PRP Records

Probable Primes Top 10000

(301421 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
22512^675060+119983203214Stefano Morozzi02/2025
22522^675060+161301203214Stefano Morozzi02/2025
22532^675061-187773203214Stefano Morozzi02/2025
22542^675062-92193203214Stefano Morozzi02/2025
22552^675058-10403203213Stefano Morozzi01/2025
22562^675058-40337203213Stefano Morozzi01/2025
22572^675057+123557203213Stefano Morozzi02/2025
22582^675057+172475203213Stefano Morozzi02/2025
22592^675053-4801203212Stefano Morozzi01/2025
22602^675054-174341203212Stefano Morozzi01/2025
22612^675054-53697203212Stefano Morozzi01/2025
22622^675054+24825203212Stefano Morozzi02/2025
22632^675055+160265203212Stefano Morozzi02/2025
22642^675050-30015203211Stefano Morozzi01/2025
22652^675051-85941203211Stefano Morozzi01/2025
22662^675051+30885203211Stefano Morozzi02/2025
22672^675052+12537203211Stefano Morozzi02/2025
22682^675047-100299203210Stefano Morozzi01/2025
22692^675048-97313203210Stefano Morozzi01/2025
22702^675046+118119203210Stefano Morozzi02/2025
22712^675048+128941203210Stefano Morozzi02/2025
22722^675049+136359203210Stefano Morozzi02/2025
22732^675044-81087203209Stefano Morozzi01/2025
22742^675042-179811203208Stefano Morozzi01/2025
22752^675036-192939203207Stefano Morozzi01/2025
22762^675037-17853203207Stefano Morozzi01/2025
22772^675036+47101203207Stefano Morozzi02/2025
22782^675038+189589203207Stefano Morozzi02/2025
22792^675034-169727203206Stefano Morozzi01/2025
22802^675035-173055203206Stefano Morozzi01/2025
22812^675035-73551203206Stefano Morozzi01/2025
22822^675033+79109203206Stefano Morozzi02/2025
22832^675034+154057203206Stefano Morozzi02/2025
22842^675030+109245203205Stefano Morozzi01/2025
22852^675030-160047203205Stefano Morozzi01/2025
22862^675027+106733203204Stefano Morozzi01/2025
22872^675026-67377203204Stefano Morozzi01/2025
22882^675021+13335203202Stefano Morozzi01/2025
22892^675020-180497203202Stefano Morozzi01/2025
22902^675016+174777203201Stefano Morozzi01/2025
22912^675017+128379203201Stefano Morozzi01/2025
22922^675017+171249203201Stefano Morozzi01/2025
22932^675018+86517203201Stefano Morozzi01/2025
22942^675019+125891203201Stefano Morozzi01/2025
22952^675019+163251203201Stefano Morozzi01/2025
22962^675016-170847203201Stefano Morozzi01/2025
22972^675019-44755203201Stefano Morozzi01/2025
22982^675015+120225203200Stefano Morozzi01/2025
22992^675013-69831203200Stefano Morozzi01/2025
23002^675014-3897203200Stefano Morozzi01/2025
23012^675006+75357203198Stefano Morozzi01/2025
23022^675008+112231203198Stefano Morozzi01/2025
23032^675007-123309203198Stefano Morozzi01/2025
23042^675003+52529203197Stefano Morozzi01/2025
23052^675002+50595203196Stefano Morozzi01/2025
23062^674627-25161203083Enzo Doria09/2013
23072^674603-69337203076Enzo Doria12/2015
2308(182*10^203048+1)/3203050Robert Price09/2023
23092^674459+74213203033Enzo Doria04/2016
23102^674116-458879202930Enzo Doria04/2015
23112^674076-114755202918Enzo Doria04/2015
23125^289937-4^289937202658Jean-Louis Charton03/2013
23135^289926-289926^5202650Henri Lifchitz07/2024
