PRP Records

Probable Primes Top 10000

(173006 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 ?
37512*10^90597-790598Dmitry Domanov11/2010
3752197^39485+290597Lelio R Paula06/2013
37537^107198+4890593Lelio R Paula04/2016
3754(86*10^90588+121)/990589Robert Price03/2017
37552^300923+5390587Lelio R Paula11/2012
37562^300874+790573Lelio R Paula10/2012
37575^129568-5690565Lelio R Paula04/2016
37582^300847-11283190564Enzo Doria06/2014
37592^300718+25525590526Lelio R Paula02/2016
37602^300637+9590501Lelio R Paula11/2012
37617^107087-2490500Lelio R Paula04/2016
3762(10^90499+3^90499)/1390498Robert Price01/2013
376313^81241+9090498Lelio R Paula06/2016
37646^116273-8590478Lelio R Paula05/2016
37656^116256-1757390465Enzo Doria02/2013
37662^300502+5461590461Lelio R Paula02/2016
3767(13*2^300487+1)/4590456Lelio R Paula09/2013
3768(3^189545-8)/590436Lelio R Paula01/2013
3769(7*2^300406-1)/390432Lelio R Paula02/2014
37704*5^129332+390400Lelio R Paula10/2014
37712^300249-1624590384Enzo Doria04/2013
3772(7*10^90371-313)/990371Robert Price11/2016
37732*6^116118+790358Lelio R Paula10/2014
3774(24737*2^300101+1)/2590343Lelio R Paula06/2014
37754*10^90334-2190335Robert Price04/2016
37762^300019-11033590315Enzo Doria05/2014
37772^299949-100590294Lelio R Paula11/2013
37782^299868-10961390270Enzo Doria04/2014
37795*2^299799-390250Lelio R Paula08/2014
378013^81008-290239Lelio R Paula09/2013
378164^49957-63^4995790232Robert Price07/2013
378210^90227+5628190228Patrick De Geest06/2016
37852^299725+31590227Lelio R Paula11/2013
378310^90227-100000000190227Robert Price05/2016
378410^90227-6876390227Patrick De Geest06/2016
37865^129082+4890225Lelio R Paula03/2016
37872^299699+19590219Lelio R Paula10/2012
3788(55*10^90211-1)/990212Ray Chandler02/2012
37893^189053+28090202Lelio R Paula04/2016
37902^299639-18790201Lelio R Paula10/2012
37912^299631+18390198Lelio R Paula10/2012
3792(21*2^299611-1)/2990192Lelio R Paula02/2014
37932^299567+11390179Lelio R Paula10/2012
37942^299550+18990174Lelio R Paula10/2012
3795(2^299535+3)/2990168Lelio R Paula01/2013
3796(97*10^90155-1)/390157Serge Batalov12/2014
37973^188938+868090147Lelio R Paula04/2016
37986^115840-5590142Lelio R Paula05/2016
37998*7^106659+590139Lelio R Paula10/2014
38002^299406-1665390131Enzo Doria05/2013
3801208049#+(216091#)/(208049#)90128Makoto Morimoto04/2016
3802(F(5)^128941-F(4)^128941)/F(3)90126Wayne Halsdorf03/2012
38036^115819-5390125Lelio R Paula05/2016
38046^115816-1685390123Enzo Doria02/2013
38056^115813-2390121Lelio R Paula05/2016
3806(22*10^90110+161)/390111Robert Price02/2017
3807(2^299330-509203)/6990106Lelio R Paula01/2013
3808(29*10^90096-17)/390097Erik Branger09/2014
38092^299247+187052990083Enzo Doria05/2016
38102^299229-279778390077Enzo Doria04/2016
38112^299220-1631790075Enzo Doria04/2013
381211^86491-135090072Enzo Doria12/2012
3813(31*10^90064-1)/390066Robert Price03/2017
38142^299112+7395190042Enzo Doria04/2016
38158^99702+7^(99702-1)90040Robert Price02/2016
38165*10^90033+390034Dmitry Domanov11/2010
3817243^37738+37738^24390029Norbert Schneider01/2015
38182^299048-11329790023Enzo Doria07/2014
38193^188648+9290008Lelio R Paula12/2015
38205*2^298991+790006Lelio R Paula08/2014
3821(25*2^298997+1)/326790005Lelio R Paula01/2013
382210^90000+886990001Patrick De Geest12/2009
382410^89999+8293990000Dirk Augustin04/2007
382310^90000-14034390000Patrick De Geest12/2009
382510^89999-19489189999Patrick De Geest11/2009
382619^70365-7889980Lelio R Paula12/2015
3827NaturalLogarithmOf2(89973)89973Eric W. Weisstein10/2015
38282^298852-6487589964Lelio R Paula11/2013
382918^71659+3789952Lelio R Paula12/2015
3830(2908*29^61501-3)/789942Curtis Bright05/2015
383117^73067+2089906Lelio R Paula11/2015
38322^298637-9989899Lelio R Paula10/2012
