PRP Records

Probable Primes Top 10000

(301822 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 ?
25012^675034-169727203206Stefano Morozzi01/2025
25022^675035-173055203206Stefano Morozzi01/2025
25032^675035-73551203206Stefano Morozzi01/2025
25042^675033+79109203206Stefano Morozzi02/2025
25052^675034+154057203206Stefano Morozzi02/2025
25062^675030+109245203205Stefano Morozzi01/2025
25072^675030-160047203205Stefano Morozzi01/2025
25082^675027+106733203204Stefano Morozzi01/2025
25092^675026-67377203204Stefano Morozzi01/2025
25102^675021+13335203202Stefano Morozzi01/2025
25112^675020-180497203202Stefano Morozzi01/2025
25122^675016+174777203201Stefano Morozzi01/2025
25132^675017+128379203201Stefano Morozzi01/2025
25142^675017+171249203201Stefano Morozzi01/2025
25152^675018+86517203201Stefano Morozzi01/2025
25162^675019+125891203201Stefano Morozzi01/2025
25172^675019+163251203201Stefano Morozzi01/2025
25182^675016-170847203201Stefano Morozzi01/2025
25192^675019-44755203201Stefano Morozzi01/2025
25202^675015+120225203200Stefano Morozzi01/2025
25212^675013-69831203200Stefano Morozzi01/2025
25222^675014-3897203200Stefano Morozzi01/2025
25232^675006+75357203198Stefano Morozzi01/2025
25242^675008+112231203198Stefano Morozzi01/2025
25252^675007-123309203198Stefano Morozzi01/2025
25262^675003+52529203197Stefano Morozzi01/2025
25272^675002+50595203196Stefano Morozzi01/2025
25282^674627-25161203083Enzo Doria09/2013
25292^674603-69337203076Enzo Doria12/2015
2530(182*10^203048+1)/3203050Robert Price09/2023
25312^674459+74213203033Enzo Doria04/2016
25322^674116-458879202930Enzo Doria04/2015
25332^674076-114755202918Enzo Doria04/2015
25345^289937-4^289937202658Jean-Louis Charton03/2013
25355^289926-289926^5202650Henri Lifchitz07/2024
2536(2^673184-7)/3202649Stefano Morozzi08/2022
2537(467617#+14534)/(2^2*13*43)202603Makoto Morimoto06/2019
2538(155^92479-1)/154202558Anonymous06/2024
25392^672773+219407202525Enzo Doria03/2024
25401374^64531-64531^1374202498Henri Lifchitz10/2024
25412^672556-1835519202460Enzo Doria04/2015
2542(7*10^202267+179)/3202268Robert Price02/2023
25432^671446-351401202126Enzo Doria07/2015
25442^671373+77747202104Enzo Doria05/2016
2545(2*10^202059+7)/9202059Rytis Slatkevicius01/2023
254698*10^202021-9202023Robert Price05/2023
25472^670726-114845201909Enzo Doria05/2015
25482^670539-25045201853Enzo Doria09/2013
254910^201801-93201801Robert Price02/2023
255043284^43519-43519^43284201769Norbert Schneider08/2018
25512^670213+282317201755Enzo Doria09/2016
25522^670133+89201731Stefano Morozzi05/2021
25532^669854-113501201647Enzo Doria08/2014
25542^669718+81619201606Enzo Doria08/2016
2555(299*10^201547-17)/3201549Robert Price02/2023
2556(145*10^201504-1)/9201506Serge Batalov12/2014
25572^668938-1839821201371Enzo Doria06/2015
2558(198^87623-1)/197201239Anonymous06/2024
25592^668492+1879303201237Enzo Doria08/2016
25607*10^201140-87201141Robert Price03/2023
25616^258413-5^258413201085Jean-Louis Charton03/2013
256210194^50161-50161^10194201063Norbert Schneider09/2020
25632^667894+1875589201057Enzo Doria06/2016
25642^667569-1836559200959Enzo Doria05/2015
