PRP Records

Probable Primes Top 10000

(252675 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 ?
37512^331256-5799718Lelio R Paula12/2012
375228192^3443+3443^2819299714Hans Havermann03/2018
37532^331185+73799697Lelio R Paula01/2013
3754(4*10^99693+149)/999693Robert Price03/2017
37552^331154+188052799688Enzo Doria10/2016
3757(19^77951+1)/2099679Paul Bourdelais03/2010
375624354^12385+12385^2435499679Hans Havermann03/2018
37582^331110+187045999675Enzo Doria05/2016
37595*2^331075+799665Lelio R Paula08/2014
376025776^7351+7351^2577699659Hans Havermann02/2018
3761(16*10^99656-31)/399657Robert Price03/2016
37622^330968+34599632Lelio R Paula09/2016
37642*5^142528-799624Lelio R Paula11/2014
37632^330942+7732999624Enzo Doria05/2016
376514^86914-9999615Lelio R Paula08/2016
3766(19*2^330902+1)/7799611Lelio R Paula11/2013
376722971^21692+21692^2297199610Hans Havermann03/2018
37682^330845+7168799595Enzo Doria04/2016
3769(23*2^330770+1)/399573Lelio R Paula11/2013
377024494^11613+11613^2449499567Hans Havermann03/2018
37712^330735+841599562Lelio R Paula09/2016
37722^330720+7407199557Enzo Doria04/2016
377331^66738-299531Lelio R Paula09/2013
37747*3^208567+499513Lelio R Paula08/2014
3775(13*10^99508+47)/399509Robert Price01/2017
37762^330553+77999507Lelio R Paula01/2013
377715^84606-9499505Lelio R Paula08/2016
37786^127858+4799493Lelio R Paula08/2016
37795^142337+4899490Lelio R Paula08/2016
37807^117724-2099489Lelio R Paula08/2016
3781(29*10^99474-17)/399475Erik Branger09/2014
3782(9*2^330407-1)/799463Lelio R Paula03/2014
3783(68*10^99441+7)/399443Robert Price03/2016
378446^59791-45^5979199418Jean-Louis Charton01/2013
378523839^14802+14802^2383999417Hans Havermann02/2018
3786(2*10^99408+529)/999408Robert Price01/2017
378753^57646-299398Lelio R Paula09/2013
37882^330165+187002599390Enzo Doria05/2016
37892^330142-15599383Lelio R Paula12/2012
37902^330088-11525999367Enzo Doria06/2015
379224216^12671+12671^2421699354Hans Havermann01/2018
3791Phi(200548,10)/320876999354Makoto Kamada04/2019
3793(746*10^99303+1)/999305Robert Price02/2017
37943^208107+4099293Lelio R Paula08/2016
3795(5*2^329833-1)/36999288Lelio R Paula02/2014
37968*3^208093+599287Lelio R Paula08/2014
37975^142043+5699284Lelio R Paula08/2016
379822*10^99275+799277Robert Price04/2016
37992^329778+187618999274Enzo Doria07/2016
3800(10^99239-13)/399239Robert Price02/2017
38013^207987+6299236Lelio R Paula08/2016
38022^329638+4999231Lelio R Paula12/2012
38037^117413-1899226Lelio R Paula08/2016
38042^329586-45890399216Enzo Doria04/2015
38052^329553+10199206Lelio R Paula12/2012
38062^329551-11289799205Enzo Doria06/2014
3807(3^207925+7)/5099204Lelio R Paula09/2013
38086^127458-1799399182Enzo Doria03/2013
380927197^4428+4428^2719799166Hans Havermann10/2017
3810(46*10^99143-1)/999144Robert Price12/2014
38117*10^99133+6999134Robert Price10/2017
381218^78968-306599127Enzo Doria03/2013
381325927^6654+6654^2592799122Hans Havermann10/2017
38142^329259+18999117Lelio R Paula12/2012
38158*10^99113+3999114Robert Price01/2017
38166^127364+7799109Lelio R Paula08/2016
38176^127285+1399047Lelio R Paula08/2016
3818(228581#+235862)/(2^3*11*71*151)99044Makoto Morimoto10/2017
38192^329007+7328399041Enzo Doria04/2016
38205*3^207543-899024Lelio R Paula08/2014
38212^328885+14999005Lelio R Paula12/2012
382223392^17075+17075^2339299004Hans Havermann09/2017
3823(2^328879-9)/11999001Lelio R Paula10/2013
38245^141618+5498987Lelio R Paula08/2016
38258*10^98982+5198983Robert Price05/2017
3826(21*2^328809-1)/770998979Lelio R Paula03/2014
38272^328794-279760198977Enzo Doria04/2016
38286^127176+598963Lelio R Paula11/2014
382924262^11989+11989^2426298960Hans Havermann09/2017
38302^328700-10970998949Enzo Doria04/2014
383146711!2-2^4671198916Robert Price09/2015
38329*7^117037+498909Lelio R Paula11/2014
