PRP Records

Probable Primes Top 10000

(271067 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 ?
475122971^21692+21692^2297199610Hans Havermann03/2018
47522^330845+7168799595Enzo Doria04/2016
4753(23*2^330770+1)/399573Lelio R Paula11/2013
475424494^11613+11613^2449499567Hans Havermann03/2018
47552^330735+841599562Lelio R Paula09/2016
47562^330720+7407199557Enzo Doria04/2016
475731^66738-299531Lelio R Paula09/2013
47587*3^208567+499513Lelio R Paula08/2014
4759(13*10^99508+47)/399509Robert Price01/2017
47602^330553+77999507Lelio R Paula01/2013
476115^84606-9499505Lelio R Paula08/2016
47626^127858+4799493Lelio R Paula08/2016
47635^142337+4899490Lelio R Paula08/2016
47647^117724-2099489Lelio R Paula08/2016
4765(29*10^99474-17)/399475Erik Branger09/2014
4766(2^330410+2038)/299464Stefano Morozzi09/2020
4767(9*2^330407-1)/799463Lelio R Paula03/2014
4768(2^330373+2114)/299452Stefano Morozzi09/2020
4769(68*10^99441+7)/399443Robert Price03/2016
477010^99434+15557199435Patrick De Geest04/2020
477110^99434-12345678999434Robert Price02/2020
477210^99434-19123799434Patrick De Geest04/2020
477346^59791-45^5979199418Jean-Louis Charton01/2013
477423839^14802+14802^2383999417Hans Havermann02/2018
4775(2*10^99408+529)/999408Robert Price01/2017
4776(2^330216+3510)/299405Stefano Morozzi09/2020
477753^57646-299398Lelio R Paula09/2013
47782^330165+187002599390Enzo Doria05/2016
47792^330142-15599383Lelio R Paula12/2012
47802^330088-11525999367Enzo Doria06/2015
478124216^12671+12671^2421699354Hans Havermann01/2018
4782Phi(200548,10)/320876999354Makoto Kamada04/2019
4783(746*10^99303+1)/999305Robert Price02/2017
47843^208107+4099293Lelio R Paula08/2016
4785(5*2^329833-1)/36999288Lelio R Paula02/2014
47868*3^208093+599287Lelio R Paula08/2014
47875^142043+5699284Lelio R Paula08/2016
478822*10^99275+799277Robert Price04/2016
47892^329778+187618999274Enzo Doria07/2016
4790(10^99239-13)/399239Robert Price02/2017
47913^207987+6299236Lelio R Paula08/2016
47922^329638+4999231Lelio R Paula12/2012
47937^117413-1899226Lelio R Paula08/2016
47942^329586-45890399216Enzo Doria04/2015
47952^329553+10199206Lelio R Paula12/2012
47962^329551-11289799205Enzo Doria06/2014
4797(3^207925+7)/5099204Lelio R Paula09/2013
47986^127458-1799399182Enzo Doria03/2013
479927197^4428+4428^2719799166Hans Havermann10/2017
4800(46*10^99143-1)/999144Robert Price12/2014
48017*10^99133+6999134Robert Price10/2017
480218^78968-306599127Enzo Doria03/2013
480325927^6654+6654^2592799122Hans Havermann10/2017
480487915!4+1699122Robert Price09/2019
48052^329259+18999117Lelio R Paula12/2012
48068*10^99113+3999114Robert Price01/2017
48076^127364+7799109Lelio R Paula08/2016
4808(2^329135+1110)/299080Stefano Morozzi09/2020
48096^127285+1399047Lelio R Paula08/2016
4810(228581#+235862)/(2^3*11*71*151)99044Makoto Morimoto10/2017
48112^329007+7328399041Enzo Doria04/2016
48125*3^207543-899024Lelio R Paula08/2014
4813(2^328930+570)/299018Stefano Morozzi09/2020
48142^328885+14999005Lelio R Paula12/2012
481523392^17075+17075^2339299004Hans Havermann09/2017
4816(2^328879-9)/11999001Lelio R Paula10/2013
48175^141618+5498987Lelio R Paula08/2016
48188*10^98982+5198983Robert Price05/2017
4819(21*2^328809-1)/770998979Lelio R Paula03/2014
48202^328794-279760198977Enzo Doria04/2016
48216^127176+598963Lelio R Paula11/2014
48222*10^98961-2198962Robert Price09/2020
482324262^11989+11989^2426298960Hans Havermann09/2017
48242^328700-10970998949Enzo Doria04/2014
482587771!4-12898944Robert Price11/2019
4826(2^328658+3042)/298936Stefano Morozzi09/2020
482746711!2-2^4671198916Robert Price09/2015
48289*7^117037+498909Lelio R Paula11/2014
4829127^47012+12698905Norbert Schneider01/2019
4830(2^328525+1250)/298896Stefano Morozzi09/2020
4831(10^98890+149)/398890Serge Batalov12/2014
483222775^21978+21978^2277598889Hans Havermann08/2017
48332^328497-21693398888Enzo Doria05/2014
48342^328487+3276998885Lelio R Paula08/2016
