PRP Records

Probable Primes Top 10000

(301141 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 ?
1501(10^(2*131020+1)+63*10^131020-1)/9262041Robert Price08/2024
15022^869601-163261776Yves Minet01/2015
1503(2*10^261704+61)/9261704Serge Batalov11/2022
15042^869326+282859261694Enzo Doria11/2016
15052^869035-114181261606Enzo Doria12/2014
15062^868817+26777261540Enzo Doria12/2023
15073^547850+9000004261391Enzo Doria10/2023
15084*10^261248+91261249Robert Price11/2022
150955083^55083+1282^1282261150Henri Lifchitz10/2024
15102^866908+34891260966Enzo Doria07/2024
15112^865715+80303260607Enzo Doria07/2016
15122^865474+23209260534Enzo Doria10/2023
15132^865238+214759260463Enzo Doria11/2023
15142^865048+1882411260406Enzo Doria12/2016
15152^864899-113871260361Enzo Doria10/2014
1516(16*10^260256-91)/3260257Robert Price11/2022
1517(7*10^260198-61)/9260198Erik Branger11/2011
15182^864298-2788421260180Enzo Doria12/2015
15192^864039-2791357260102Enzo Doria01/2016
15202^863621-113833259976Enzo Doria10/2014
152110^259945-11259945Mischa Rodermond04/2023
15222^863433+34877259920Enzo Doria07/2024
1523(28*10^259897+113)/3259898Robert Price06/2023
15242^862837+75767259740Enzo Doria05/2016
15252^862637-31259680Jorge Menendez05/2019
15262^862088+1874941259515Enzo Doria06/2016
15272^861987-134557259484Hans Havermann10/2018
1528(14*10^259431-143)/3259432Robert Price05/2023
15292^861516-1854029259343Enzo Doria09/2015
15302^860975-1853977259180Enzo Doria09/2015
15313^543128+16259138Robert Price04/2020
15322^860625-1858843259074Enzo Doria10/2015
15332^860110+77689258919Enzo Doria05/2016
15342^859600+1880371258766Enzo Doria10/2016
15352^859433+494711258716Makoto Morimoto10/2013
1537(2^859433-44)/(2^2*3)258715Makoto Morimoto08/2019
1536(2^859431-11)/3258715Stefano Morozzi08/2022
1538(13*10^258710-43)/3258711Robert Price08/2023
1539(2^859433+39899)/(73*3907*46301)258705Makoto Morimoto10/2016
15402^859240+1875271258658Enzo Doria06/2016
1541Tau(971^15738)258571Nik Lygeros / Olivier Rozier05/2015
15422^858812+30421258529Enzo Doria03/2024
1543(23*10^258494-47)/3258495Robert Price09/2023
1544(144^119671+1)/145258292Paul Bourdelais08/2019
15452^857608+105258166Stefano Morozzi05/2021
1546(11*2^857159-13)/15258031Renaud Lifchitz08/2011
15472^857016-633113257988Enzo Doria12/2013
15482^855732-113969257602Enzo Doria10/2014
1549(5*10^257431+91)/3257432Robert Price08/2023
15502^853682-3911256984Enzo Doria05/2014
155111^246668-90256879Enzo Doria12/2012
15522^853181+30287256834Enzo Doria03/2024
15535*2^852698+3256689Jon Grantham07/2023
1554(23*10^256654+7)/3256655Robert Price05/2023
15552^851904-113939256449Enzo Doria10/2014
15562^851725-851725^2256395Henri Lifchitz03/2019
155711^246167-90256357Enzo Doria12/2012
1558(85*10^256301-1)/3256303Robert Price12/2022
1559(10^256187+7)/63443/148782853256175Alfred Reich10/2021
15602^850700-569049256087Enzo Doria11/2013
15612^850675+153256079Stefano Morozzi05/2021
156221^193601-20^193601255983Jean-Louis Charton02/2015
1563(37^163193+1)/38255918Paul Bourdelais07/2019
1564(14*10^255805-83)/3255806Robert Price11/2022
15652^849316+25861255670Enzo Doria12/2023
15662^849177-114025255628Enzo Doria12/2014
15672*10^255442-21255443Robert Price08/2023
15682^848502-3173255425Yves Minet07/2016
15692^848178-140291255328Enzo Doria01/2014
15707*10^255167+87255168Robert Price11/2022
15712^847622-2441255160Yves Minet02/2016
15722^847291+182843255061Enzo Doria11/2016
15732^847174+1879429255025Enzo Doria09/2016
15742^846881+215837254937Enzo Doria12/2023
157524*29^174239+13361254809Curtis Bright04/2015
157622*10^254639+7254641Robert Price10/2022
15772^845633-933075254561Paul Bourdelais11/2021
15782^845610-1868591254554Enzo Doria04/2016
15792^845484+81931254517Enzo Doria08/2016
15802^845402-114761254492Enzo Doria05/2015
158198*10^254173-9254175Robert Price05/2023
15822^844334-2792441254170Enzo Doria02/2016
