PRP Records

Probable Primes Top 10000

(291910 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 ?
825110^99434+15557199435Patrick De Geest04/2020
825210^99434-12345678999434Robert Price02/2020
825310^99434-19123799434Patrick De Geest04/2020
825446^59791-45^5979199418Jean-Louis Charton01/2013
825523839^14802+14802^2383999417Hans Havermann02/2018
8256(2*10^99408+529)/999408Robert Price01/2017
8257(2^330216+3510)/299405Stefano Morozzi09/2020
825853^57646-299398Lelio R Paula09/2013
82592^330165+187002599390Enzo Doria05/2016
82607*10^99383+9799384Robert Price09/2021
82612^330142-15599383Lelio R Paula12/2012
82622^330088-11525999367Enzo Doria06/2015
826324216^12671+12671^2421699354Hans Havermann01/2018
8264Phi(200548,10)/320876999354Makoto Kamada04/2019
8265(746*10^99303+1)/999305Robert Price02/2017
82663^208107+4099293Lelio R Paula08/2016
8267(3939^27617-1)/393899291Serge Batalov06/2022
8268(5*2^329833-1)/36999288Lelio R Paula02/2014
82698*3^208093+599287Lelio R Paula08/2014
82705^142043+5699284Lelio R Paula08/2016
8271(13*10^99282-157)/999283Robert Price05/2021
8272(10^99284+7)/53/6799281Alfred Reich06/2021
827322*10^99275+799277Robert Price04/2016
82742^329778+187618999274Enzo Doria07/2016
8275(6580^25997-1)/657999259Serge Batalov06/2022
8276(2249^29611-1)/224899253Serge Batalov06/2022
8277(10^99239-13)/399239Robert Price02/2017
8278(1199^32233-1)/119899237Serge Batalov06/2022
82803^207987+6299236Lelio R Paula08/2016
8279(62*10^99235+91)/999236Robert Price07/2021
82812^329638+4999231Lelio R Paula12/2012
82827^117413-1899226Lelio R Paula08/2016
82832^329586-45890399216Enzo Doria04/2015
8284(6290^26119-1)/628999214Serge Batalov06/2022
82862^329553+10199206Lelio R Paula12/2012
8285(21297^22921-1)/2129699206Serge Batalov06/2022
82872^329551-11289799205Enzo Doria06/2014
8288(3^207925+7)/5099204Lelio R Paula09/2013
82896^127458-1799399182Enzo Doria03/2013
829027197^4428+4428^2719799166Hans Havermann10/2017
8291(46*10^99143-1)/999144Robert Price12/2014
8292(64*10^99135+161)/999136Robert Price08/2022
82937*10^99133+6999134Robert Price10/2017
8294(21701^22861-1)/2170099132Serge Batalov06/2022
829518^78968-306599127Enzo Doria03/2013
829725927^6654+6654^2592799122Hans Havermann10/2017
829687915!4+1699122Robert Price09/2019
82982^329259+18999117Lelio R Paula12/2012
82998*10^99113+3999114Robert Price01/2017
83006^127364+7799109Lelio R Paula08/2016
8301(82*10^99103+143)/999104Robert Price06/2021
8302(11414^24421-1)/1141399083Serge Batalov06/2022
8303(2^329135+1110)/299080Stefano Morozzi09/2020
8304(22089^22807-1)/2208899074Serge Batalov06/2022
8305(59*10^99069+391)/999070Robert Price03/2021
8306(797*10^99061-41)/999063Robert Price04/2022
83072^329058-28768199057Harrison Mesh06/2022
83086^127285+1399047Lelio R Paula08/2016
8309(228581#+235862)/(2^3*11*71*151)99044Makoto Morimoto10/2017
83102^329007+7328399041Enzo Doria04/2016
83115*3^207543-899024Lelio R Paula08/2014
8312(2^328930+570)/299018Stefano Morozzi09/2020
