PRP Records

Probable Primes Top 10000

(259919 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 ?
8501(2^232653+1494)/270036Stefano Morozzi01/2020
850218^55786-536370027Enzo Doria03/2013
8503(2^(77537*3+1)+243)/770023Kevin Acres11/2013
85042^232602+16970021Lelio R Paula02/2012
8505(137^32768+29^32768)/270016Jeppe Stig Nielsen04/2018
85062^232580+7213370014Enzo Doria04/2016
85074*6^89958-770002Lelio R Paula09/2014
850810^70000+8048770001Milton L. Brown05/2006
850910^69999+13485770000Patrick De Geest02/2007
851010^70000-927370000Patrick De Geest08/2009
8511(79*10^69999-7)/970000Robert Price01/2015
8512((2^43112609)/10^38420)%10^7000070000Michael Vang10/2016
8513(2^756839/10^36014)%10^7000070000Michael Vang12/2016
8514(2^74207281/10^32641)%10^7000070000Michael Vang12/2016
851510^69999-8825169999Patrick De Geest08/2009
85162^232507+108969992Lelio R Paula04/2012
8517(2^232506+498)/269991Stefano Morozzi01/2020
8518(17*2^232445+1)/569974Lelio R Paula08/2012
8519(529^25693+1)/53069972Richard Fischer12/2017
8520(2^232416+498)/269964Stefano Morozzi01/2020
8521(2^232410+2794)/269963Stefano Morozzi01/2020
85227^82778+4869956Lelio R Paula09/2013
85247*2^232381+369955Lelio R Paula04/2014
852319305^4204+4204^1930569955Hans Havermann10/2019
85252^232362-11054169948Enzo Doria05/2014
852619442^3957+3957^1944269940Hans Havermann09/2019
85272^232326-11239169938Enzo Doria06/2014
85283^146575+23669935Lelio R Paula09/2013
852930^47341-2969929Norbert Schneider02/2014
8530(2^232294+1218)/269928Stefano Morozzi01/2020
85315^100040-6869925Lelio R Paula09/2013
85329946^17491+17491^994669923Norbert Schneider07/2019
853316351^16592-16592^1635169912Norbert Schneider11/2019
8534(2^232139+3746)/269881Stefano Morozzi01/2020
8535(2^232132+2566)/269879Stefano Morozzi01/2020
8536(35*10^69866-593)/969867Robert Price08/2017
85372^232045-1729569853Lelio R Paula04/2012
8538(2^231987+78557)/9569834Lelio R Paula05/2012
85392^231955+7424369826Yves Minet03/2011
8540(2^231949+3290)/269824Stefano Morozzi01/2020
85412^231946-1587369823Enzo Doria04/2013
854218^55618+9569816Lelio R Paula09/2013
85436^89712+5^(89712-1)69810Robert Price02/2016
8544(2^231876+670)/269802Stefano Morozzi01/2020
85452^231870+13569800Lelio R Paula02/2012
8546(23*2^231827-1)/417969785Lelio R Paula01/2014
85472^231778+5461569773Lelio R Paula04/2012
8548(19*2^231780+1)/23569772Lelio R Paula08/2012
8549(2^231775+2430)/269771Stefano Morozzi01/2020
855014^60866+2769761Lelio R Paula09/2013
855113^62619-4469755Lelio R Paula09/2013
8552(2^231715-509203)/3569752Lelio R Paula05/2012
85532^231711-11046769752Enzo Doria05/2014
8555(19^54547+18^54547)/3769751Robert Price08/2013
8554(2^231707+998)/269751Stefano Morozzi01/2020
8556(23*2^231697-1)/4569748Lelio R Paula01/2014
85572^231696-186149969748Enzo Doria03/2016
85582^231684-14769744Lelio R Paula02/2012
8559(23*2^231686-1)/118369743Lelio R Paula01/2014
85602^231591-47739769716Paul Bourdelais03/2013
856116916^13209+13209^1691669709Hans Havermann09/2019
