PRP Records

Probable Primes Top 10000

(303322 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 ?
27512^675142+160903203238Stefano Morozzi06/2025
27522^675138-52371203237Stefano Morozzi04/2025
27532^675138+114979203237Stefano Morozzi06/2025
27542^675133-7273203236Stefano Morozzi04/2025
27552^675134-73473203236Stefano Morozzi04/2025
27562^675129+146825203235Stefano Morozzi06/2025
27572^675131+198275203235Stefano Morozzi06/2025
27582^675132+156585203235Stefano Morozzi06/2025
27592^675124-51675203233Stefano Morozzi04/2025
27602^675124+3907203233Stefano Morozzi06/2025
27612^675124+58711203233Stefano Morozzi06/2025
27622^675124+115557203233Stefano Morozzi06/2025
27632^675120-40809203232Stefano Morozzi04/2025
27642^675120-50573203232Stefano Morozzi04/2025
27652^675122+185715203232Stefano Morozzi06/2025
27662^675116-109889203231Stefano Morozzi04/2025
27672^675116+90607203231Stefano Morozzi06/2025
27682^675113+69461203230Stefano Morozzi06/2025
27692^675110+147825203229Stefano Morozzi06/2025
27702^675110+179107203229Stefano Morozzi06/2025
27712^675106-73241203228Stefano Morozzi02/2025
27722^675103-188727203227Stefano Morozzi02/2025
27732^675104-16199203227Stefano Morozzi02/2025
27742^675104-195303203227Stefano Morozzi02/2025
27752^675105-94521203227Stefano Morozzi02/2025
27762^675103+31599203227Stefano Morozzi04/2025
27772^675103+124629203227Stefano Morozzi06/2025
27782^675100-2775203226Stefano Morozzi02/2025
27792^675098-170703203225Stefano Morozzi02/2025
27802^675097+50651203225Stefano Morozzi04/2025
27812^675093-162123203224Stefano Morozzi02/2025
27822^675093-48955203224Stefano Morozzi02/2025
27832^675095-73591203224Stefano Morozzi02/2025
27842^675095-89937203224Stefano Morozzi02/2025
27852^675093+87767203224Stefano Morozzi04/2025
2786Phi(220603,-9)203224Henri Lifchitz12/2025
27872^675092-144539203223Stefano Morozzi02/2025
27882^675090+92253203223Stefano Morozzi04/2025
27892^675086-186387203222Stefano Morozzi02/2025
27902^675088-68505203222Stefano Morozzi02/2025
27912^675083-149199203221Stefano Morozzi02/2025
27922^675081-91425203220Stefano Morozzi02/2025
27932^675082-80213203220Stefano Morozzi02/2025
27942^675080+112651203220Stefano Morozzi04/2025
27952^675082+25435203220Stefano Morozzi04/2025
27962^675082+180613203220Stefano Morozzi04/2025
27972^675077-152683203219Stefano Morozzi02/2025
27982^675077-79213203219Stefano Morozzi02/2025
27992^675077+172221203219Stefano Morozzi04/2025
28002^675073-149065203218Stefano Morozzi02/2025
28012^675073-19663203218Stefano Morozzi02/2025
28022^675074+25755203218Stefano Morozzi04/2025
28032^675075+151203203218Stefano Morozzi04/2025
28042^675069-147135203217Stefano Morozzi02/2025
28052^675069-161461203217Stefano Morozzi02/2025
28062^675071-175189203217Stefano Morozzi02/2025
28072^675071+105575203217Stefano Morozzi04/2025
28082^675071+162299203217Stefano Morozzi04/2025
28092^675067+124541203216Stefano Morozzi04/2025
28102^675068+163695203216Stefano Morozzi04/2025
28112^675064+116445203215Stefano Morozzi04/2025
28122^675065+26045203215Stefano Morozzi04/2025
28132^675060+119983203214Stefano Morozzi02/2025
28142^675060+161301203214Stefano Morozzi02/2025
28152^675061-187773203214Stefano Morozzi02/2025
28162^675062-92193203214Stefano Morozzi02/2025
28172^675058-10403203213Stefano Morozzi01/2025
28182^675058-40337203213Stefano Morozzi01/2025
28192^675057+123557203213Stefano Morozzi02/2025
28202^675057+172475203213Stefano Morozzi02/2025
28212^675053-4801203212Stefano Morozzi01/2025
28222^675054-174341203212Stefano Morozzi01/2025
28232^675054-53697203212Stefano Morozzi01/2025
28242^675054+24825203212Stefano Morozzi02/2025
28252^675055+160265203212Stefano Morozzi02/2025
28262^675050-30015203211Stefano Morozzi01/2025
28272^675051-85941203211Stefano Morozzi01/2025
28282^675051+30885203211Stefano Morozzi02/2025
28292^675052+12537203211Stefano Morozzi02/2025