83132^328885+14999005Lelio R Paula12/2012
831523392^17075+17075^2339299004Hans Havermann09/2017
8314(7424^25579-1)/742399004Serge Batalov06/2022
8316(2^328879-9)/11999001Lelio R Paula10/2013
83175^141618+5498987Lelio R Paula08/2016
83188*10^98982+5198983Robert Price05/2017
8319(21*2^328809-1)/770998979Lelio R Paula03/2014
83202^328794-279760198977Enzo Doria04/2016
8321(88331^20011-1)/8833098972Serge Batalov06/2022
83226^127176+598963Lelio R Paula11/2014
83232*10^98961-2198962Robert Price09/2020
832424262^11989+11989^2426298960Hans Havermann09/2017
8325(60138^20707-1)/6013798958Serge Batalov06/2022
83262^328700-10970998949Enzo Doria04/2014
8327(2^328698+1810)/298948Stefano Morozzi01/2021
8328(1014^32917-1)/101398947Serge Batalov06/2022
832987771!4-12898944Robert Price11/2019
8330(4576^27031-1)/457598943Serge Batalov06/2022
8331(2^328658+3042)/298936Stefano Morozzi09/2020
8332(1933^30103-1)/193298923Serge Batalov06/2022
833346711!2-2^4671198916Robert Price09/2015
83349*7^117037+498909Lelio R Paula11/2014
8335127^47012+12698905Norbert Schneider01/2019
8336(93826^19891-1)/9382598900Serge Batalov06/2022
8337(2^328525+1250)/298896Stefano Morozzi09/2020
8338(10^98890+149)/398890Serge Batalov12/2014
833922775^21978+21978^2277598889Hans Havermann08/2017
83402^328497-21693398888Enzo Doria05/2014
83412^328487+3276998885Lelio R Paula08/2016
83423^207250-11235898884Enzo Doria06/2014
834313^88754-9098867Lelio R Paula08/2016
83442^328406+70998861Lelio R Paula02/2013
83452*10^98860-2198861Robert Price09/2020
8346(17*2^328413-1)/1617398860Lelio R Paula03/2014
83477^116976+7698857Lelio R Paula08/2016
8348(2^328378+2710)/298852Stefano Morozzi09/2020
8349(25411^22441-1)/2541098849Serge Batalov06/2022
8350(18668^23143-1)/1866798842Serge Batalov06/2022
83522^328335+115598839Lelio R Paula08/2016
83512^328333-34900398839Harrison Mesh06/2022
8354(3*2^328311+1)/598832Lelio R Paula11/2013
8353287^40210+40210^28798832Norbert Schneider11/2014
8355(2^328284+9)/132598821Lelio R Paula10/2013
8356(21*2^328258+1)/212598814Lelio R Paula11/2013
8357(28623^22171-1)/2862298806Serge Batalov06/2022
835824746^9825+9825^2474698795Hans Havermann07/2020
835926620^5143+5143^2662098793Hans Havermann07/2020
836065^54491+4898788Lelio R Paula04/2016
83613^207042+9898785Lelio R Paula08/2016
8362(2^328121+3110)/298774Stefano Morozzi09/2020
836310^98754+7338398755Patrick De Geest02/2021
83663^206977-11275698754Enzo Doria07/2014
836510^98754-4000000000198754Robert Price09/2020
836410^98754-16934398754Patrick De Geest02/2021
83677^116846-5098747Lelio R Paula08/2016
8368(19152^23059-1)/1915198740Serge Batalov06/2022
836923267^17512+17512^2326798730Hans Havermann04/2020
83702^327967-2863598728Lelio R Paula08/2016
8371707^34642+34642^70798710Norbert Schneider12/2017
8372(10771^24481-1)/1077098710Serge Batalov06/2022
83736^126850-4798709Lelio R Paula08/2016
8374(2^327886+2170)/298704Stefano Morozzi09/2020
8375(22*10^98697+47)/398698Robert Price06/2021
83768*6^126830-798694Lelio R Paula11/2014
