PRP Records

Probable Primes Top 10000

(301723 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 ?
2501p(38635)#-p(38635+1)200356Henri Lifchitz11/2024
2502(19*10^200260+101)/3200261Robert Price06/2023
250343183^43183+4^4200167Serge Batalov04/2024
2504(86^103471+1)/87200163Paul Bourdelais05/2018
2505(10^(2*100072+1)+36*10^100072-1)/9200145Robert Price09/2023
25062^664778+34789200119Enzo Doria07/2024
2507103*(10^100000+20110)^2-4707*(10^100000+20110)+50383200003Robert Price05/2017
2508103*(10^100000+33798)^2-4707*(10^100000+33798)+50383200003Robert Price01/2018
2509numbpart(32235776596)200002Serge Batalov04/2017
2510(10^200001+149)/3200001Serge Batalov12/2014
251110^200000+571791200001Patrick De Geest08/2019
2512(3^419180-621444)/3200000Stefano Morozzi06/2019
2513(3^419180-1941384)/3200000Stefano Morozzi08/2019
251410^200000-45557200000Patrick De Geest08/2019
2516(10^200000-1)/9-10^58838200000Akihiko Yoshida04/2020
25152593604092947240127723272^8192+2593604092947240127722755^8192200000Youcef Lemsafer01/2023
2517(2593604092947240127723019^8192+2593604092947240127723011^8192)/2199999Youcef Lemsafer01/2023
2518(2593604092947240127723087^8192+2593604092947240127722984^8192)/147457199994Youcef Lemsafer01/2023
2519(2593604092947240127723229^8192+2593604092947240127723171^8192)/15032745986199989Youcef Lemsafer01/2023
2520(2593604092947240127723215^8192+2593604092947240127722938^8192)/12728329863169199986Youcef Lemsafer01/2023
252192*10^199980-9199982Robert Price12/2021
2522(2593604092947240127723216^8192+2593604092947240127723163^8192)/20172788859482903707649199977Youcef Lemsafer01/2023
2523(85*10^199951-139)/9199952Robert Price08/2021
2524(10^199926+7)/29/373/2339199919Alfred Reich08/2021
25252^663838+25819199836Enzo Doria11/2023
252623*10^199833-9199835Robert Price10/2021
2527fibonacci(956176)-4199829Jon Grantham08/2023
2528(299*10^199801-17)/3199803Robert Price04/2020
25296*10^199788+77199789Robert Price06/2020
2530(2^663604+1)/270750449199757Anonymous10/2024
2531(23*10^199615+37)/3199616Robert Price02/2022
2532(17*10^199607-167)/3199608Robert Price05/2022
25332^663020-933075199589Paul Bourdelais06/2021
25342^663007+29963199585Enzo Doria03/2024
25353*2^662703-5199494Jon Grantham07/2023
2536(14*10^199447+73)/3199448Robert Price12/2018
2537(2^662424-15)/7199409Stefano Morozzi08/2022
25382^662194+22189199341Enzo Doria09/2023
25392^662103-29287199313Enzo Doria08/2015
2540(2*10^199283+457)/9199283Robert Price01/2018
2541(10^199248-19)/9199248Robert Price01/2018
2542(83*10^199213+529)/9199214Robert Price12/2021
2543(194*10^199146-17)/3199148Robert Price09/2020
2544(151*10^199003-1)/3199005Robert Price03/2020
25459*10^198946-73198947Robert Price01/2021
254645*10^198931-7198933Robert Price07/2020
25472^660482-2891198825Yves Minet05/2016
25482^659594+37729198558Enzo Doria10/2024
25492^659589-21198557Stefano Morozzi07/2022
25502^659583+1879223198555Enzo Doria08/2016
2551(53*10^198529+1)/9198530Serge Batalov07/2010
2552(17^161333-1)/913790128198504Paul Vanderveen05/2025
2553(49*10^198403+311)/9198404Robert Price06/2019
255496*10^198376-7198378Robert Price03/2021