2314(2^673184-7)/3202649Stefano Morozzi08/2022
2315(467617#+14534)/(2^2*13*43)202603Makoto Morimoto06/2019
2316(155^92479-1)/154202558Anonymous06/2024
23172^672773+219407202525Enzo Doria03/2024
23181374^64531-64531^1374202498Henri Lifchitz10/2024
23192^672556-1835519202460Enzo Doria04/2015
2320(7*10^202267+179)/3202268Robert Price02/2023
23212^671446-351401202126Enzo Doria07/2015
23222^671373+77747202104Enzo Doria05/2016
2323(2*10^202059+7)/9202059Rytis Slatkevicius01/2023
232498*10^202021-9202023Robert Price05/2023
23252^670726-114845201909Enzo Doria05/2015
23262^670539-25045201853Enzo Doria09/2013
232710^201801-93201801Robert Price02/2023
232843284^43519-43519^43284201769Norbert Schneider08/2018
23292^670213+282317201755Enzo Doria09/2016
23302^670133+89201731Stefano Morozzi05/2021
23312^669854-113501201647Enzo Doria08/2014
23322^669718+81619201606Enzo Doria08/2016
2333(299*10^201547-17)/3201549Robert Price02/2023
2334(145*10^201504-1)/9201506Serge Batalov12/2014
23352^668938-1839821201371Enzo Doria06/2015
2336(198^87623-1)/197201239Anonymous06/2024
23372^668492+1879303201237Enzo Doria08/2016
23387*10^201140-87201141Robert Price03/2023
23396^258413-5^258413201085Jean-Louis Charton03/2013
234010194^50161-50161^10194201063Norbert Schneider09/2020
23412^667894+1875589201057Enzo Doria06/2016
23422^667569-1836559200959Enzo Doria05/2015
2343(172*10^200746-1)/9200748Serge Batalov12/2014
2344(166^90407-1)/165200712Anonymous06/2024
23452^666430+782569200616Enzo Doria10/2016
2346(13*10^200610-43)/3200611Robert Price08/2023
2347(8*10^200408-11)/3200409Robert Price07/2023
2348p(38635)#-p(38635+1)200356Henri Lifchitz11/2024
2349(19*10^200260+101)/3200261Robert Price06/2023
235043183^43183+4^4200167Serge Batalov04/2024
2351(86^103471+1)/87200163Paul Bourdelais05/2018
2352(10^(2*100072+1)+36*10^100072-1)/9200145Robert Price09/2023
23532^664778+34789200119Enzo Doria07/2024
2354103*(10^100000+20110)^2-4707*(10^100000+20110)+50383200003Robert Price05/2017
2355103*(10^100000+33798)^2-4707*(10^100000+33798)+50383200003Robert Price01/2018
2356numbpart(32235776596)200002Serge Batalov04/2017
2357(10^200001+149)/3200001Serge Batalov12/2014
235810^200000+571791200001Patrick De Geest08/2019
2359(3^419180-621444)/3200000Stefano Morozzi06/2019
2360(3^419180-1941384)/3200000Stefano Morozzi08/2019
236110^200000-45557200000Patrick De Geest08/2019
2363(10^200000-1)/9-10^58838200000Akihiko Yoshida04/2020
23622593604092947240127723272^8192+2593604092947240127722755^8192200000Youcef Lemsafer01/2023
2364(2593604092947240127723019^8192+2593604092947240127723011^8192)/2199999Youcef Lemsafer01/2023
2365(2593604092947240127723087^8192+2593604092947240127722984^8192)/147457199994Youcef Lemsafer01/2023
2366(2593604092947240127723229^8192+2593604092947240127723171^8192)/15032745986199989Youcef Lemsafer01/2023
2367(2593604092947240127723215^8192+2593604092947240127722938^8192)/12728329863169199986Youcef Lemsafer01/2023
236892*10^199980-9199982Robert Price12/2021
2369(2593604092947240127723216^8192+2593604092947240127723163^8192)/20172788859482903707649199977Youcef Lemsafer01/2023