48353^207250-11235898884Enzo Doria06/2014
483613^88754-9098867Lelio R Paula08/2016
48382^328406+70998861Lelio R Paula02/2013
48372*10^98860-2198861Robert Price09/2020
4839(17*2^328413-1)/1617398860Lelio R Paula03/2014
48407^116976+7698857Lelio R Paula08/2016
4841(2^328378+2710)/298852Stefano Morozzi09/2020
48422^328335+115598839Lelio R Paula08/2016
4844(3*2^328311+1)/598832Lelio R Paula11/2013
4843287^40210+40210^28798832Norbert Schneider11/2014
4845(2^328284+9)/132598821Lelio R Paula10/2013
4846(21*2^328258+1)/212598814Lelio R Paula11/2013
484724746^9825+9825^2474698795Hans Havermann07/2020
484826620^5143+5143^2662098793Hans Havermann07/2020
484965^54491+4898788Lelio R Paula04/2016
48503^207042+9898785Lelio R Paula08/2016
4851(2^328121+3110)/298774Stefano Morozzi09/2020
48533^206977-11275698754Enzo Doria07/2014
485210^98754-4000000000198754Robert Price09/2020
48547^116846-5098747Lelio R Paula08/2016
485523267^17512+17512^2326798730Hans Havermann04/2020
48562^327967-2863598728Lelio R Paula08/2016
4857707^34642+34642^70798710Norbert Schneider12/2017
48586^126850-4798709Lelio R Paula08/2016
4859(2^327886+2170)/298704Stefano Morozzi09/2020
48608*6^126830-798694Lelio R Paula11/2014
486111^94770-27098693Enzo Doria08/2012
48622^327832+4398688Lelio R Paula12/2012
48632^327795+76198677Lelio R Paula02/2013
4864(2^327796+1522)/298677Stefano Morozzi09/2020
486510^98669+14741198670Patrick De Geest11/2016
486710^98669-9^(98669-1)98669Robert Price05/2016
486610^98669-10524998669Patrick De Geest11/2016
48682^327671-10980198639Enzo Doria04/2014
486924398^11037+11037^2439898638Hans Havermann10/2019
48705^141090-1498618Lelio R Paula08/2016
487120^75799+4798617Lelio R Paula08/2016
487228101^3226+3226^2810198597Hans Havermann07/2020
48732^327515-101798592Lelio R Paula08/2016
48746^126692+9768198586Mike Oakes04/2011
48752^327467-74198578Lelio R Paula08/2016
487622713^21800+21800^2271398540Hans Havermann05/2020
4877(2^327329+9)/1998535Lelio R Paula10/2013
48787^116577-6698519Lelio R Paula08/2016
4880(3*2^327250+1)/798512Lelio R Paula11/2013
487923220^17479+17479^2322098512Hans Havermann03/2020
4881(19*2^327192+1)/27598494Lelio R Paula11/2013
48822^327162-6694598486Lelio R Paula08/2016
488330139^1852+1852^3013998484Hans Havermann02/2020
488423182^17703+17703^2318298479Hans Havermann01/2020
48854*10^98472-398473Erik Branger11/2013
488626167^5794+5794^2616798466Hans Havermann01/2020
4887(6883*2^327047-1)/7798453Lelio R Paula05/2015
4888(71*10^98446+1)/998447Serge Batalov11/2010
488913^88363+9498432Lelio R Paula08/2016
489048^58543-47^5854398425Jean-Louis Charton11/2005
48916^126481+4198422Lelio R Paula08/2016
489278*10^98413-798415Robert Price05/2017
489322634^22263+22263^2263498404Hans Havermann07/2020
48947^116416+4698383Lelio R Paula08/2016
48957^116407-2498376Lelio R Paula07/2016
4896439^37228+37228^43998374Norbert Schneider08/2018
48982^326782-186067198372Enzo Doria03/2016
489717^79948+5898372Lelio R Paula08/2016
489922499^22602-22602^2249998368Norbert Schneider08/2020
49003^206143-9898356Lelio R Paula08/2016
49018*5^140705+798350Lelio R Paula11/2014
4902(2^326632+1662)/298326Stefano Morozzi09/2020
49032^326585+1198312Lelio R Paula12/2012
49042^326582-45916198311Enzo Doria05/2015
4906(2^326548+9)/598301Lelio R Paula10/2013
4905(2^326549+18)/1098301Stefano Morozzi03/2020
49072^326538+7165998298Enzo Doria04/2016
4908(2^326520+2082)/298293Stefano Morozzi09/2020
4909(2^326521+1002)/298293Stefano Morozzi09/2020
491015^83575-5898292Lelio R Paula08/2016
491110^98288+398289Robert Price03/2011
491210^98288-11701798288Patrick De Geest11/2011
4913(44*10^98284-719)/998285Robert Price12/2017
491423466^15419+15419^2346698277Hans Havermann02/2020
49152^326421-279757398263Enzo Doria04/2016
49162^326401+1609598257Lelio R Paula07/2016
49177^116240-116240^798235Norbert Schneider05/2017
491817^79826-7898222Lelio R Paula08/2016