2555(10^198375+7)/59/1201/87589198366Alfred Reich08/2021
25562^658828-29819198327Enzo Doria08/2015
25572^658776-2791229198312Enzo Doria01/2016
2558(35*10^198294-377)/9198295Robert Price07/2018
2559(4*10^198268+137)/3198269Robert Price03/2018
25602^658544-1854029198242Enzo Doria09/2015
2561(62*10^198229-233)/9198230Robert Price02/2022
2562(26*10^198200-41)/3198201Robert Price02/2022
2563(157^90239-1)/156198154Alexander Zhirkov06/2016
25642^657815+26213198023Enzo Doria12/2023
25652*10^197959-37197960Robert Price11/2021
2566(29*10^197941-41)/3197942Tyler Busby03/2024
2567(232*10^197897+17)/3197899Robert Price04/2021
2568(4*10^197778+173)/3197779Robert Price02/2018
25692^656964+6561197766Henri Lifchitz01/2025
25702^656763+211373197706Enzo Doria08/2023
257178*10^197702-7197704Robert Price10/2020
2572(17*10^197640-23)/3197641Robert Price03/2021
2573(29*10^197629-77)/3197630Robert Price02/2020
25742^656462+1874419197615Enzo Doria06/2016
2575(89^101363+1)/90197595Paul Bourdelais11/2017
25762^656172+229051197528Enzo Doria11/2024
25772^655893-344563197444Enzo Doria07/2015
25782^655875+71333197439Enzo Doria04/2016
25792^655845-9197430Robert Price01/2017
2580(299*10^197426+1)/3197428Robert Price04/2020
25812^655682-1849121197380Enzo Doria08/2015
25824*10^197268-89197269Robert Price11/2018
2583(11*10^197198-89)/3197199Robert Price05/2021
25842^655045-49603197189Enzo Doria10/2015
25852^655000-2784089197175Enzo Doria10/2015
2586(18^157051-1)/17197141Paul Bourdelais03/2010
2587(4*10^197061+41)/9197061Serge Batalov11/2022
2588(154*10^197005+17)/9197007Robert Price06/2022
25892^654400-39719196995Enzo Doria09/2015
2590(5^281807-2^281807)/3196975Jon Grantham08/2023
2591(14*10^196965-221)/9196966Robert Price04/2018
2592(7^233069-1)/52258731186196956Paul Vanderveen05/2025
25932^654216-459995196939Enzo Doria06/2015
2594(17*10^196921+31)/3196922Robert Price01/2019
2595(14*10^196885-89)/3196886Robert Price05/2020
25963*10^196881-59196882Robert Price09/2018
25972^653851+82295196829Enzo Doria09/2016
2598(38*10^196792+691)/9196793Robert Price10/2018
2599(65*10^196768+493)/9196769Robert Price08/2021
26012^653636-29429196765Enzo Doria08/2015
26002^653638-11196765Stefano Morozzi07/2022
26022^653601-69673196754Enzo Doria02/2016
2603(44*10^196684+1)/9196685Serge Batalov07/2010
26042^652786-1852571196509Enzo Doria08/2015
26052^652752-1325196498Yves Minet07/2015
26062^652470-1859141196414Enzo Doria10/2015
26072^652346+29329196376Enzo Doria02/2024
26082^652307+1877483196364Enzo Doria08/2016
26092^652293-115273196360Enzo Doria06/2015
2610(47*10^196281+403)/9196282Robert Price03/2019
26112^652025+218027196280Enzo Doria01/2024
26122^652004+23961196273Enzo Doria10/2023
2613(7*10^196125-31)/3196126Robert Price12/2021
261433^129128+129128^33196083Norbert Schneider06/2022
26156*10^196070+73196071Robert Price04/2019
26162^651218-1868201196037Enzo Doria04/2016
26172^651047-49687195985Enzo Doria10/2015
261810^195968-700001195968Robert Price08/2021
2619fibonacci(937485)+3195923Jon Grantham08/2023
2620(29*10^195875-197)/3195876Robert Price08/2021
2621(25*10^195808-97)/9195809Robert Price01/2022
26222^650285-2785333195756Enzo Doria10/2015