28302^675047-100299203210Stefano Morozzi01/2025
28312^675048-97313203210Stefano Morozzi01/2025
28322^675046+118119203210Stefano Morozzi02/2025
28332^675048+128941203210Stefano Morozzi02/2025
28342^675049+136359203210Stefano Morozzi02/2025
28352^675044-81087203209Stefano Morozzi01/2025
28362^675042-179811203208Stefano Morozzi01/2025
28372^675036-192939203207Stefano Morozzi01/2025
28382^675037-17853203207Stefano Morozzi01/2025
28392^675036+47101203207Stefano Morozzi02/2025
28402^675038+189589203207Stefano Morozzi02/2025
28412^675034-169727203206Stefano Morozzi01/2025
28422^675035-173055203206Stefano Morozzi01/2025
28432^675035-73551203206Stefano Morozzi01/2025
28442^675033+79109203206Stefano Morozzi02/2025
28452^675034+154057203206Stefano Morozzi02/2025
28462^675030+109245203205Stefano Morozzi01/2025
28472^675030-160047203205Stefano Morozzi01/2025
28482^675027+106733203204Stefano Morozzi01/2025
28492^675026-67377203204Stefano Morozzi01/2025
28502^675021+13335203202Stefano Morozzi01/2025
28512^675020-180497203202Stefano Morozzi01/2025
28522^675016+174777203201Stefano Morozzi01/2025
28532^675017+128379203201Stefano Morozzi01/2025
28542^675017+171249203201Stefano Morozzi01/2025
28552^675018+86517203201Stefano Morozzi01/2025
28562^675019+125891203201Stefano Morozzi01/2025
28572^675019+163251203201Stefano Morozzi01/2025
28582^675016-170847203201Stefano Morozzi01/2025
28592^675019-44755203201Stefano Morozzi01/2025
28602^675015+120225203200Stefano Morozzi01/2025
28612^675013-69831203200Stefano Morozzi01/2025
28622^675014-3897203200Stefano Morozzi01/2025
28632^675006+75357203198Stefano Morozzi01/2025
28642^675008+112231203198Stefano Morozzi01/2025
28652^675007-123309203198Stefano Morozzi01/2025
28662^675003+52529203197Stefano Morozzi01/2025
28672^675002+50595203196Stefano Morozzi01/2025
28682^674627-25161203083Enzo Doria09/2013
28692^674603-69337203076Enzo Doria12/2015
2870(182*10^203048+1)/3203050Robert Price09/2023
28712^674459+74213203033Enzo Doria04/2016
28722^674116-458879202930Enzo Doria04/2015
28732^674076-114755202918Enzo Doria04/2015
28745^289937-4^289937202658Jean-Louis Charton03/2013
28755^289926-289926^5202650Henri Lifchitz07/2024
2876(2^673184-7)/3202649Stefano Morozzi08/2022
2877(467617#+14534)/(2^2*13*43)202603Makoto Morimoto06/2019
2878(155^92479-1)/154202558Anonymous06/2024
28792^672773+219407202525Enzo Doria03/2024
28801374^64531-64531^1374202498Henri Lifchitz10/2024
28812^672556-1835519202460Enzo Doria04/2015
2882(7*10^202267+179)/3202268Robert Price02/2023
28832^671446-351401202126Enzo Doria07/2015
28842^671373+77747202104Enzo Doria05/2016
2885(2*10^202059+7)/9202059Rytis Slatkevicius01/2023
288698*10^202021-9202023Robert Price05/2023
2887Phi(265967,7)202013Henri Lifchitz02/2026
28882^670726-114845201909Enzo Doria05/2015
28892^670539-25045201853Enzo Doria09/2013
289010^201801-93201801Robert Price02/2023
289143284^43519-43519^43284201769Norbert Schneider08/2018
28922^670213+282317201755Enzo Doria09/2016
28932^670133+89201731Stefano Morozzi05/2021
2894Sm(42558)/1793778201677Youcef Lemsafer06/2026
28952^669854-113501201647Enzo Doria08/2014
28962^669718+81619201606Enzo Doria08/2016
2897(299*10^201547-17)/3201549Robert Price02/2023
2898(145*10^201504-1)/9201506Serge Batalov12/2014
28992^668938-1839821201371Enzo Doria06/2015
2900(198^87623-1)/197201239Anonymous06/2024
29012^668492+1879303201237Enzo Doria08/2016
29027*10^201140-87201141Robert Price03/2023
29036^258413-5^258413201085Jean-Louis Charton03/2013
290410194^50161-50161^10194201063Norbert Schneider09/2020
29052^667894+1875589201057Enzo Doria06/2016
2906Phi(253483,-7)201019Henri Lifchitz02/2026
29072^667569-1836559200959Enzo Doria05/2015
2908(172*10^200746-1)/9200748Serge Batalov12/2014
2909(166^90407-1)/165200712Anonymous06/2024
29102^666430+782569200616Enzo Doria10/2016