15832*10^254162+69254163Robert Price08/2023
1584(4*10^254107+11)/3254108Tyler Busby02/2023
158511^243796-90253888Enzo Doria12/2012
1586(10^253891+7)/44777/79843/16940711253875Alfred Reich10/2021
158730^171733-29^171733253671Jean-Louis Charton10/2018
15882^842325+25907253566Enzo Doria11/2023
15892^842209+1876037253531Enzo Doria07/2016
15902^842123-59197253505Enzo Doria10/2015
1591(8*10^253313-53)/9253313Serge Batalov11/2022
1592(28*10^253210+191)/3253211Robert Price07/2023
15932^840797-3253106Paul Bourdelais06/2019
15942^840716-2969253081Yves Minet05/2016
15952^840358-462491252973Enzo Doria08/2015
15962^840310+1878379252959Enzo Doria08/2016
15972^840203-21252927Stefano Morozzi07/2022
159811^242579-60252620Enzo Doria10/2012
159945^152659+2252378Robert Price09/2015
1600(95^127583+1)/96252322Paul Bourdelais07/2019
16017*10^252209-17252210Robert Price12/2022
16022^837725+1869377252181Enzo Doria05/2016
16032^837536-311039252124Enzo Doria06/2015
160421^190632-2252058Robert Price07/2015
16052^837242+1873297252035Enzo Doria06/2016
16062^836995+226575251961Enzo Doria10/2024
16072^836656-2787929251859Enzo Doria11/2015
16082^836548+219061251827Enzo Doria02/2024
16092^836380+1875541251776Enzo Doria07/2016
1610(359^98327-1)/358251233Alexander Zhirkov11/2017
1611tau(41^28288)250924Nik Lygeros / Olivier Rozier10/2013
1612(28*10^250655+113)/3250656Robert Price06/2023
16132^832511-461197250611Enzo Doria07/2015
16142^832505+1881137250609Enzo Doria11/2016
16152^832363+583295250567Enzo Doria12/2016
16162^832244-403635250531Enzo Doria01/2014
1617(14*10^250336-41)/9250337Serge Batalov01/2023
16182^831528+24811250315Enzo Doria11/2023
16192^831157+1880657250204Enzo Doria11/2016
16202^831088-7200899250183Enzo Doria01/2015
16212^830956-1349250143Yves Minet07/2015
16222^830699+220583250066Enzo Doria03/2024
16232^830037+282317249867Enzo Doria09/2016
16242^829589-113653249732Enzo Doria09/2014
1625(4*10^249550-7)/3249551Serge Batalov01/2023
1626(103*10^249399+17)/3249401Robert Price04/2023
16272^828281-3193249338Yves Minet08/2016
1628(2^828140-19)/3249295Stefano Morozzi08/2022
16292^828064-2785619249273Enzo Doria10/2015
16302^827602+60409249134Enzo Doria03/2016
16312^827306+212419249044Enzo Doria09/2023
163210^249010+348861249011Patrick De Geest04/2016
163310^249010-21249010Serge Batalov12/2014
16342^826733+1882907248872Enzo Doria12/2016
16352^825800+22441248591Enzo Doria10/2023
16362^825682+1876549248556Enzo Doria07/2016
16372^824991-114121248348Enzo Doria12/2014
16382^824642-362727248242Enzo Doria12/2013
16392^824565-114265248219Enzo Doria01/2015
16402^824325-25248147Boyan Hu12/2024
1641(73*10^248145-1)/9248146Robert Price01/2015
16422^823321+219407247845Enzo Doria02/2024
1643(2^823337+1)/(3*362268281)247841Gord Palameta08/2018
1644(13*10^247793-43)/3247794Robert Price08/2023
1645(2^822971-1)/6583769/28211445881/21255852651726486149207247700Robert Kinser09/2016
16462^822296+76501247536Enzo Doria05/2016
16472^821590-114167247324Enzo Doria12/2014
16482^821512-2790659247300Enzo Doria12/2015
1649(21996^57121-1)/(21996^239-1)247002Ryan Propper11/2023
16502^820356+7246952Jon Grantham08/2023
16512^820077+382847246868Enzo Doria11/2016
16522^820008+81246848Henri Lifchitz01/2025
16532^820001+81269246845Enzo Doria07/2016
16542^819463-59197246683Enzo Doria10/2015
16552^819296+80581246633Enzo Doria07/2016
16562^818764+21573246473Enzo Doria11/2023
16572^817852+215491246198Enzo Doria11/2023
16582^817160-350369245990Enzo Doria06/2015
16592^816039-19245653Stefano Morozzi07/2022
16602^816029+219407245650Enzo Doria02/2024
1661(71*10^245558-17)/9245559Serge Batalov01/2023
16625*3^514648+2^514648245551Jon Grantham08/2023
166388093#+(653879#)/(88093#)245374Makoto Morimoto11/2017
16642^815111-113857245373Enzo Doria10/2014
1665(34555^54289-1)/(34555^233-1)245334Ryan Propper11/2023
16662^814914-4001245314Yves Minet05/2017
1667846^83761-845^83761245200Jean-Louis Charton12/2012