856216568^16095+16095^1656869697Hans Havermann09/2019
856311^66916-42069686Enzo Doria08/2012
85645^99680-1370669674Enzo Doria02/2013
8565(8*10^69674-53)/969674Robert Price11/2014
8566(44*10^69663-413)/969664Robert Price10/2017
856718950^4743+4743^1895069662Hans Havermann10/2019
8568(77*10^69656-23)/969657Robert Price10/2015
8569(2^231385+3710)/269654Stefano Morozzi01/2020
85706^89509+13169652Lelio R Paula09/2013
8571(2^231364+3030)/269648Stefano Morozzi01/2020
8572(78557*2^231349+1)/3569647Lelio R Paula06/2014
8573(11*10^69645+19)/369646Robert Price03/2016
857411^66875-2869644Lelio R Paula09/2013
85752^231347+7148369643Enzo Doria04/2016
8576(14^60763+3^60763)/1769641Robert Price04/2013
8577(2^231340+3126)/269640Stefano Morozzi01/2020
8578(4*10^69626+173)/369627Robert Price01/2017
85792^231289+25569625Lelio R Paula04/2012
858019794^3287+3287^1979469612Hans Havermann09/2019
85812^231234-11291369609Enzo Doria06/2014
8582(265*10^69602-7)/369604Robert Price07/2016
85832^231182-11284169593Enzo Doria06/2014
8584(15*2^231129+1)/2369577Lelio R Paula08/2012
85853^145806-2869568Lelio R Paula09/2013
8586(265*10^69554-7)/369556Robert Price07/2016
85872^231052-11315969554Enzo Doria07/2014
8588(10^9+1)*(10^129+1)*(10^831+1)*(10^107199+1)/1001/(10^387+1)/(10^2493+1)/(10^35733+1)69552Makoto Kamada03/2019
858911^66784-869549Lelio R Paula09/2013
8590Phi(104409,10)/229699969546Maksym Voznyy07/2015
8591(2^231023+1758)/269545Stefano Morozzi01/2020
85922^231016-11052369543Enzo Doria05/2014
85932^231014+57729457569543Lelio R Paula02/2016
8594(2^230982+970)/269533Stefano Morozzi01/2020
859514^60658+6769522Lelio R Paula09/2013
8596(2^230898+2422)/269507Stefano Morozzi01/2020
85975^99418+3669491Lelio R Paula06/2013
85987^82203-3069470Lelio R Paula09/2013
8599(63^38609-1)/6269469Paul Bourdelais08/2017
8600(2^230746+3114)/269462Stefano Morozzi01/2020
86015^99359-2^9936069449Mike Oakes12/2010
8602(29*2^230684+1)/139569442Lelio R Paula08/2012
860317692^8411+8411^1769269439Hans Havermann09/2019
8604(2^230638+1278)/269429Stefano Morozzi01/2020
8605(19*10^69424+77)/369425Robert Price08/2016
8606(2^230610+1222)/269421Stefano Morozzi01/2020
860719^54287-9669420Lelio R Paula09/2013
860820739^2222+2222^2073969409Hans Havermann09/2019
86102^230541+5890569400Lelio R Paula04/2012
8609(2^230540+2818)/269400Stefano Morozzi01/2020
86112^230506+1270569390Lelio R Paula02/2013
86128*6^89156-569378Lelio R Paula09/2014
8613(2^230443+3594)/269370Stefano Morozzi01/2020
86142^230438-11134769369Enzo Doria05/2014
8615(2^230434+3150)/269368Stefano Morozzi01/2020
86162^230428-9969366Lelio R Paula02/2012
8617(62^38699+1)/6369362Paul Bourdelais08/2017
8618(2^230413+3090)/269361Stefano Morozzi01/2020
86193*10^69354+1769355Robert Price03/2017
8620(493*10^69340-7)/969342Robert Price07/2016
8621(2^230325+590)/269335Stefano Morozzi01/2020
8623(41*10^69321+373)/969322Robert Price04/2017
8622(2^230282+1990)/269322Stefano Morozzi01/2020
86246^89072+5369312Lelio R Paula09/2013