2623(10^195732+7)/18089/49605893195721Alfred Reich08/2021
2624(29*10^195648-41)/3195649Tyler Busby03/2024
2625(69^106397-1)/68195647Paul Bourdelais10/2017
26262^649811+1877573195613Enzo Doria08/2016
26272^649662-170531195568Hans Havermann10/2018
26282^649586+182839195545Enzo Doria11/2016
26292^649537-1867363195531Enzo Doria04/2016
26302^649536-1861499195530Enzo Doria12/2015
26312^649493+25907195517Enzo Doria11/2023
2632(103*10^195478-1)/3195480Serge Batalov12/2014
26332^649102-59351195400Enzo Doria10/2015
2634(2*10^195399+529)/9195399Robert Price01/2018
2635(202*10^195383-13)/9195385Robert Price01/2020
26362^648988+1178971195365Enzo Doria06/2016
26372^648975-114319195361Enzo Doria02/2015
2638(11*10^195350-137)/9195351Robert Price01/2018
26392^648619-24835195254Enzo Doria09/2013
26405*10^195250-21195251Robert Price12/2021
2641(14*10^195234-83)/3195235Robert Price12/2018
26425*10^195221+81195222Robert Price03/2019
264310^195143-5001195143Robert Price12/2021
26442^648190-24737195125Enzo Doria09/2013
2645(57^111119+1)/58195110Paul Bourdelais10/2017
2646(29*10^195098-197)/3195099Robert Price08/2021
264710^195060+89701195061Patrick De Geest02/2021
264910^195060-40000000001195060Robert Price09/2020
264810^195060-110337195060Patrick De Geest02/2021
265056*10^195032-3195034Robert Price03/2020
265111^187185-90194934Enzo Doria09/2012
26522^647545-25194931Boyan Hu12/2024
26532^647468+220141194908Enzo Doria03/2024
2654(83^101533-1)/91545628589416644493342194827Paul Vanderveen06/2025
2655(86*10^194818-437)/9194819Robert Price03/2021
26567^230492-230492^7194789Henri Lifchitz07/2024
26572^647068+77281194787Enzo Doria05/2016
26582*10^194716-93194717Robert Price12/2021
265915^165559-14^165559194713Jean-Louis Charton03/2011
2660F(931517)194676Henri Lifchitz09/2008
26614*10^194668+49194669Robert Price01/2019
26622^646589+1179407194643Enzo Doria06/2016
26632^646289-114621194553Enzo Doria05/2015
26642^646236-39659194537Enzo Doria09/2015
2665(16*10^194536+53)/3194537Robert Price03/2019
26662^646161-59833194514Enzo Doria11/2015
2667(17*10^194502+31)/3194503Robert Price01/2019
2668(19*10^194428+287)/9194429Robert Price10/2021
26692*10^194413+3194414Robert Price07/2015
26702^645360-1848599194273Enzo Doria08/2015
267122470^44641+44641^22470194260Norbert Schneider08/2023
2672(112*10^194150-1)/3194152Serge Batalov12/2014
2673Phi(293127,10)194041Makoto Kamada12/2023
26742*10^193981-43193982Robert Price04/2018
26752^644382+75169193979Enzo Doria04/2016
26762^644304-1861409193955Enzo Doria11/2015
2677(29*10^193950-23)/3193951Robert Price03/2022
26785*10^193907-9193908Robert Price05/2015
26792^644043+1876703193877Enzo Doria07/2016
26802*10^193841-63193842Robert Price01/2022
26812^643735+1879733193784Enzo Doria09/2016
2682(5^277183+1)/6193742Paul Bourdelais07/2010
26839*10^193712+71193713Robert Price08/2020
26842^643216-286565193628Enzo Doria07/2015
26852^643204+215011193624Enzo Doria11/2023
268610^193566+1126339193567Patrick De Geest09/2022
268810^193566-10000000001193566Robert Price04/2021
268710^193566-454041193566Patrick De Geest08/2021
26902^642888-24965193529Enzo Doria09/2013