38339^94188+3*8^94188-2*4^94188-3*2^9418889879Mike Oakes01/2011
38349*10^89858+1989859Robert Price05/2016
38352^298501+187006789858Enzo Doria05/2016
383611^86280-9889852Lelio R Paula11/2015
38372^298473-11005989850Enzo Doria04/2014
383819^70263-3289850Lelio R Paula12/2015
3839(299*10^89836-17)/389838Robert Price01/2017
38403^188286+1489836Robert Price09/2013
3841gcd(V(1091095),5*F(218219)*(F(218219)+1)+1)89822Serge Batalov04/2015
38422^298367+5890589818Lelio R Paula11/2013
38432^298319-10965789803Enzo Doria04/2014
384418^71505-9189759Lelio R Paula12/2015
3845(7^106187+1)/889738Paul Bourdelais04/2008
38462^298079-10953189731Enzo Doria04/2014
3847(22699*2^298016+1)/38589714Lelio R Paula06/2014
3848156*(10^(4*22427)-1)/101-189709Robert Price05/2014
38492^298003-6694589708Lelio R Paula11/2013
385017^72900-5489700Lelio R Paula11/2015
38513*2^297956+589695Lelio R Paula08/2014
385220^68938-1189691Lelio R Paula01/2016
385389*10^89687-789689Robert Price03/2017
38542^297923+7778389684Enzo Doria05/2016
385511^86107-2457600089672Enzo Doria02/2013
38562^297878-11191189671Enzo Doria05/2014
38577^106084+4089652Lelio R Paula10/2015
38583^187780-1103889594Enzo Doria05/2014
3859(13*2^297560-1)/4915178789568Lelio R Paula02/2014
38605^128141-3689567Lelio R Paula10/2015
38614*7^105951+989540Lelio R Paula10/2014
38622^297397+17725789526Enzo Doria05/2016
38632^297346-1624189511Enzo Doria04/2013
38654^148663-3^14866389505Jean-Louis Charton11/2005
38642^297328-86968810589505Lelio R Paula07/2016
38662^297325-45904389504Enzo Doria05/2015
38672^297310-11239189500Enzo Doria06/2014
38682^297296-11215789496Enzo Doria06/2014
386957^50966-289490Lelio R Paula08/2013
3870(266*10^89482+1)/389484Robert Price02/2016
3871(14*10^89480-101)/389481Robert Price04/2017
38722^297122+9989443Lelio R Paula10/2012
3873(3^187435-5)/128689427Lelio R Paula01/2013
3874(25*10^89413+161)/389414Robert Price01/2017
38752^296990+187069989403Enzo Doria05/2016
38762^296972-101789398Lelio R Paula11/2013
3877(85*10^89375-31)/989376Robert Price11/2015
38789*2^296870+789368Lelio R Paula08/2014
3879100^44683-99^4468389366Robert Price07/2013
38802^296810+7651989349Enzo Doria05/2016
38818^98928+7^(98928+1)89341Robert Price06/2016
3882(3^187247+4)/102789337Lelio R Paula01/2013
3883(3^187235-2)/204589331Lelio R Paula01/2013
38852^296736-43214989327Paul Bourdelais05/2013
38842^296737-11251989327Enzo Doria06/2014
38862^296718-364589322Lelio R Paula11/2013
38872^296681-1622189310Enzo Doria04/2013
38882^296669-1651389307Enzo Doria04/2013
38892^296619-1635789292Enzo Doria04/2013
38902^296614-11005189290Enzo Doria04/2014
3891(3^187138+8)/8314789283Lelio R Paula01/2013
3892(2*10^89279+457)/989279Robert Price01/2017
389315^75907-2889274Lelio R Paula11/2015
38942^296547-3789270Yves Minet01/2012
38952^296485+19189251Lelio R Paula10/2012
38962^296467-7589246Lelio R Paula10/2012
38972^296416-10953589231Enzo Doria04/2014
3898(23*2^296406+1)/389228Lelio R Paula01/2013
389966^49037-6589225Norbert Schneider11/2014
39002^296377-1624589219Enzo Doria04/2013
39012^296372-6487589217Lelio R Paula11/2013
39025*6^114648-789215Lelio R Paula10/2014
39037*3^186960-489204Lelio R Paula08/2014
39042^296290-11213389193Enzo Doria06/2014
39056^114620-1700389192Enzo Doria02/2013
3906(4*10^89189+41)/989189Robert Price11/2014
39072^296261-16118189184Enzo Doria04/2013
3908(19*2^296269-1)/53062389182Lelio R Paula02/2014
39093^186903-1089176Robert Price09/2013
39117*10^89169-389170Dmitry Domanov11/2010
3910(2^296221-1017)/3589170Lelio R Paula01/2013
3912(10^89160+29)/389160Serge Batalov12/2014
3913(28*10^89141-97)/389142Robert Price07/2016
39142^296116-73463989140Paul Bourdelais04/2013
39156^114544-13389133Lelio R Paula12/2015
39162^296076-11329789128Enzo Doria07/2014
3917(11*2^296060-1)/21589122Lelio R Paula02/2014