2565(172*10^200746-1)/9200748Serge Batalov12/2014
2566(166^90407-1)/165200712Anonymous06/2024
25672^666430+782569200616Enzo Doria10/2016
2568(13*10^200610-43)/3200611Robert Price08/2023
2569(8*10^200408-11)/3200409Robert Price07/2023
2570p(38635)#-p(38635+1)200356Henri Lifchitz11/2024
2571(19*10^200260+101)/3200261Robert Price06/2023
257243183^43183+4^4200167Serge Batalov04/2024
2573(86^103471+1)/87200163Paul Bourdelais05/2018
2574(10^(2*100072+1)+36*10^100072-1)/9200145Robert Price09/2023
25752^664778+34789200119Enzo Doria07/2024
2576103*(10^100000+20110)^2-4707*(10^100000+20110)+50383200003Robert Price05/2017
2577103*(10^100000+33798)^2-4707*(10^100000+33798)+50383200003Robert Price01/2018
2578numbpart(32235776596)200002Serge Batalov04/2017
2579(10^200001+149)/3200001Serge Batalov12/2014
258010^200000+571791200001Patrick De Geest08/2019
2581(3^419180-621444)/3200000Stefano Morozzi06/2019
2582(3^419180-1941384)/3200000Stefano Morozzi08/2019
258310^200000-45557200000Patrick De Geest08/2019
2585(10^200000-1)/9-10^58838200000Akihiko Yoshida04/2020
25842593604092947240127723272^8192+2593604092947240127722755^8192200000Youcef Lemsafer01/2023
2586(2593604092947240127723019^8192+2593604092947240127723011^8192)/2199999Youcef Lemsafer01/2023
2587(2593604092947240127723087^8192+2593604092947240127722984^8192)/147457199994Youcef Lemsafer01/2023
2588(2593604092947240127723229^8192+2593604092947240127723171^8192)/15032745986199989Youcef Lemsafer01/2023
2589(2593604092947240127723215^8192+2593604092947240127722938^8192)/12728329863169199986Youcef Lemsafer01/2023
259092*10^199980-9199982Robert Price12/2021
2591(2593604092947240127723216^8192+2593604092947240127723163^8192)/20172788859482903707649199977Youcef Lemsafer01/2023
2592(85*10^199951-139)/9199952Robert Price08/2021
2593(10^199926+7)/29/373/2339199919Alfred Reich08/2021
25942^663838+25819199836Enzo Doria11/2023
259523*10^199833-9199835Robert Price10/2021
2596fibonacci(956176)-4199829Jon Grantham08/2023
2597(299*10^199801-17)/3199803Robert Price04/2020
25986*10^199788+77199789Robert Price06/2020
2599(2^663604+1)/270750449199757Anonymous10/2024
2600(23*10^199615+37)/3199616Robert Price02/2022
2601(17*10^199607-167)/3199608Robert Price05/2022
26022^663020-933075199589Paul Bourdelais06/2021
26032^663007+29963199585Enzo Doria03/2024
26043*2^662703-5199494Jon Grantham07/2023
2605(14*10^199447+73)/3199448Robert Price12/2018
2606(2^662424-15)/7199409Stefano Morozzi08/2022
26072^662194+22189199341Enzo Doria09/2023
26082^662103-29287199313Enzo Doria08/2015
2609(2*10^199283+457)/9199283Robert Price01/2018
2610(10^199248-19)/9199248Robert Price01/2018
2611(83*10^199213+529)/9199214Robert Price12/2021
2612(194*10^199146-17)/3199148Robert Price09/2020
2613(151*10^199003-1)/3199005Robert Price03/2020
26149*10^198946-73198947Robert Price01/2021
261545*10^198931-7198933Robert Price07/2020
26162^660482-2891198825Yves Minet05/2016
26172^659594+37729198558Enzo Doria10/2024
26182^659589-21198557Stefano Morozzi07/2022
26192^659583+1879223198555Enzo Doria08/2016
2620(53*10^198529+1)/9198530Serge Batalov07/2010