837711^94770-27098693Enzo Doria08/2012
8378(2^327846+3250)/298692Stefano Morozzi01/2021
83792^327832+4398688Lelio R Paula12/2012
83802^327795+76198677Lelio R Paula02/2013
8381(2^327796+1522)/298677Stefano Morozzi09/2020
838210^98669+14741198670Patrick De Geest11/2016
838410^98669-9^(98669-1)98669Robert Price05/2016
838310^98669-10524998669Patrick De Geest11/2016
8385(7911^25309-1)/791098657Serge Batalov06/2022
83862^327671-10980198639Enzo Doria04/2014
838724398^11037+11037^2439898638Hans Havermann10/2019
83885^141090-1498618Lelio R Paula08/2016
838920^75799+4798617Lelio R Paula08/2016
8390(5452^26393-1)/545198616Serge Batalov06/2022
839128101^3226+3226^2810198597Hans Havermann07/2020
83922^327515-101798592Lelio R Paula08/2016
83936^126692+9768198586Mike Oakes04/2011
83942^327467-74198578Lelio R Paula08/2016
8395(2947^28411-1)/294698566Serge Batalov06/2022
839622713^21800+21800^2271398540Hans Havermann05/2020
8397(2^327329+9)/1998535Lelio R Paula10/2013
83987^116577-6698519Lelio R Paula08/2016
8399(3*2^327250+1)/798512Lelio R Paula11/2013
840023220^17479+17479^2322098512Hans Havermann03/2020
8401(2^327240+3798)/298509Stefano Morozzi02/2021
8402(28514^22111-1)/2851398502Serge Batalov06/2022
8403(19*2^327192+1)/27598494Lelio R Paula11/2013
84042^327162-6694598486Lelio R Paula08/2016
840530139^1852+1852^3013998484Hans Havermann02/2020
840623182^17703+17703^2318298479Hans Havermann01/2020
84074*10^98472-398473Erik Branger11/2013
840826167^5794+5794^2616798466Hans Havermann01/2020
8409(6883*2^327047-1)/7798453Lelio R Paula05/2015
8410(71*10^98446+1)/998447Serge Batalov11/2010
8411(2009^29803-1)/200898436Serge Batalov06/2022
841213^88363+9498432Lelio R Paula08/2016
841348^58543-47^5854398425Jean-Louis Charton11/2005
84146^126481+4198422Lelio R Paula08/2016
841578*10^98413-798415Robert Price05/2017
841622634^22263+22263^2263498404Hans Havermann07/2020
8417(47*10^98386+241)/998387Robert Price06/2022
84187^116416+4698383Lelio R Paula08/2016
84197^116407-2498376Lelio R Paula07/2016
8420439^37228+37228^43998374Norbert Schneider08/2018
84212^326782-186067198372Enzo Doria03/2016
842217^79948+5898372Lelio R Paula08/2016
842322499^22602-22602^2249998368Norbert Schneider08/2020
84243^206143-9898356Lelio R Paula08/2016
84258*5^140705+798350Lelio R Paula11/2014
8426(2^326632+1662)/298326Stefano Morozzi09/2020
8427(638^35053-1)/63798315Serge Batalov06/2022
84282^326585+1198312Lelio R Paula12/2012
84292^326582-45916198311Enzo Doria05/2015
8430(1266^31687-1)/126598304Serge Batalov06/2022
8432(2^326548+9)/598301Lelio R Paula10/2013
8431(2^326549+18)/1098301Stefano Morozzi03/2020
84332^326538+7165998298Enzo Doria04/2016
8434(2^326520+2082)/298293Stefano Morozzi09/2020
8435(2^326521+1002)/298293Stefano Morozzi09/2020
843615^83575-5898292Lelio R Paula08/2016
843710^98288+398289Robert Price03/2011
843810^98288-11701798288Patrick De Geest11/2011
8439(44*10^98284-719)/998285Robert Price12/2017
8440(5985^26021-1)/598498280Serge Batalov06/2022
