PRP Records

Probable Primes Top 10000

(172751 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
3751(21*2^299611-1)/2990192Lelio R Paula02/2014
37522^299567+11390179Lelio R Paula10/2012
37532^299550+18990174Lelio R Paula10/2012
3754(2^299535+3)/2990168Lelio R Paula01/2013
3755(97*10^90155-1)/390157Serge Batalov12/2014
37563^188938+868090147Lelio R Paula04/2016
37576^115840-5590142Lelio R Paula05/2016
37588*7^106659+590139Lelio R Paula10/2014
37592^299406-1665390131Enzo Doria05/2013
3760208049#+(216091#)/(208049#)90128Makoto Morimoto04/2016
3761(F(5)^128941-F(4)^128941)/F(3)90126Wayne Halsdorf03/2012
37626^115819-5390125Lelio R Paula05/2016
37636^115816-1685390123Enzo Doria02/2013
37646^115813-2390121Lelio R Paula05/2016
3765(22*10^90110+161)/390111Robert Price02/2017
3766(2^299330-509203)/6990106Lelio R Paula01/2013
3767(29*10^90096-17)/390097Erik Branger09/2014
37682^299247+187052990083Enzo Doria05/2016
37692^299229-279778390077Enzo Doria04/2016
37702^299220-1631790075Enzo Doria04/2013
377111^86491-135090072Enzo Doria12/2012
3772(31*10^90064-1)/390066Robert Price03/2017
37732^299112+7395190042Enzo Doria04/2016
37748^99702+7^(99702-1)90040Robert Price02/2016
37755*10^90033+390034Dmitry Domanov11/2010
3776243^37738+37738^24390029Norbert Schneider01/2015
37772^299048-11329790023Enzo Doria07/2014
37783^188648+9290008Lelio R Paula12/2015
37795*2^298991+790006Lelio R Paula08/2014
3780(25*2^298997+1)/326790005Lelio R Paula01/2013
378110^90000+886990001Patrick De Geest12/2009
378310^89999+8293990000Dirk Augustin04/2007
378210^90000-14034390000Patrick De Geest12/2009
378410^89999-19489189999Patrick De Geest11/2009
378519^70365-7889980Lelio R Paula12/2015
3786NaturalLogarithmOf2(89973)89973Eric W. Weisstein10/2015
37872^298852-6487589964Lelio R Paula11/2013
378818^71659+3789952Lelio R Paula12/2015
3789(2908*29^61501-3)/789942Curtis Bright05/2015
379017^73067+2089906Lelio R Paula11/2015
37912^298637-9989899Lelio R Paula10/2012
37929^94188+3*8^94188-2*4^94188-3*2^9418889879Mike Oakes01/2011
37939*10^89858+1989859Robert Price05/2016
37942^298501+187006789858Enzo Doria05/2016
379511^86280-9889852Lelio R Paula11/2015
37962^298473-11005989850Enzo Doria04/2014
379719^70263-3289850Lelio R Paula12/2015
3798(299*10^89836-17)/389838Robert Price01/2017
37993^188286+1489836Robert Price09/2013
3800gcd(V(1091095),5*F(218219)*(F(218219)+1)+1)89822Serge Batalov04/2015
38012^298367+5890589818Lelio R Paula11/2013
38022^298319-10965789803Enzo Doria04/2014
380318^71505-9189759Lelio R Paula12/2015
3804(7^106187+1)/889738Paul Bourdelais04/2008
38052^298079-10953189731Enzo Doria04/2014
3806(22699*2^298016+1)/38589714Lelio R Paula06/2014
3807156*(10^(4*22427)-1)/101-189709Robert Price05/2014
38082^298003-6694589708Lelio R Paula11/2013
380917^72900-5489700Lelio R Paula11/2015
38103*2^297956+589695Lelio R Paula08/2014
381120^68938-1189691Lelio R Paula01/2016
381289*10^89687-789689Robert Price03/2017
38132^297923+7778389684Enzo Doria05/2016
381411^86107-2457600089672Enzo Doria02/2013
38152^297878-11191189671Enzo Doria05/2014
38167^106084+4089652Lelio R Paula10/2015
38173^187780-1103889594Enzo Doria05/2014
3818(13*2^297560-1)/4915178789568Lelio R Paula02/2014
38195^128141-3689567Lelio R Paula10/2015
38204*7^105951+989540Lelio R Paula10/2014
38212^297397+17725789526Enzo Doria05/2016
38222^297346-1624189511Enzo Doria04/2013
38244^148663-3^14866389505Jean-Louis Charton11/2005
38232^297328-86968810589505Lelio R Paula07/2016
38252^297325-45904389504Enzo Doria05/2015
38262^297310-11239189500Enzo Doria06/2014
38272^297296-11215789496Enzo Doria06/2014
382857^50966-289490Lelio R Paula08/2013
3829(266*10^89482+1)/389484Robert Price02/2016
3830(14*10^89480-101)/389481Robert Price04/2017
38312^297122+9989443Lelio R Paula10/2012