2621(17^161333-1)/913790128198504Paul Vanderveen05/2025
2622(5^329624)%(4^329624)198454Henri Lifchitz07/2025
2623(49*10^198403+311)/9198404Robert Price06/2019
262496*10^198376-7198378Robert Price03/2021
2625(10^198375+7)/59/1201/87589198366Alfred Reich08/2021
26262^658828-29819198327Enzo Doria08/2015
26272^658776-2791229198312Enzo Doria01/2016
2628(35*10^198294-377)/9198295Robert Price07/2018
2629(4*10^198268+137)/3198269Robert Price03/2018
26302^658544-1854029198242Enzo Doria09/2015
2631(62*10^198229-233)/9198230Robert Price02/2022
2632(26*10^198200-41)/3198201Robert Price02/2022
2633(157^90239-1)/156198154Alexander Zhirkov06/2016
26342^657815+26213198023Enzo Doria12/2023
26352*10^197959-37197960Robert Price11/2021
2636(29*10^197941-41)/3197942Tyler Busby03/2024
2637(232*10^197897+17)/3197899Robert Price04/2021
2638(4*10^197778+173)/3197779Robert Price02/2018
26392^656964+6561197766Henri Lifchitz01/2025
26402^656763+211373197706Enzo Doria08/2023
264178*10^197702-7197704Robert Price10/2020
2642(17*10^197640-23)/3197641Robert Price03/2021
2643(29*10^197629-77)/3197630Robert Price02/2020
26442^656462+1874419197615Enzo Doria06/2016
2645(89^101363+1)/90197595Paul Bourdelais11/2017
26462^656172+229051197528Enzo Doria11/2024
26472^655893-344563197444Enzo Doria07/2015
26482^655875+71333197439Enzo Doria04/2016
26492^655845-9197430Robert Price01/2017
2650(299*10^197426+1)/3197428Robert Price04/2020
26512^655682-1849121197380Enzo Doria08/2015
26524*10^197268-89197269Robert Price11/2018
2653(11*10^197198-89)/3197199Robert Price05/2021
26542^655045-49603197189Enzo Doria10/2015
26552^655000-2784089197175Enzo Doria10/2015
2656(18^157051-1)/17197141Paul Bourdelais03/2010
2657(4*10^197061+41)/9197061Serge Batalov11/2022
2658(154*10^197005+17)/9197007Robert Price06/2022
26592^654400-39719196995Enzo Doria09/2015
2660(5^281807-2^281807)/3196975Jon Grantham08/2023
2661(14*10^196965-221)/9196966Robert Price04/2018
2662(7^233069-1)/52258731186196956Paul Vanderveen05/2025
26632^654216-459995196939Enzo Doria06/2015
2664(17*10^196921+31)/3196922Robert Price01/2019
2665(14*10^196885-89)/3196886Robert Price05/2020
26663*10^196881-59196882Robert Price09/2018
26672^653851+82295196829Enzo Doria09/2016
2668(38*10^196792+691)/9196793Robert Price10/2018
2669(65*10^196768+493)/9196769Robert Price08/2021
26712^653636-29429196765Enzo Doria08/2015
26702^653638-11196765Stefano Morozzi07/2022
26722^653601-69673196754Enzo Doria02/2016
2673(44*10^196684+1)/9196685Serge Batalov07/2010
26742^652786-1852571196509Enzo Doria08/2015
26752^652752-1325196498Yves Minet07/2015
26762^652470-1859141196414Enzo Doria10/2015
26772^652346+29329196376Enzo Doria02/2024
26782^652307+1877483196364Enzo Doria08/2016
26792^652293-115273196360Enzo Doria06/2015
2680(47*10^196281+403)/9196282Robert Price03/2019
26812^652025+218027196280Enzo Doria01/2024
26822^652004+23961196273Enzo Doria10/2023
2683(7*10^196125-31)/3196126Robert Price12/2021
268433^129128+129128^33196083Norbert Schneider06/2022
26856*10^196070+73196071Robert Price04/2019
26862^651218-1868201196037Enzo Doria04/2016