16682^814356-2790449245146Enzo Doria12/2015
16692^814276-459029245122Enzo Doria04/2015
16702^814023+180923245046Enzo Doria07/2016
16712^813496+216751244887Enzo Doria12/2023
1672(3^513059-2^513059)/(1026119*5430216457)244776Mike Oakes03/2017
16733^513007+16244767Robert Price04/2020
1674(46^147197-31^147197)/15244752Aurel Gibier06/2024
16752^811882+27289244401Enzo Doria12/2023
16762^811842-113675244389Enzo Doria09/2014
16772^811132-2787929244176Enzo Doria11/2015
16782^809746-2790971243758Enzo Doria01/2016
1679(14*10^243724-197)/3243725Robert Price03/2023
16802^808767-3295243464Yves Minet12/2016
16812^808621-113809243420Enzo Doria09/2014
16822^808199+29693243293Enzo Doria03/2024
16832^807724+1879621243150Enzo Doria09/2016
16842^807417+217787243057Enzo Doria01/2024
1685(23*10^242909+91)/3242910Robert Price03/2023
16862^806708+20371242844Enzo Doria08/2023
16872*10^242822-91242823Robert Price02/2023
168820^186554-3242713Paul Bourdelais12/2020
16892^805843-113611242583Enzo Doria08/2014
16902^805745-459763242554Enzo Doria05/2015
16912^805353+782687242436Enzo Doria11/2016
1692(19*10^242362-7)/3242363Robert Price12/2023
16932^804895+29963242298Enzo Doria03/2024
16942^804725+28229242247Enzo Doria01/2024
16956^311257+5242206Paul Bourdelais02/2021
16962^804277-417933242112Enzo Doria01/2014
16972^803468-269039241868Enzo Doria10/2013
16982^803172+80851241779Enzo Doria07/2016
16992^803011+220073241731Enzo Doria03/2024
17003^506233-2241535Robert Price11/2013
17012^802025-25999241434Enzo Doria10/2013
1702(3^505823+3^252912+1)/7241339Serge Batalov03/2014
17032^801575+25073241299Enzo Doria11/2023
17042^801303+1872923241217Enzo Doria05/2016
17052^801105+216977241157Enzo Doria12/2023
1706(23*10^241048-143)/3241049Robert Price12/2023
17072^800579-1862947240999Enzo Doria12/2015
17082^799999+16205240824Norman Luhn09/2023
17093^504206+2240568Luke W. Richards03/2018
17102^798973-26283240515Enzo Doria10/2013
17112^798671-69487240424Enzo Doria12/2015
17122^797220+79831239988Enzo Doria06/2016
17132^796910-26001239894Enzo Doria10/2013
17142^796598+653119239800Enzo Doria12/2016
17152^796432-1859729239750Enzo Doria11/2015
17162^796002-1852211239621Enzo Doria08/2015
17172^795884+214081239585Enzo Doria10/2023
17182^795709+75767239533Enzo Doria04/2016
17192^795708+81721239532Enzo Doria08/2016
17202^795468-2786249239460Enzo Doria10/2015
17212^795442+80779239452Enzo Doria07/2016
17222^795075-1852057239342Enzo Doria08/2015
1723(86^123677+1)/87239252Paul Bourdelais01/2019
17242^794043+1875023239031Enzo Doria06/2016
17252^793347-69577238822Enzo Doria01/2016
17265*2^793288+3238805Jon Grantham07/2023
17272^792988-344429238714Enzo Doria08/2015
17282^792700-2786369238627Enzo Doria11/2015
17292^792663-1844797238616Enzo Doria06/2015
17302^792605-291943238598Enzo Doria07/2015
17312^792366+218599238526Enzo Doria01/2024
1732(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
17332^791321+30077238212Enzo Doria03/2024
17344*10^238163+21238164Robert Price12/2022
1735(26*10^238157-77)/3238158Robert Price03/2023
173610^237670+9237671Robert Price08/2023
17372^789373+1869377237625Enzo Doria05/2016
1738((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961237544Serge Batalov04/2015
1739Phi(1187740M,10)237544Anonymous03/2025
17402^789033+218537237523Enzo Doria01/2024
17412^788942+1866409237496Enzo Doria02/2016
17422^788844-114329237466Enzo Doria01/2015
17432^788705-1859713237424Enzo Doria11/2015
17442^788325+224789237310Enzo Doria07/2024
174515^201475+14236953Alfred Reich10/2023
17462^786663+219173236810Enzo Doria02/2024
17472^786180+1871971236664Enzo Doria05/2016
174811^227092-90236492Enzo Doria11/2012
17492^785260+1866361236387Enzo Doria02/2016
17502^785220+1880611236375Enzo Doria10/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 26 2025 22:40 (Time in France)

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