49192^326268-80998217Yves Minet04/2011
492022659^21590+21590^2265998210Hans Havermann10/2019
492122268^22587-22587^2226898202Norbert Schneider08/2020
4922(418*10^98199+23)/998201Robert Price08/2017
492312*10^98198-798200Robert Price11/2017
492415^83496-7698199Lelio R Paula08/2016
4925(10223*2^326179+1)/612598190Lelio R Paula07/2014
49269*5^140471-498186Lelio R Paula11/2014
492722774^20455+20455^2277498175Hans Havermann07/2020
49282^326069-238398157Yves Minet10/2013
49292^325973+118598128Lelio R Paula07/2016
4930(25*2^325949-1)/1798121Lelio R Paula02/2014
49312^325945-184726998120Enzo Doria07/2015
49328*10^98111-6798112Robert Price10/2017
4933(2^325902+1138)/298106Stefano Morozzi09/2020
49342^325866+1598096Lelio R Paula12/2012
493522591^21952+21952^2259198079Hans Havermann02/2020
49362^325765+197430598066Enzo Doria06/2016
49372^325733-5869598056Lelio R Paula07/2016
49382^325717-364598051Lelio R Paula07/2016
4939(2^325704+718)/298047Stefano Morozzi09/2020
494023968^12293+12293^2396898021Hans Havermann11/2019
4941(23*2^325583-1)/2198011Lelio R Paula02/2014
4942(7*10^98007-13)/398008Robert Price06/2016
4943(2^325544+1110)/297999Stefano Morozzi09/2020
49442^325512-45995997989Enzo Doria05/2015
4945(2^325492+682)/297983Stefano Morozzi09/2020
4946(3^205354-8)/1797978Lelio R Paula09/2013
49472^325433+7681797966Enzo Doria05/2016
49485*10^97963+8197964Robert Price08/2017
49492^325390-10906197953Enzo Doria04/2014
495013^87921+2497940Lelio R Paula08/2016
4951961^32831-960^3283197926Jean-Louis Charton02/2011
495222600^21499+21499^2260097913Hans Havermann05/2020
49532^325215+1290997900Lelio R Paula07/2016
495422619^21286+21286^2261997898Hans Havermann04/2020
49557*10^97874-6997875Robert Price01/2017
4957(17^79537+5^79537)/2297865Robert Price06/2013
495615^83212+2297865Lelio R Paula08/2016
49582^325087-10905797861Enzo Doria04/2014
49592^325074+187065797858Enzo Doria05/2016
49612^325066-211197855Yves Minet08/2013
4960CopelandErdos(97855)97855Eric W. Weisstein10/2015
496226660^4677+4677^2666097842Hans Havermann12/2019
496318^77944-8997841Lelio R Paula07/2016
4964119^47136+11897833Norbert Schneider09/2018
49656^125720-1766397830Enzo Doria02/2013
49662^324972-206997827Yves Minet05/2013
49672^324958-469197823Yves Minet05/2019
49682^324944-278831997818Enzo Doria03/2016
496922845^19112+19112^2284597807Hans Havermann10/2019
4970(2^324898+1270)/297804Stefano Morozzi09/2020
49724*10^97799-997800Erik Branger11/2013
49712^324882+57729457597800Lelio R Paula09/2016
49732^324863-186792197794Enzo Doria04/2016
49746^125662-1847397785Enzo Doria03/2013
497512^90604+1197779Lelio R Paula07/2016
49765^139830+2497737Lelio R Paula04/2016
4977(2^324672+1198)/297736Stefano Morozzi09/2020
49782^324612+115597718Lelio R Paula07/2016
4979(2^324597+3542)/297714Stefano Morozzi09/2020
498019^76404-4497702Lelio R Paula07/2016
49812^324505-298397686Yves Minet04/2011
4982(144^45259+1)/14597684Paul Bourdelais08/2019
4983(31*2^324496-1)/4597683Lelio R Paula02/2014
49846^125488-1784397649Enzo Doria02/2013
4985(2^324350+3198)/297639Stefano Morozzi09/2020
49867^115515-297622Lelio R Paula09/2013
4987(89^50069-1)/8897603Paul Bourdelais08/2017
49886^125418-597595Lelio R Paula11/2014
4989(2^324193+3522)/297592Stefano Morozzi09/2020
4990(2^324172+666)/297586Stefano Morozzi09/2020
49912^324076+115597557Lelio R Paula07/2016
4992(2^324074+9)/1397555Lelio R Paula10/2013
4993(55459*2^323993+1)/2197536Lelio R Paula07/2014
499413^87557-12^8755797534Jean-Louis Charton12/2008
49952^323946+7393997518Enzo Doria04/2016
49962^323937+186694797515Enzo Doria03/2016
49986^125290-1853397495Enzo Doria03/2013
4997(2^323870+1650)/297495Stefano Morozzi09/2020
49992^323845+10197488Lelio R Paula12/2012
500018^77662+6597487Lelio R Paula07/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 30 2020 10:03 (Time in France)

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