2370(85*10^199951-139)/9199952Robert Price08/2021
2371(10^199926+7)/29/373/2339199919Alfred Reich08/2021
23722^663838+25819199836Enzo Doria11/2023
237323*10^199833-9199835Robert Price10/2021
2374fibonacci(956176)-4199829Jon Grantham08/2023
2375(299*10^199801-17)/3199803Robert Price04/2020
23766*10^199788+77199789Robert Price06/2020
2377(2^663604+1)/270750449199757Anonymous10/2024
2378(23*10^199615+37)/3199616Robert Price02/2022
2379(17*10^199607-167)/3199608Robert Price05/2022
23802^663020-933075199589Paul Bourdelais06/2021
23812^663007+29963199585Enzo Doria03/2024
23823*2^662703-5199494Jon Grantham07/2023
2383(14*10^199447+73)/3199448Robert Price12/2018
2384(2^662424-15)/7199409Stefano Morozzi08/2022
23852^662194+22189199341Enzo Doria09/2023
23862^662103-29287199313Enzo Doria08/2015
2387(2*10^199283+457)/9199283Robert Price01/2018
2388(10^199248-19)/9199248Robert Price01/2018
2389(83*10^199213+529)/9199214Robert Price12/2021
2390(194*10^199146-17)/3199148Robert Price09/2020
2391(151*10^199003-1)/3199005Robert Price03/2020
23929*10^198946-73198947Robert Price01/2021
239345*10^198931-7198933Robert Price07/2020
23942^660482-2891198825Yves Minet05/2016
23952^659594+37729198558Enzo Doria10/2024
23962^659589-21198557Stefano Morozzi07/2022
23972^659583+1879223198555Enzo Doria08/2016
2398(53*10^198529+1)/9198530Serge Batalov07/2010
2399(17^161333-1)/913790128198504Paul Vanderveen05/2025
2400(49*10^198403+311)/9198404Robert Price06/2019
240196*10^198376-7198378Robert Price03/2021
2402(10^198375+7)/59/1201/87589198366Alfred Reich08/2021
24032^658828-29819198327Enzo Doria08/2015
24042^658776-2791229198312Enzo Doria01/2016
2405(35*10^198294-377)/9198295Robert Price07/2018
2406(4*10^198268+137)/3198269Robert Price03/2018
24072^658544-1854029198242Enzo Doria09/2015
2408(62*10^198229-233)/9198230Robert Price02/2022
2409(26*10^198200-41)/3198201Robert Price02/2022
2410(157^90239-1)/156198154Alexander Zhirkov06/2016
24112^657815+26213198023Enzo Doria12/2023
24122*10^197959-37197960Robert Price11/2021
2413(29*10^197941-41)/3197942Tyler Busby03/2024
2414(232*10^197897+17)/3197899Robert Price04/2021
2415(4*10^197778+173)/3197779Robert Price02/2018
24162^656964+6561197766Henri Lifchitz01/2025
24172^656763+211373197706Enzo Doria08/2023
241878*10^197702-7197704Robert Price10/2020
2419(17*10^197640-23)/3197641Robert Price03/2021
2420(29*10^197629-77)/3197630Robert Price02/2020
24212^656462+1874419197615Enzo Doria06/2016
2422(89^101363+1)/90197595Paul Bourdelais11/2017
24232^656172+229051197528Enzo Doria11/2024
24242^655893-344563197444Enzo Doria07/2015
24252^655875+71333197439Enzo Doria04/2016
24262^655845-9197430Robert Price01/2017
2427(299*10^197426+1)/3197428Robert Price04/2020
24282^655682-1849121197380Enzo Doria08/2015
24294*10^197268-89197269Robert Price11/2018
2430(11*10^197198-89)/3197199Robert Price05/2021
24312^655045-49603197189Enzo Doria10/2015
24322^655000-2784089197175Enzo Doria10/2015
2433(18^157051-1)/17197141Paul Bourdelais03/2010
2434(4*10^197061+41)/9197061Serge Batalov11/2022
2435(154*10^197005+17)/9197007Robert Price06/2022