3832(3^187435-5)/128689427Lelio R Paula01/2013
3833(25*10^89413+161)/389414Robert Price01/2017
38342^296990+187069989403Enzo Doria05/2016
38352^296972-101789398Lelio R Paula11/2013
3836(85*10^89375-31)/989376Robert Price11/2015
38379*2^296870+789368Lelio R Paula08/2014
3838100^44683-99^4468389366Robert Price07/2013
38392^296810+7651989349Enzo Doria05/2016
38408^98928+7^(98928+1)89341Robert Price06/2016
3841(3^187247+4)/102789337Lelio R Paula01/2013
3842(3^187235-2)/204589331Lelio R Paula01/2013
38432^296736-43214989327Paul Bourdelais05/2013
38442^296737-11251989327Enzo Doria06/2014
38452^296718-364589322Lelio R Paula11/2013
38462^296681-1622189310Enzo Doria04/2013
38472^296669-1651389307Enzo Doria04/2013
38482^296619-1635789292Enzo Doria04/2013
38492^296614-11005189290Enzo Doria04/2014
3850(3^187138+8)/8314789283Lelio R Paula01/2013
3851(2*10^89279+457)/989279Robert Price01/2017
385215^75907-2889274Lelio R Paula11/2015
38532^296547-3789270Yves Minet01/2012
38542^296485+19189251Lelio R Paula10/2012
38552^296467-7589246Lelio R Paula10/2012
38562^296416-10953589231Enzo Doria04/2014
3857(23*2^296406+1)/389228Lelio R Paula01/2013
385866^49037-6589225Norbert Schneider11/2014
38592^296377-1624589219Enzo Doria04/2013
38602^296372-6487589217Lelio R Paula11/2013
38615*6^114648-789215Lelio R Paula10/2014
38627*3^186960-489204Lelio R Paula08/2014
38632^296290-11213389193Enzo Doria06/2014
38646^114620-1700389192Enzo Doria02/2013
3865(4*10^89189+41)/989189Robert Price11/2014
38662^296261-16118189184Enzo Doria04/2013
3867(19*2^296269-1)/53062389182Lelio R Paula02/2014
38683^186903-1089176Robert Price09/2013
38707*10^89169-389170Dmitry Domanov11/2010
3869(2^296221-1017)/3589170Lelio R Paula01/2013
3871(10^89160+29)/389160Serge Batalov12/2014
3872(28*10^89141-97)/389142Robert Price07/2016
38732^296116-73463989140Paul Bourdelais04/2013
38746^114544-13389133Lelio R Paula12/2015
38752^296076-11329789128Enzo Doria07/2014
3876(11*2^296060-1)/21589122Lelio R Paula02/2014
38772^296037-141189117Yves Minet01/2013
38782^296020-260480989111Enzo Doria05/2015
38792^296016+8189110Henri Lifchitz02/2007
38802^296010-1189108Lelio R Paula10/2012
38812^295998-11191189105Enzo Doria05/2014
3882(2^296014+47)/9399114989102Lelio R Paula01/2013
38832^295939-1662189087Enzo Doria04/2013
38842^295934-10969189086Enzo Doria04/2014
3885(185*10^89063+7)/389065Robert Price02/2017
38862^295831+14389055Lelio R Paula10/2012
388731^59713-3089054Theodore Burton02/2007
3888(7*2^295834-1)/2766389052Lelio R Paula02/2014
3889123^42608+289047Lelio R Paula05/2013
38902^295800-45965989045Enzo Doria05/2015
3891(52*10^89037-1)/389039Robert Price02/2017
3892(6^114398-11)/589019Paul Bourdelais11/2011
389311^85470-585089008Enzo Doria02/2013
3894(27*2^295634+1)/468788993Lelio R Paula01/2013
38952^295564-18988974Lelio R Paula10/2012
38962^295557+7309788972Enzo Doria04/2016
389711^85433-576088970Enzo Doria01/2013
389815^75619-8888935Lelio R Paula11/2015
38992^295385-8588920Lelio R Paula10/2012
39002^295385-1633388920Enzo Doria04/2013
39012^295309+5988897Lelio R Paula10/2012
39022^295288-10979988891Enzo Doria04/2014
39032^295245+6588878Lelio R Paula10/2012
3904Padovan(727734)88874Eric W. Weisstein04/2011
390518^70793-1788865Lelio R Paula11/2015
39066^114196-1757388862Enzo Doria02/2013
3907302^35829+35829^30288857Norbert Schneider12/2014
39083^186223+1688851Robert Price10/2013
39093*2^295139+788847Lelio R Paula08/2014
39103^186212-11300888846Enzo Doria07/2014
391187^45803-8688836Norbert Schneider11/2015
39122^295094-11027388833Enzo Doria05/2014
39132^295080+186915188828Enzo Doria05/2016
39142^295027-11340788812Enzo Doria07/2014
3915(2*10^88808-71)/388808Robert Price01/2017
391613^79722-8088806Lelio R Paula11/2015
39173^186103+10488794Lelio R Paula12/2015
3918(3*2^294971+1)/2556588792Lelio R Paula01/2013
