135090072Enzo Doria12/2012
453010^90071-123390071Patrick De Geest09/2018
453110^90069-784190069Patrick De Geest09/2018
4532(31*10^90064-1)/390066Robert Price03/2017
453310^90060-83990060Patrick De Geest09/2018
453410^90052+236190053Patrick De Geest09/2018
453510^90047+61990048Patrick De Geest09/2018
4536L(430949)/861899/144038756153990045Serge Batalov07/2017
45372^299112+7395190042Enzo Doria04/2016
45388^99702+7^(99702-1)90040Robert Price02/2016
453910^90038-968790038Patrick De Geest09/2018
45405*10^90033+390034Dmitry Domanov11/2010
454110^90030-146190030Patrick De Geest09/2018
4542243^37738+37738^24390029Norbert Schneider01/2015
454310^90025-870390025Patrick De Geest09/2018
45442^299048-11329790023Enzo Doria07/2014
454510^90015+84990016Patrick De Geest09/2018
454610^90010+681190011Patrick De Geest09/2018
454710^90010-18359790010Patrick De Geest11/2018
454810^90009+5832190010Patrick De Geest11/2018
454910^90008+84790009Patrick De Geest09/2018
455010^90009-35601390009Patrick De Geest11/2018
45523^188648+9290008Lelio R Paula12/2015
455110^90008-70604990008Patrick De Geest11/2018
45535*2^298991+790006Lelio R Paula08/2014
4554(25*2^298997+1)/326790005Lelio R Paula01/2013
455510^90000+886990001Patrick De Geest12/2009
455710^89999+8293990000Dirk Augustin04/2007
455610^90000-14034390000Patrick De Geest12/2009
455810^89999-19489189999Patrick De Geest11/2009
455919^70365-7889980Lelio R Paula12/2015
4560NaturalLogarithmOf2(89973)89973Eric W. Weisstein10/2015
45612^298852-6487589964Lelio R Paula11/2013
456218^71659+3789952Lelio R Paula12/2015
4563(2908*29^61501-3)/789942Curtis Bright05/2015
456417^73067+2089906Lelio R Paula11/2015
45652^298637-9989899Lelio R Paula10/2012
45669^94188+3*8^94188-2*4^94188-3*2^9418889879Mike Oakes01/2011
45679*10^89858+1989859Robert Price05/2016
45682^298501+187006789858Enzo Doria05/2016
456911^86280-9889852Lelio R Paula11/2015
45702^298473-11005989850Enzo Doria04/2014
457119^70263-3289850Lelio R Paula12/2015
4572(299*10^89836-17)/389838Robert Price01/2017
45733^188286+1489836Robert Price09/2013
4574gcd(V(1091095),5*F(218219)*(F(218219)+1)+1)89822Serge Batalov04/2015
45752^298367+5890589818Lelio R Paula11/2013
45762^298319-10965789803Enzo Doria04/2014
45778*10^89800+8189801Robert Price05/2017
457818^71505-9189759Lelio R Paula12/2015
4579(7^106187+1)/889738Paul Bourdelais04/2008
45802^298079-10953189731Enzo Doria04/2014
4581117^43380+11689718Norbert Schneider08/2018
4582(22699*2^298016+1)/38589714Lelio R Paula06/2014
4583156*(10^(4*22427)-1)/101-189709Robert Price05/2014
45842^298003-6694589708Lelio R Paula11/2013
4585(23*10^89705-83)/389706Robert Price09/2017
458617^72900-5489700Lelio R Paula11/2015
45873*2^297956+589695Lelio R Paula08/2014
458820^68938-1189691Lelio R Paula01/2016
458989*10^89687-789689Robert Price03/2017
45902^297923+7778389684Enzo Doria05/2016
459111^86107-2457600089672Enzo Doria02/2013
45922^297878-11191189671Enzo Doria05/2014
45937^106084+4089652Lelio R Paula10/2015
4594(86*10^89640-311)/989641Robert Price10/2017
45953*10^89608-5989609Robert Price10/2017
45963^187780-1103889594Enzo Doria05/2014
4597(13*2^297560-1)/4915178789568Lelio R Paula02/2014
45985^128141-3689567Lelio R Paula10/2015
45994*7^105951+989540Lelio R Paula10/2014
4600(7*10^89539-439)/989539Robert Price09/2017
46012^297397+17725789526Enzo Doria05/2016
46022^297346-1624189511Enzo Doria04/2013