844123466^15419+15419^2346698277Hans Havermann02/2020
84422^326421-279757398263Enzo Doria04/2016
84432^326401+1609598257Lelio R Paula07/2016
8444(6494^25771-1)/649398249Serge Batalov06/2022
84457^116240-116240^798235Norbert Schneider05/2017
844617^79826-7898222Lelio R Paula08/2016
84472^326268-80998217Yves Minet04/2011
844822659^21590+21590^2265998210Hans Havermann10/2019
844922268^22587-22587^2226898202Norbert Schneider08/2020
8450(418*10^98199+23)/998201Robert Price08/2017
845112*10^98198-798200Robert Price11/2017
845215^83496-7698199Lelio R Paula08/2016
8453(10223*2^326179+1)/612598190Lelio R Paula07/2014
84549*5^140471-498186Lelio R Paula11/2014
8455(35103^21601-1)/3510298180Serge Batalov06/2022
845722774^20455+20455^2277498175Hans Havermann07/2020
8456(4516^26863-1)/451598175Serge Batalov06/2022
84582^326069-238398157Yves Minet10/2013
8459(9661^24631-1)/966098152Serge Batalov06/2022
8460(4175^27109-1)/417498149Serge Batalov06/2022
8461(57801^20611-1)/5780098144Serge Batalov06/2022
84622^325973+118598128Lelio R Paula07/2016
8463(25*2^325949-1)/1798121Lelio R Paula02/2014
84642^325945-184726998120Enzo Doria07/2015
84658*10^98111-6798112Robert Price10/2017
8466(2^325902+1138)/298106Stefano Morozzi09/2020
8467(215^42061-1)/21498103Serge Batalov06/2022
8468(6775^25609-1)/677498102Serge Batalov06/2022
8469(6718^25633-1)/671798100Serge Batalov06/2022
84702^325866+1598096Lelio R Paula12/2012
847122591^21952+21952^2259198079Hans Havermann02/2020
84722^325765+197430598066Enzo Doria06/2016
84732^325733-5869598056Lelio R Paula07/2016
8474(7*10^98055-529)/998055Robert Price08/2021
84752^325717-364598051Lelio R Paula07/2016
8476(2^325704+718)/298047Stefano Morozzi09/2020
8477(15679^23371-1)/1567898045Serge Batalov06/2022
8478(23342^22441-1)/2334198022Serge Batalov06/2022
847923968^12293+12293^2396898021Hans Havermann11/2019
8480(23*2^325583-1)/2198011Lelio R Paula02/2014
8481(7*10^98007-13)/398008Robert Price06/2016
8482(2^325544+1110)/297999Stefano Morozzi09/2020
84832^325512-45995997989Enzo Doria05/2015
8484(2^325492+682)/297983Stefano Morozzi09/2020
8485(3^205354-8)/1797978Lelio R Paula09/2013
84862^325433+7681797966Enzo Doria05/2016
84875*10^97963+8197964Robert Price08/2017
8488(13208^23773-1)/1320797961Serge Batalov06/2022
84892^325390-10906197953Enzo Doria04/2014
8490(55*10^97940+323)/997941Robert Price10/2021
849113^87921+2497940Lelio R Paula08/2016
849210^97930+18827797931Patrick De Geest09/2022
849410^97930-700000197930Robert Price06/2021
849310^97930-6695197930Patrick De Geest09/2022
8495961^32831-960^3283197926Jean-Louis Charton02/2011
8496(17968^23017-1)/1796797922Serge Batalov06/2022
8497(3337^27793-1)/333697922Serge Batalov06/2022
849922600^21499+21499^2260097913Hans Havermann05/2020
8498(18703^22921-1)/1870297913Serge Batalov06/2022
85002^325215+1290997900Lelio R Paula07/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 02 2023 13:22 (Time in France)

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