26872^651047-49687195985Enzo Doria10/2015
268810^195968-700001195968Robert Price08/2021
2689fibonacci(937485)+3195923Jon Grantham08/2023
2690(29*10^195875-197)/3195876Robert Price08/2021
2691(25*10^195808-97)/9195809Robert Price01/2022
26922^650285-2785333195756Enzo Doria10/2015
2693(10^195732+7)/18089/49605893195721Alfred Reich08/2021
2694(29*10^195648-41)/3195649Tyler Busby03/2024
2695(69^106397-1)/68195647Paul Bourdelais10/2017
26962^649811+1877573195613Enzo Doria08/2016
26972^649662-170531195568Hans Havermann10/2018
26982^649586+182839195545Enzo Doria11/2016
26992^649537-1867363195531Enzo Doria04/2016
27002^649536-1861499195530Enzo Doria12/2015
27012^649493+25907195517Enzo Doria11/2023
2702(103*10^195478-1)/3195480Serge Batalov12/2014
27032^649102-59351195400Enzo Doria10/2015
2704(2*10^195399+529)/9195399Robert Price01/2018
2705(202*10^195383-13)/9195385Robert Price01/2020
27062^648988+1178971195365Enzo Doria06/2016
27072^648975-114319195361Enzo Doria02/2015
2708(11*10^195350-137)/9195351Robert Price01/2018
27092^648619-24835195254Enzo Doria09/2013
27105*10^195250-21195251Robert Price12/2021
2711(14*10^195234-83)/3195235Robert Price12/2018
27125*10^195221+81195222Robert Price03/2019
271310^195143-5001195143Robert Price12/2021
27142^648190-24737195125Enzo Doria09/2013
2715(57^111119+1)/58195110Paul Bourdelais10/2017
2716(29*10^195098-197)/3195099Robert Price08/2021
271710^195060+89701195061Patrick De Geest02/2021
271910^195060-40000000001195060Robert Price09/2020
271810^195060-110337195060Patrick De Geest02/2021
272056*10^195032-3195034Robert Price03/2020
272111^187185-90194934Enzo Doria09/2012
27222^647545-25194931Boyan Hu12/2024
27232^647468+220141194908Enzo Doria03/2024
2724(83^101533-1)/91545628589416644493342194827Paul Vanderveen06/2025
2725(86*10^194818-437)/9194819Robert Price03/2021
27267^230492-230492^7194789Henri Lifchitz07/2024
27272^647068+77281194787Enzo Doria05/2016
27282*10^194716-93194717Robert Price12/2021
272915^165559-14^165559194713Jean-Louis Charton03/2011
2730F(931517)194676Henri Lifchitz09/2008
27314*10^194668+49194669Robert Price01/2019
27322^646589+1179407194643Enzo Doria06/2016
27332^646289-114621194553Enzo Doria05/2015
27342^646236-39659194537Enzo Doria09/2015
2735(16*10^194536+53)/3194537Robert Price03/2019
27362^646161-59833194514Enzo Doria11/2015
2737(17*10^194502+31)/3194503Robert Price01/2019
2738(19*10^194428+287)/9194429Robert Price10/2021
27392*10^194413+3194414Robert Price07/2015
27402^645360-1848599194273Enzo Doria08/2015
274122470^44641+44641^22470194260Norbert Schneider08/2023
2742(112*10^194150-1)/3194152Serge Batalov12/2014
2743Phi(293127,10)194041Makoto Kamada12/2023
27442*10^193981-43193982Robert Price04/2018
27452^644382+75169193979Enzo Doria04/2016
27462^644304-1861409193955Enzo Doria11/2015
2747(29*10^193950-23)/3193951Robert Price03/2022
27485*10^193907-9193908Robert Price05/2015
27492^644043+1876703193877Enzo Doria07/2016
27502*10^193841-63193842Robert Price01/2022


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 23 2025 10:09 (Time in France)

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