4603(5*10^89510+79)/389511Robert Price11/2017
46054^148663-3^14866389505Jean-Louis Charton11/2005
46042^297328-86968810589505Lelio R Paula07/2016
46062^297325-45904389504Enzo Doria05/2015
46072^297310-11239189500Enzo Doria06/2014
46082^297296-11215789496Enzo Doria06/2014
460957^50966-289490Lelio R Paula08/2013
4610(266*10^89482+1)/389484Robert Price02/2016
4611(14*10^89480-101)/389481Robert Price04/2017
46122^297122+9989443Lelio R Paula10/2012
4613(3^187435-5)/128689427Lelio R Paula01/2013
4614(25*10^89413+161)/389414Robert Price01/2017
46152^296990+187069989403Enzo Doria05/2016
46162^296972-101789398Lelio R Paula11/2013
4617(7*10^89383+167)/389384Robert Kinser10/2017
4618(85*10^89375-31)/989376Robert Price11/2015
46199*2^296870+789368Lelio R Paula08/2014
4620100^44683-99^4468389366Robert Price07/2013
46212^296810+7651989349Enzo Doria05/2016
46228^98928+7^(98928+1)89341Robert Price06/2016
4623(3^187247+4)/102789337Lelio R Paula01/2013
4624(3^187235-2)/204589331Lelio R Paula01/2013
46262^296736-43214989327Paul Bourdelais05/2013
46252^296737-11251989327Enzo Doria06/2014
46272^296718-364589322Lelio R Paula11/2013
46282^296681-1622189310Enzo Doria04/2013
46292^296669-1651389307Enzo Doria04/2013
46302^296619-1635789292Enzo Doria04/2013
46312^296614-11005189290Enzo Doria04/2014
4632(3^187138+8)/8314789283Lelio R Paula01/2013
4633(2*10^89279+457)/989279Robert Price01/2017
463415^75907-2889274Lelio R Paula11/2015
46352^296547-3789270Yves Minet01/2012
46362^296485+19189251Lelio R Paula10/2012
46372^296467-7589246Lelio R Paula10/2012
46382^296416-10953589231Enzo Doria04/2014
4639(23*2^296406+1)/389228Lelio R Paula01/2013
464066^49037-6589225Norbert Schneider11/2014
46412^296377-1624589219Enzo Doria04/2013
46422^296372-6487589217Lelio R Paula11/2013
46435*6^114648-789215Lelio R Paula10/2014
46443*10^89206+1389207Robert Price08/2017
46457*3^186960-489204Lelio R Paula08/2014
46462^296290-11213389193Enzo Doria06/2014
46476^114620-1700389192Enzo Doria02/2013
4648(4*10^89189+41)/989189Robert Price11/2014
46492^296261-16118189184Enzo Doria04/2013
4650(19*2^296269-1)/53062389182Lelio R Paula02/2014
46513^186903-1089176Robert Price09/2013
46537*10^89169-389170Dmitry Domanov11/2010
4654(2^296221-1017)/3589170Lelio R Paula01/2013
4652(43*10^89169+47)/989170Robert Price12/2017
4655(10^89160+29)/389160Serge Batalov12/2014
4656(28*10^89141-97)/389142Robert Price07/2016
46572^296116-73463989140Paul Bourdelais04/2013
46586^114544-13389133Lelio R Paula12/2015
46592^296076-11329789128Enzo Doria07/2014
4660(11*2^296060-1)/21589122Lelio R Paula02/2014
46615*10^89118+8189119Robert Price08/2017
46622^296037-141189117Yves Minet01/2013
46632^296020-260480989111Enzo Doria05/2015
46642^296016+8189110Henri Lifchitz02/2007
46652^296010-1189108Lelio R Paula10/2012
46662^295998-11191189105Enzo Doria05/2014
4667(2^296014+47)/9399114989102Lelio R Paula01/2013
46682^295939-1662189087Enzo Doria04/2013
46692^295934-10969189086Enzo Doria04/2014
4670(185*10^89063+7)/389065Robert Price02/2017
46712^295831+14389055Lelio R Paula10/2012
467231^59713-3089054Theodore Burton02/2007
4673(7*2^295834-1)/2766389052Lelio R Paula02/2014
4675123^42608+289047Lelio R Paula05/2013
46746^114433-114433^689047Norbert Schneider04/2017
46762^295800-45965989045Enzo Doria05/2015
4677(52*10^89037-1)/389039Robert Price02/2017
4678(6^114398-11)/589019Paul Bourdelais11/2011