3833127^47012+12698905Norbert Schneider01/2019
3834(10^98890+149)/398890Serge Batalov12/2014
383522775^21978+21978^2277598889Hans Havermann08/2017
38362^328497-21693398888Enzo Doria05/2014
38372^328487+3276998885Lelio R Paula08/2016
38383^207250-11235898884Enzo Doria06/2014
383913^88754-9098867Lelio R Paula08/2016
38402^328406+70998861Lelio R Paula02/2013
3841(17*2^328413-1)/1617398860Lelio R Paula03/2014
38427^116976+7698857Lelio R Paula08/2016
38432^328335+115598839Lelio R Paula08/2016
3845(3*2^328311+1)/598832Lelio R Paula11/2013
3844287^40210+40210^28798832Norbert Schneider11/2014
3846(2^328284+9)/132598821Lelio R Paula10/2013
3847(21*2^328258+1)/212598814Lelio R Paula11/2013
384865^54491+4898788Lelio R Paula04/2016
38493^207042+9898785Lelio R Paula08/2016
38503^206977-11275698754Enzo Doria07/2014
38517^116846-5098747Lelio R Paula08/2016
38522^327967-2863598728Lelio R Paula08/2016
3853707^34642+34642^70798710Norbert Schneider12/2017
38546^126850-4798709Lelio R Paula08/2016
38558*6^126830-798694Lelio R Paula11/2014
385611^94770-27098693Enzo Doria08/2012
38572^327832+4398688Lelio R Paula12/2012
38582^327795+76198677Lelio R Paula02/2013
385910^98669+14741198670Patrick De Geest11/2016
386110^98669-9^(98669-1)98669Robert Price05/2016
386010^98669-10524998669Patrick De Geest11/2016
38622^327671-10980198639Enzo Doria04/2014
38635^141090-1498618Lelio R Paula08/2016
386420^75799+4798617Lelio R Paula08/2016
38652^327515-101798592Lelio R Paula08/2016
38666^126692+9768198586Mike Oakes04/2011
38672^327467-74198578Lelio R Paula08/2016
3868(2^327329+9)/1998535Lelio R Paula10/2013
38697^116577-6698519Lelio R Paula08/2016
3870(3*2^327250+1)/798512Lelio R Paula11/2013
3871(19*2^327192+1)/27598494Lelio R Paula11/2013
38722^327162-6694598486Lelio R Paula08/2016
38734*10^98472-398473Erik Branger11/2013
3874(6883*2^327047-1)/7798453Lelio R Paula05/2015
3875(71*10^98446+1)/998447Serge Batalov11/2010
387613^88363+9498432Lelio R Paula08/2016
387748^58543-47^5854398425Jean-Louis Charton11/2005
38786^126481+4198422Lelio R Paula08/2016
387978*10^98413-798415Robert Price05/2017
38807^116416+4698383Lelio R Paula08/2016
38817^116407-2498376Lelio R Paula07/2016
3882439^37228+37228^43998374Norbert Schneider08/2018
38832^326782-186067198372Enzo Doria03/2016
388417^79948+5898372Lelio R Paula08/2016
38853^206143-9898356Lelio R Paula08/2016
38868*5^140705+798350Lelio R Paula11/2014
38872^326585+1198312Lelio R Paula12/2012
38882^326582-45916198311Enzo Doria05/2015
3889(2^326548+9)/598301Lelio R Paula10/2013
38902^326538+7165998298Enzo Doria04/2016
389115^83575-5898292Lelio R Paula08/2016
389210^98288+398289Robert Price03/2011
389310^98288-11701798288Patrick De Geest11/2011
3894(44*10^98284-719)/998285Robert Price12/2017
38952^326421-279757398263Enzo Doria04/2016
38962^326401+1609598257Lelio R Paula07/2016
38977^116240-116240^798235Norbert Schneider05/2017
389817^79826-7898222Lelio R Paula08/2016
38992^326268-80998217Yves Minet04/2011
3900(418*10^98199+23)/998201Robert Price08/2017
390112*10^98198-798200Robert Price11/2017
390215^83496-7698199Lelio R Paula08/2016
3903(10223*2^326179+1)/612598190Lelio R Paula07/2014
39049*5^140471-498186Lelio R Paula11/2014
39052^326069-238398157Yves Minet10/2013
39062^325973+118598128Lelio R Paula07/2016
3907(25*2^325949-1)/1798121Lelio R Paula02/2014
39082^325945-184726998120Enzo Doria07/2015
39098*10^98111-6798112Robert Price10/2017
39102^325866+1598096Lelio R Paula12/2012
39112^325765+197430598066Enzo Doria06/2016
39122^325733-5869598056Lelio R Paula07/2016
39132^325717-364598051Lelio R Paula07/2016
3914(23*2^325583-1)/2198011Lelio R Paula02/2014
3915(7*10^98007-13)/398008Robert Price06/2016
39162^325512-45995997989Enzo Doria05/2015
3917(3^205354-8)/1797978Lelio R Paula09/2013
39182^325433+7681797966Enzo Doria05/2016