26892^642889+25367193529Enzo Doria11/2023
26912^642448-114825193397Enzo Doria05/2015
26922^642437-1856623193393Enzo Doria10/2015
26932^642039-59797193273Enzo Doria11/2015
26942^641987+39193258Jon Grantham08/2023
269510^193230+513861193231Patrick De Geest07/2018
269610^193230-8001193230Robert Price03/2018
2697(62*10^193225-233)/9193226Robert Price02/2022
26982^641692-286349193169Enzo Doria07/2015
26992^641690-24737193168Enzo Doria09/2013
270022268^44421+44421^22268193129Norbert Schneider06/2023
27012^641514+1876549193115Enzo Doria07/2016
27022^640888-2785619192927Enzo Doria10/2015
27032^640874-2783741192923Enzo Doria09/2015
270410^192922+192207192923Patrick De Geest08/2021
270510^192922-7001192922Robert Price04/2021
27062^640854+25192917Stefano Morozzi05/2021
270734*10^192868-9192870Robert Price06/2020
2708(46*10^192841+683)/9192842Robert Price03/2019
27092^640181+467192714Lelio R Paula08/2013
27102^640072+27541192681Enzo Doria01/2024
2711(10^192700)/(192700^10)192648Henri Lifchitz05/2025
27122^639536-1850249192520Enzo Doria08/2015
271340714<>40712<>...<>1086421357911<>...<>40711<>40713192464Hans Havermann12/2019
27145*10^192422-43192423Robert Price01/2019
27152^639110-2792441192392Enzo Doria02/2016
2716(241^80761-1)/240192372Anonymous04/2024
27172^638955-29827192345Enzo Doria08/2015
271815^163539+14192337Alfred Reich10/2023
27192^638713-2784223192272Enzo Doria10/2015
2720(10^192216+7)/149192214Alfred Reich07/2021
27212^638490-113507192205Enzo Doria08/2014
27222^638189-39943192115Enzo Doria09/2015
27232^638110+1877119192091Enzo Doria07/2016
2724MillsLike(2,1,4,12,4,22,12,114,4,138,142,2956,6388,5248,17532,96930,83782,1464,897448,300832)+82440192083Sergey Batalov05/2024
2725MillsLike(2,1,4,12,4,22,12,114,4,138,142,2956,6388,5248,17532,96930,83782,1464,897448,300832)192083Sergey Batalov05/2024
27262^638066-2785211192078Enzo Doria10/2015
2727(35*10^191973-341)/9191974Robert Price08/2021
2728(112*10^191900+17)/3191902Robert Price03/2020
27292^637475-115309191900Enzo Doria07/2015
2730(68*10^191754-113)/9191755Robert Price03/2021
27312^636930-11191736Stefano Morozzi07/2022
2732(47*10^191732+259)/9191733Robert Price03/2022
273341459^41522-41522^41459191733Norbert Schneider04/2025
27342^636661+1876577191655Enzo Doria07/2016
2735(9^200807-2^200807)/7191618Jon Grantham07/2023
2736(34^125101-1)/33191589Paul Bourdelais11/2017
2737fibonacci(916540)-2191546Jon Grantham08/2023
27382^636177-1855123191509Enzo Doria09/2015
27392^636158-113627191503Enzo Doria08/2014
2740(37*25^136966+63)/4191472Curtis Bright05/2015
27412^636035+79823191466Enzo Doria06/2016
27422^636011-1860847191459Enzo Doria11/2015
27432^635926-1860611191433Enzo Doria11/2015
27443*2^635755+5191382Jon Grantham07/2023
27453*10^191152-7191153Robert Price08/2015
27462^634883-1865677191119Enzo Doria02/2016
27472^634801+1871957191095Enzo Doria05/2016
2748(77*10^191080+157)/9191081Robert Price05/2022
2749(35*10^191073+1)/9191074Serge Batalov07/2010
27509*10^191018-41191019Robert Price08/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 10 2025 14:11 (Time in France)

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