8625155^31639+269300Lelio R Paula05/2013
8626(2^230117+3462)/269272Stefano Morozzi01/2020
86273*7^81965-469269Lelio R Paula09/2014
8628(16*10^69265+41)/369266Robert Price10/2017
8629(86*10^69260-77)/969261Robert Price05/2016
86309*5^99087+469260Lelio R Paula09/2014
86313^145145+266069252Lelio R Paula09/2013
863211^66492-114069245Enzo Doria11/2012
86335*3^145129-469245Lelio R Paula04/2014
86347*3^145126+869244Lelio R Paula04/2014
863511^66480-237069232Enzo Doria12/2012
8636(2^229965+3482)/269227Stefano Morozzi01/2020
8637(2^229968+3010)/269227Stefano Morozzi01/2020
86382^229962-6569226Lelio R Paula02/2012
86392^229958-11073369225Enzo Doria05/2014
8640V(332407)69225Serge Batalov03/2015
86416^88959+769224Lelio R Paula09/2013
864215^58855-9469219Lelio R Paula09/2013
8643(2^229941+774)/269219Stefano Morozzi01/2020
8644(2^229931+3270)/269216Stefano Morozzi01/2020
8645159773#-p(159773)69212Henri Lifchitz12/2018
864620223^2638+2638^2022369189Hans Havermann09/2019
8648(2^229838+47)/1208169185Lelio R Paula04/2012
8647(2^229828+3810)/269185Stefano Morozzi01/2020
86493^144952+9869160Lelio R Paula09/2013
86505^98941-7269157Lelio R Paula06/2013
865163329!4+25669147Robert Price09/2019
865216422^16229+16229^1642269142Hans Havermann09/2019
8653(17*2^229604-1)/22969117Lelio R Paula01/2014
86542^229585-106369112Yves Minet11/2012
8655(13*2^229567-1)/1969107Lelio R Paula01/2014
8656(2^229419+1946)/269062Stefano Morozzi01/2020
8657(2^229399+1890)/269056Stefano Morozzi01/2020
8658(13*2^229393-1)/569055Lelio R Paula01/2014
8659(2^229388+3666)/269053Stefano Morozzi01/2020
8660(53*10^69050-17)/969051Robert Price09/2015
8661(43*10^69048+47)/969049Robert Price12/2017
86622^229305-186853369028Enzo Doria04/2016
86632^229297+138569026Lelio R Paula04/2012
866418^54986-244169023Enzo Doria03/2013
8665(34*10^69021-7)/9/3/6769020Makoto Morimoto04/2016
86665^98736-1463669014Enzo Doria02/2013
8667(2^229252+2346)/269012Stefano Morozzi01/2020
8669(13^61949-5^61949)/869007Robert Price03/2013
8668(2^229235+2966)/269007Stefano Morozzi01/2020
8670(2^229227+5)/61169002Lelio R Paula04/2012
86712^229216-11327969001Enzo Doria07/2014
867210^68994+5191368995Patrick De Geest03/2016
867410^68994-10^5814-168994Serge Batalov01/2011
867310^68994-8294768994Patrick De Geest03/2016
8675(2^229182+814)/268991Stefano Morozzi01/2020
8676(17*2^229136-1)/238168975Lelio R Paula01/2014
86772^229113+10768970Lelio R Paula02/2012
867816877^12198+12198^1687768965Hans Havermann09/2019
8679(2^229056+2010)/268953Stefano Morozzi01/2020
868011^66202-441068943Enzo Doria01/2013
868112^63883+568942Lelio R Paula07/2013
8683(9913*2^229002-1)/39990368935Lelio R Paula04/2015
8682(2^228997+2454)/268935Stefano Morozzi01/2020
8684(2^228982+3118)/268931Stefano Morozzi01/2020
8685(2^228982+3490)/268931Stefano Morozzi01/2020
86862^228962-11158168925Enzo Doria05/2014
86872^228944+8168920Henri Lifchitz01/2007
868811^66174-5468914Lelio R Paula09/2013
8689(2^228926+694)/268914Stefano Morozzi01/2020