467911^85470-585089008Enzo Doria02/2013
4680(27*2^295634+1)/468788993Lelio R Paula01/2013
4681(p(18424)#-4)/288985Robert Price09/2017
46822^295564-18988974Lelio R Paula10/2012
46832^295557+7309788972Enzo Doria04/2016
468411^85433-576088970Enzo Doria01/2013
46856*10^88938-9188939Robert Price11/2017
468615^75619-8888935Lelio R Paula11/2015
46872^295385-8588920Lelio R Paula10/2012
46882^295385-1633388920Enzo Doria04/2013
46892^295309+5988897Lelio R Paula10/2012
46902^295288-10979988891Enzo Doria04/2014
469110^88888+17037388889Stefano Morozzi07/2018
469210^88888+27139988889Stefano Morozzi07/2018
469310^88888+37539788889Stefano Morozzi07/2018
469410^88888+54882388889Stefano Morozzi07/2018
469510^88888+82086188889Stefano Morozzi07/2018
469610^88888+120634988889Stefano Morozzi07/2018
469710^88888+129204788889Stefano Morozzi07/2018
469810^88888+145602988889Stefano Morozzi07/2018
469910^88888-49028788888Patrick De Geest09/2018
47002^295245+6588878Lelio R Paula10/2012
4701Padovan(727734)88874Eric W. Weisstein04/2011
470218^70793-1788865Lelio R Paula11/2015
47036^114196-1757388862Enzo Doria02/2013
4704302^35829+35829^30288857Norbert Schneider12/2014
47053^186223+1688851Robert Price10/2013
47063*2^295139+788847Lelio R Paula08/2014
47073^186212-11300888846Enzo Doria07/2014
470887^45803-8688836Norbert Schneider11/2015
47092^295094-11027388833Enzo Doria05/2014
47102^295080+186915188828Enzo Doria05/2016
47112^295027-11340788812Enzo Doria07/2014
4712(2*10^88808-71)/388808Robert Price01/2017
471313^79722-8088806Lelio R Paula11/2015
47143^186103+10488794Lelio R Paula12/2015
4715(3*2^294971+1)/2556588792Lelio R Paula01/2013
47162^294937-11500388785Enzo Doria06/2015
47172^294868-10970988765Enzo Doria04/2014
47182^294864-298588763Yves Minet09/2014
4719(17*10^88761-41)/388762Robert Price09/2017
47202^294754+1501588730Lelio R Paula10/2013
4721(3^185951-7)/2088720Lelio R Paula01/2013
4722(2^294661+5)/44369338388694Lelio R Paula01/2013
4723(10^88680+11)/388680Robert Price11/2014
47242*7^104928-988675Lelio R Paula10/2014
472511^85150+1288675Lelio R Paula11/2015
47268*6^113951+588673Lelio R Paula10/2014
47286^113940-1856388663Enzo Doria03/2013
472738^56123-56123^3888663Norbert Schneider02/2017
47292^294492-6588651Lelio R Paula10/2012
473020^68120-5388627Lelio R Paula01/2016
4731122^42477-12188623Norbert Schneider10/2018
47322^294391-11325788621Enzo Doria07/2014
47335^126784-1547688619Enzo Doria02/2013
47342^294327+988602Lelio R Paula10/2012
47352^294320+1891588600Lelio R Paula10/2013
4736(98*10^88595-89)/9988595Ray Chandler07/2011
4737(17*2^294262-1)/1388582Lelio R Paula02/2014
4739(2*10^88545+7)/988545Erik Branger03/2011
47382^294137-13388545Lelio R Paula10/2012
4740(2^294092-1017)/117188528Lelio R Paula01/2013
47414^147036+147036^4+188525Robert Price04/2014
4742(14^77213-5^77213)/988496Robert Price04/2013
47432^293965+279337788493Enzo Doria03/2016
474411^84971-15088489Enzo Doria08/2012
474548^52626-4788478Norbert Schneider08/2018
4746(2^293956-1017)/3985137669667788476Lelio R Paula01/2013
474711^84958-219088475Enzo Doria12/2012
47482^293880-11134788467Enzo Doria05/2014
4749(106*10^88459-1)/388461Serge Batalov12/2014
475010^88457+27873388458Patrick De Geest07/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 11 2018 05:54 (Time in France)

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