39192^294937-11500388785Enzo Doria06/2015
39202^294868-10970988765Enzo Doria04/2014
39212^294864-298588763Yves Minet09/2014
39222^294754+1501588730Lelio R Paula10/2013
3923(3^185951-7)/2088720Lelio R Paula01/2013
3924(2^294661+5)/44369338388694Lelio R Paula01/2013
3925(10^88680+11)/388680Robert Price11/2014
39262*7^104928-988675Lelio R Paula10/2014
392711^85150+1288675Lelio R Paula11/2015
39288*6^113951+588673Lelio R Paula10/2014
39296^113940-1856388663Enzo Doria03/2013
393038^56123-56123^3888663Norbert Schneider02/2017
39312^294492-6588651Lelio R Paula10/2012
393220^68120-5388627Lelio R Paula01/2016
39332^294391-11325788621Enzo Doria07/2014
39345^126784-1547688619Enzo Doria02/2013
39352^294327+988602Lelio R Paula10/2012
39362^294320+1891588600Lelio R Paula10/2013
3937(98*10^88595-89)/9988595Ray Chandler07/2011
3938(17*2^294262-1)/1388582Lelio R Paula02/2014
3939(2*10^88545+7)/988545Erik Branger03/2011
39402^294137-13388545Lelio R Paula10/2012
3941(2^294092-1017)/117188528Lelio R Paula01/2013
39424^147036+147036^4+188525Robert Price04/2014
3943(14^77213-5^77213)/988496Robert Price04/2013
39442^293965+279337788493Enzo Doria03/2016
394511^84971-15088489Enzo Doria08/2012
3946(2^293956-1017)/3985137669667788476Lelio R Paula01/2013
394711^84958-219088475Enzo Doria12/2012
39482^293880-11134788467Enzo Doria05/2014
3949(106*10^88459-1)/388461Serge Batalov12/2014
395011^84908-168088423Enzo Doria12/2012
39512^293679-11207588407Enzo Doria06/2014
39526^113608-6588405Lelio R Paula12/2015
39532^293624+8287588390Lelio R Paula10/2013
39542^293612-11233788387Enzo Doria06/2014
3955gcd(V(1062695),5*F(212539)*(F(212539)-1)+1)88383Serge Batalov04/2015
39565*10^88377+7788378Robert Price06/2016
3957(5*2^293526+1)/30388359Lelio R Paula01/2013
39582^293461-278584388341Enzo Doria03/2016
39592^293416-103788328Yves Minet11/2012
3960(2^293384-7)/388317Lelio R Paula01/2013
3961(3^185092-5)/488311Lelio R Paula01/2013
396214^77039-5788297Lelio R Paula11/2015
39635^126303+4288283Lelio R Paula10/2015
396419^69025-1888266Theodore Burton01/2006
39655*10^88261-388262Dmitry Domanov11/2010
39668^97731-7^(97731-1)88260Robert Price04/2016
39675*10^88254+5988255Robert Price09/2016
39684*3^184968-788253Lelio R Paula08/2014
39697^104426+8888251Lelio R Paula10/2015
39702^293142+9988245Lelio R Paula10/2012
397111^84736-213088244Enzo Doria12/2012
39722^293068-8988223Lelio R Paula10/2012
39732^293014-10965588207Enzo Doria04/2014
39748*7^104371-388205Lelio R Paula10/2014
39752^292995-214588201Lelio R Paula10/2013
39765*10^88182+7788183Robert Price06/2016
39782^292929+4387788181Donovan Johnson04/2005
39776^113321+13188181Lelio R Paula12/2015
39792^292904-58394988173Paul Bourdelais04/2013
39802^292894-11185188170Enzo Doria05/2014
39812^292872-279734988164Enzo Doria03/2016
39822^292860-10968588160Enzo Doria04/2014
39839*6^113288-588157Lelio R Paula10/2014
3984(73*10^88105+17)/988106Robert Price10/2015
398511^84588+7888090Lelio R Paula11/2015
3986(265*10^88077+11)/388079Robert Price03/2017
398791^44959-90^4495988077Robert Price07/2015
39886^113177-5^11317788069Jean-Louis Charton01/2009
3989(10^88020+101)/388020Robert Price04/2016
3990(10^(2*43982+1)-6*10^43982-1)/387965Robert Price02/2016
3991p(18225)#/2+12887929Robert Price04/2017
39924*6^112977+787914Lelio R Paula10/2014
399314^76677+6987882Lelio R Paula11/2015
3994(22*10^87863-1)/387864Robert Price12/2014
39952^291822-279781187848Enzo Doria04/2016
39962^291716-11138987816Enzo Doria05/2014
39973^184039+182087809Lelio R Paula12/2015
399812^81356+4187798Lelio R Paula11/2015
39996^112792-1898387770Enzo Doria03/2013
40003*6^112787-587766Lelio R Paula10/2014


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 24 2017 22:44 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!