39195*10^97963+8197964Robert Price08/2017
39202^325390-10906197953Enzo Doria04/2014
392113^87921+2497940Lelio R Paula08/2016
3922961^32831-960^3283197926Jean-Louis Charton02/2011
39232^325215+1290997900Lelio R Paula07/2016
39247*10^97874-6997875Robert Price01/2017
3926(17^79537+5^79537)/2297865Robert Price06/2013
392515^83212+2297865Lelio R Paula08/2016
39272^325087-10905797861Enzo Doria04/2014
39282^325074+187065797858Enzo Doria05/2016
39292^325066-211197855Yves Minet08/2013
3930CopelandErdos(97855)97855Eric W. Weisstein10/2015
393118^77944-8997841Lelio R Paula07/2016
3932119^47136+11897833Norbert Schneider09/2018
39336^125720-1766397830Enzo Doria02/2013
39342^324972-206997827Yves Minet05/2013
39352^324944-278831997818Enzo Doria03/2016
39374*10^97799-997800Erik Branger11/2013
39362^324882+57729457597800Lelio R Paula09/2016
39382^324863-186792197794Enzo Doria04/2016
39396^125662-1847397785Enzo Doria03/2013
394012^90604+1197779Lelio R Paula07/2016
39415^139830+2497737Lelio R Paula04/2016
39422^324612+115597718Lelio R Paula07/2016
394319^76404-4497702Lelio R Paula07/2016
39442^324505-298397686Yves Minet04/2011
3945(31*2^324496-1)/4597683Lelio R Paula02/2014
39466^125488-1784397649Enzo Doria02/2013
39477^115515-297622Lelio R Paula09/2013
3948(89^50069-1)/8897603Paul Bourdelais08/2017
39496^125418-597595Lelio R Paula11/2014
39502^324076+115597557Lelio R Paula07/2016
3951(2^324074+9)/1397555Lelio R Paula10/2013
3952(55459*2^323993+1)/2197536Lelio R Paula07/2014
395313^87557-12^8755797534Jean-Louis Charton12/2008
39542^323946+7393997518Enzo Doria04/2016
39552^323937+186694797515Enzo Doria03/2016
39566^125290-1853397495Enzo Doria03/2013
39572^323845+10197488Lelio R Paula12/2012
395818^77662+6597487Lelio R Paula07/2016
39592^323772+7677197466Enzo Doria05/2016
39602^323765-11221397463Enzo Doria06/2014
39612^323720-655597450Lelio R Paula07/2016
39622^323694-186040197442Enzo Doria03/2016
396320^74886+397429Lelio R Paula06/2016
39653*10^97399+7397400Robert Price04/2016
39647^115252-5097400Lelio R Paula07/2016
3966224737#+39358197389Nicolas PALAU12/2016
3967(26*10^97353+31)/397354Robert Price07/2016
396861^54517-60^5451797331Jean-Louis Charton09/2005
3969(38*10^97329+187)/997330Robert Price11/2017
3970p(19982)#/2-102497293Robert Price09/2017
39716^125021-8597286Lelio R Paula08/2016
39722^323164-4735597283Lelio R Paula07/2016
3973(3^203902+4)/3605101515797276Lelio R Paula09/2013
39742^323054-655597249Lelio R Paula07/2016
39759*10^97247-2997248Robert Price05/2017
3976(31*10^97242+41)/997243Robert Price04/2015
3977GoldenRatioPrime[97241]97241Eric W. Weisstein06/2009
397812^90098-4197233Lelio R Paula07/2016
39792^322928-21692997212Enzo Doria05/2014
3980(7*2^322896-1)/5797201Lelio R Paula02/2014
3981(2^322897+5)/314610748997193Lelio R Paula10/2013
39822^322725+7576197150Enzo Doria04/2016
3983(13*2^322686+1)/11997138Lelio R Paula11/2013
3984(41*10^97085+373)/997086Robert Price04/2017
39852^322413+7797056Lelio R Paula12/2012
39862^322406+17797054Lelio R Paula12/2012
3987(14*10^97044+31)/997045Robert Price02/2015
39882^322302+25525597023Lelio R Paula07/2016
39892^322196-11309396991Enzo Doria07/2014
39902^322000-186146996932Enzo Doria03/2016
39912^321971-11274796923Enzo Doria06/2014
399211^93062-9296915Lelio R Paula06/2016
3993(11*2^321841-7)/1596884Renaud Lifchitz03/2011
39943^203051+3496880Lelio R Paula05/2016
39952*10^96867-5196868Robert Price11/2017
3996(64*10^96863-1)/2796864Serge Batalov05/2010
39972^321716-278693996847Enzo Doria03/2016
39992^321701-11305396842Enzo Doria07/2014
39982^321700-2863596842Lelio R Paula06/2016
4000(5*2^321691-1)/2796838Lelio R Paula02/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 20 2019 09:21 (Time in France)

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