869016756^12959+12959^1675668911Hans Havermann09/2019
86912^228913-11126568910Enzo Doria05/2014
869218917^4392+4392^1891768909Hans Havermann09/2019
86942^228902+7351968907Enzo Doria04/2016
8693(2^228903+3018)/268907Stefano Morozzi01/2020
8695(2^228892+3046)/268904Stefano Morozzi01/2020
8696(47*2^228884+1)/6368901Lelio R Paula04/2015
8697(2^228857+3782)/268893Stefano Morozzi01/2020
869816542^14591+14591^1654268883Hans Havermann09/2019
86992^228821+7642768882Enzo Doria05/2016
8700(2^228798+442)/268875Stefano Morozzi01/2020
8701(2^228784+1222)/268871Stefano Morozzi01/2020
87023^144340+5068868Lelio R Paula09/2013
8703(2^228766+3850)/268866Stefano Morozzi01/2020
87042^228758-11296768864Enzo Doria06/2014
87052^228743-11137968859Enzo Doria05/2014
87062^228741-11091168858Enzo Doria05/2014
8708lucasU(1926,1,20964)-lucasU(1926,1,20963)68857Mike Oakes05/2009
87073*5^98511-868857Lelio R Paula09/2014
87092^228717+46768851Lelio R Paula02/2011
8710(2^228714+2110)/268850Stefano Morozzi01/2020
8711Phi(153218,10)/2211855049/23592660859/49771411729168849Maksym Voznyy10/2011
8712(2^228704+3990)/268847Stefano Morozzi01/2020
8713(509203*2^228665-1)/3568840Lelio R Paula04/2015
8714(2^228648+2910)/268830Stefano Morozzi01/2020
87158^76213-7^7621368828Ananda Tallur & Jean-Louis Charton11/2003
8716(2^228580+3762)/268810Stefano Morozzi01/2020
871711^66074-105068809Enzo Doria11/2012
8718(68*10^68798-11)/368800Robert Price10/2017
87192^228484+18168781Lelio R Paula02/2012
87202^228479-5869568780Lelio R Paula04/2012
87212^228465-1585368775Enzo Doria04/2013
872211^66040-540068774Enzo Doria01/2013
8723(13*2^228441-1)/57568766Lelio R Paula01/2014
8724(17*2^228393+1)/29568752Lelio R Paula08/2012
872517859^7072+7072^1785968749Hans Havermann09/2019
8726(2^228368+1950)/268746Stefano Morozzi01/2020
87272*10^68744+4168745Robert Price01/2017
872811^66011-15068744Enzo Doria08/2012
8729(2^228307+3570)/268727Stefano Morozzi01/2020
8730(13*2^228304-1)/8168726Lelio R Paula01/2014
87312^228295-11107968724Enzo Doria05/2014
8733(3^144039+7)/2268723Lelio R Paula04/2012
8732(8*10^68722+49)/368723Robert Price03/2016
8734(35*10^68718+1)/968719Serge Batalov11/2010
87352^228271-22827168717Henri Lifchitz11/2004
87362^228257+8287568713Lelio R Paula02/2013
87373^144013+4068712Lelio R Paula09/2013
873813^61671-8668699Lelio R Paula09/2013
8739(46*10^68698+683)/968699Robert Price12/2017
874017^55828-7268694Lelio R Paula09/2013
874118675^4762+4762^1867568683Hans Havermann09/2019
87426^88259+6168679Lelio R Paula09/2013
874318^54699-568663Lelio R Paula09/2013
874433^45216+268662Lelio R Paula05/2013
8746(2^228073-5)/368657Lelio R Paula04/2012
8745(2^(6*38012+1)-5)/368657Kevin Acres11/2013
87472^228055-11160768652Enzo Doria05/2014
87482^228054-11476168652Enzo Doria05/2015
87492^228041+118568648Lelio R Paula04/2012
87502^228040-103768647Yves Minet11/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 29 2020 17:41 (Time in France)

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