39182^296037-141189117Yves Minet01/2013
39192^296020-260480989111Enzo Doria05/2015
39202^296016+8189110Henri Lifchitz02/2007
39212^296010-1189108Lelio R Paula10/2012
39222^295998-11191189105Enzo Doria05/2014
3923(2^296014+47)/9399114989102Lelio R Paula01/2013
39242^295939-1662189087Enzo Doria04/2013
39252^295934-10969189086Enzo Doria04/2014
3926(185*10^89063+7)/389065Robert Price02/2017
39272^295831+14389055Lelio R Paula10/2012
392831^59713-3089054Theodore Burton02/2007
3929(7*2^295834-1)/2766389052Lelio R Paula02/2014
3931123^42608+289047Lelio R Paula05/2013
39306^114433-114433^689047Norbert Schneider04/2017
39322^295800-45965989045Enzo Doria05/2015
3933(52*10^89037-1)/389039Robert Price02/2017
3934(6^114398-11)/589019Paul Bourdelais11/2011
393511^85470-585089008Enzo Doria02/2013
3936(27*2^295634+1)/468788993Lelio R Paula01/2013
39372^295564-18988974Lelio R Paula10/2012
39382^295557+7309788972Enzo Doria04/2016
393911^85433-576088970Enzo Doria01/2013
394015^75619-8888935Lelio R Paula11/2015
39412^295385-8588920Lelio R Paula10/2012
39422^295385-1633388920Enzo Doria04/2013
39432^295309+5988897Lelio R Paula10/2012
39442^295288-10979988891Enzo Doria04/2014
39452^295245+6588878Lelio R Paula10/2012
3946Padovan(727734)88874Eric W. Weisstein04/2011
394718^70793-1788865Lelio R Paula11/2015
39486^114196-1757388862Enzo Doria02/2013
3949302^35829+35829^30288857Norbert Schneider12/2014
39503^186223+1688851Robert Price10/2013
39513*2^295139+788847Lelio R Paula08/2014
39523^186212-11300888846Enzo Doria07/2014
395387^45803-8688836Norbert Schneider11/2015
39542^295094-11027388833Enzo Doria05/2014
39552^295080+186915188828Enzo Doria05/2016
39562^295027-11340788812Enzo Doria07/2014
3957(2*10^88808-71)/388808Robert Price01/2017
395813^79722-8088806Lelio R Paula11/2015
39593^186103+10488794Lelio R Paula12/2015
3960(3*2^294971+1)/2556588792Lelio R Paula01/2013
39612^294937-11500388785Enzo Doria06/2015
39622^294868-10970988765Enzo Doria04/2014
39632^294864-298588763Yves Minet09/2014
39642^294754+1501588730Lelio R Paula10/2013
3965(3^185951-7)/2088720Lelio R Paula01/2013
3966(2^294661+5)/44369338388694Lelio R Paula01/2013
3967(10^88680+11)/388680Robert Price11/2014
39682*7^104928-988675Lelio R Paula10/2014
396911^85150+1288675Lelio R Paula11/2015
39708*6^113951+588673Lelio R Paula10/2014
39716^113940-1856388663Enzo Doria03/2013
397238^56123-56123^3888663Norbert Schneider02/2017
39732^294492-6588651Lelio R Paula10/2012
397420^68120-5388627Lelio R Paula01/2016
39752^294391-11325788621Enzo Doria07/2014
39765^126784-1547688619Enzo Doria02/2013
39772^294327+988602Lelio R Paula10/2012
39782^294320+1891588600Lelio R Paula10/2013
3979(98*10^88595-89)/9988595Ray Chandler07/2011
3980(17*2^294262-1)/1388582Lelio R Paula02/2014
3981(2*10^88545+7)/988545Erik Branger03/2011
39822^294137-13388545Lelio R Paula10/2012
3983(2^294092-1017)/117188528Lelio R Paula01/2013
39844^147036+147036^4+188525Robert Price04/2014
3985(14^77213-5^77213)/988496Robert Price04/2013
39862^293965+279337788493Enzo Doria03/2016
398711^84971-15088489Enzo Doria08/2012
3988(2^293956-1017)/3985137669667788476Lelio R Paula01/2013
398911^84958-219088475Enzo Doria12/2012
39902^293880-11134788467Enzo Doria05/2014
3991(106*10^88459-1)/388461Serge Batalov12/2014
399211^84908-168088423Enzo Doria12/2012
39932^293679-11207588407Enzo Doria06/2014
39946^113608-6588405Lelio R Paula12/2015
39952^293624+8287588390Lelio R Paula10/2013
39962^293612-11233788387Enzo Doria06/2014
3997gcd(V(1062695),5*F(212539)*(F(212539)-1)+1)88383Serge Batalov04/2015
39985*10^88377+7788378Robert Price06/2016
3999(5*2^293526+1)/30388359Lelio R Paula01/2013
40002^293461-278584388341Enzo Doria03/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

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