24362^654400-39719196995Enzo Doria09/2015
2437(5^281807-2^281807)/3196975Jon Grantham08/2023
2438(14*10^196965-221)/9196966Robert Price04/2018
24392^654216-459995196939Enzo Doria06/2015
2440(17*10^196921+31)/3196922Robert Price01/2019
2441(14*10^196885-89)/3196886Robert Price05/2020
24423*10^196881-59196882Robert Price09/2018
24432^653851+82295196829Enzo Doria09/2016
2444(38*10^196792+691)/9196793Robert Price10/2018
2445(65*10^196768+493)/9196769Robert Price08/2021
24472^653636-29429196765Enzo Doria08/2015
24462^653638-11196765Stefano Morozzi07/2022
24482^653601-69673196754Enzo Doria02/2016
2449(44*10^196684+1)/9196685Serge Batalov07/2010
24502^652786-1852571196509Enzo Doria08/2015
24512^652752-1325196498Yves Minet07/2015
24522^652470-1859141196414Enzo Doria10/2015
24532^652346+29329196376Enzo Doria02/2024
24542^652307+1877483196364Enzo Doria08/2016
24552^652293-115273196360Enzo Doria06/2015
2456(47*10^196281+403)/9196282Robert Price03/2019
24572^652025+218027196280Enzo Doria01/2024
24582^652004+23961196273Enzo Doria10/2023
2459(7*10^196125-31)/3196126Robert Price12/2021
246033^129128+129128^33196083Norbert Schneider06/2022
24616*10^196070+73196071Robert Price04/2019
24622^651218-1868201196037Enzo Doria04/2016
24632^651047-49687195985Enzo Doria10/2015
246410^195968-700001195968Robert Price08/2021
2465fibonacci(937485)+3195923Jon Grantham08/2023
2466(29*10^195875-197)/3195876Robert Price08/2021
2467(25*10^195808-97)/9195809Robert Price01/2022
24682^650285-2785333195756Enzo Doria10/2015
2469(10^195732+7)/18089/49605893195721Alfred Reich08/2021
2470(29*10^195648-41)/3195649Tyler Busby03/2024
2471(69^106397-1)/68195647Paul Bourdelais10/2017
24722^649811+1877573195613Enzo Doria08/2016
24732^649662-170531195568Hans Havermann10/2018
24742^649586+182839195545Enzo Doria11/2016
24752^649537-1867363195531Enzo Doria04/2016
24762^649536-1861499195530Enzo Doria12/2015
24772^649493+25907195517Enzo Doria11/2023
2478(103*10^195478-1)/3195480Serge Batalov12/2014
24792^649102-59351195400Enzo Doria10/2015
2480(2*10^195399+529)/9195399Robert Price01/2018
2481(202*10^195383-13)/9195385Robert Price01/2020
24822^648988+1178971195365Enzo Doria06/2016
24832^648975-114319195361Enzo Doria02/2015
2484(11*10^195350-137)/9195351Robert Price01/2018
24852^648619-24835195254Enzo Doria09/2013
24865*10^195250-21195251Robert Price12/2021
2487(14*10^195234-83)/3195235Robert Price12/2018
24885*10^195221+81195222Robert Price03/2019
248910^195143-5001195143Robert Price12/2021
24902^648190-24737195125Enzo Doria09/2013
2491(57^111119+1)/58195110Paul Bourdelais10/2017
2492(29*10^195098-197)/3195099Robert Price08/2021
249310^195060+89701195061Patrick De Geest02/2021
249510^195060-40000000001195060Robert Price09/2020
249410^195060-110337195060Patrick De Geest02/2021
249656*10^195032-3195034Robert Price03/2020
249711^187185-90194934Enzo Doria09/2012
24982^647545-25194931Boyan Hu12/2024
24992^647468+220141194908Enzo Doria03/2024
2500(86*10^194818-437)/9194819Robert Price03/2021


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 19 2025 12:52 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!