2911Phi(81682,-81682)200612Henri Lifchitz12/2025
2912(13*10^200610-43)/3200611Robert Price08/2023
2913Phi(221863,-9)200552Henri Lifchitz12/2025
2914(8*10^200408-11)/3200409Robert Price07/2023
2915p(38635)#-p(38635+1)200356Henri Lifchitz11/2024
2916(19*10^200260+101)/3200261Robert Price06/2023
291743183^43183+4^4200167Serge Batalov04/2024
2918(86^103471+1)/87200163Paul Bourdelais05/2018
2919(10^(2*100072+1)+36*10^100072-1)/9200145Robert Price09/2023
29202^664778+34789200119Enzo Doria07/2024
2921Phi(23488,19!)200101Henri Lifchitz12/2025
2922103*(10^100000+20110)^2-4707*(10^100000+20110)+50383200003Robert Price05/2017
2923103*(10^100000+33798)^2-4707*(10^100000+33798)+50383200003Robert Price01/2018
2924numbpart(32235776596)200002Serge Batalov04/2017
2925(10^200001+149)/3200001Serge Batalov12/2014
292610^200000+571791200001Patrick De Geest08/2019
2927(3^419180-621444)/3200000Stefano Morozzi06/2019
2928(3^419180-1941384)/3200000Stefano Morozzi08/2019
292910^200000-45557200000Patrick De Geest08/2019
2931(10^200000-1)/9-10^58838200000Akihiko Yoshida04/2020
29302593604092947240127723272^8192+2593604092947240127722755^8192200000Youcef Lemsafer01/2023
2932(2593604092947240127723019^8192+2593604092947240127723011^8192)/2199999Youcef Lemsafer01/2023
2933(2593604092947240127723087^8192+2593604092947240127722984^8192)/147457199994Youcef Lemsafer01/2023
2934(2593604092947240127723229^8192+2593604092947240127723171^8192)/15032745986199989Youcef Lemsafer01/2023
2935(2593604092947240127723215^8192+2593604092947240127722938^8192)/12728329863169199986Youcef Lemsafer01/2023
293692*10^199980-9199982Robert Price12/2021
2937(2593604092947240127723216^8192+2593604092947240127723163^8192)/20172788859482903707649199977Youcef Lemsafer01/2023
2938(85*10^199951-139)/9199952Robert Price08/2021
2939(10^199926+7)/29/373/2339199919Alfred Reich08/2021
2940Sm(42193)/106739199854Youcef Lemsafer06/2026
29412^663838+25819199836Enzo Doria11/2023
294223*10^199833-9199835Robert Price10/2021
2943fibonacci(956176)-4199829Jon Grantham08/2023
2944(299*10^199801-17)/3199803Robert Price04/2020
29456*10^199788+77199789Robert Price06/2020
2946(2^663604+1)/270750449199757Anonymous10/2024
2947(23*10^199615+37)/3199616Robert Price02/2022
2948(17*10^199607-167)/3199608Robert Price05/2022
29492^663020-933075199589Paul Bourdelais06/2021
29502^663007+29963199585Enzo Doria03/2024
29513*2^662703-5199494Jon Grantham07/2023
2952(14*10^199447+73)/3199448Robert Price12/2018
2953(2^662424-15)/7199409Stefano Morozzi08/2022
29542^662194+22189199341Enzo Doria09/2023
29552^662103-29287199313Enzo Doria08/2015
2956(2*10^199283+457)/9199283Robert Price01/2018
2957(10^199248-19)/9199248Robert Price01/2018
2958(83*10^199213+529)/9199214Robert Price12/2021
2959(194*10^199146-17)/3199148Robert Price09/2020
2960(151*10^199003-1)/3199005Robert Price03/2020
29619*10^198946-73198947Robert Price01/2021
296245*10^198931-7198933Robert Price07/2020
29632^660482-2891198825Yves Minet05/2016
29642^659594+37729198558Enzo Doria10/2024
29652^659589-21198557Stefano Morozzi07/2022
29662^659583+1879223198555Enzo Doria08/2016
2967(53*10^198529+1)/9198530Serge Batalov07/2010
2968(17^161333-1)/913790128198504Paul Vanderveen05/2025
2969(5^329624)%(4^329624)198454Henri Lifchitz07/2025
2970(49*10^198403+311)/9198404Robert Price06/2019
297196*10^198376-7198378Robert Price03/2021
2972(10^198375+7)/59/1201/87589198366Alfred Reich08/2021
29732^658828-29819198327Enzo Doria08/2015
29742^658776-2791229198312Enzo Doria01/2016
2975(35*10^198294-377)/9198295Robert Price07/2018
2976(4*10^198268+137)/3198269Robert Price03/2018
29772^658544-1854029198242Enzo Doria09/2015
2978(62*10^198229-233)/9198230Robert Price02/2022
2979(26*10^198200-41)/3198201Robert Price02/2022
2980(157^90239-1)/156198154Alexander Zhirkov06/2016
29812^657815+26213198023Enzo Doria12/2023
29822*10^197959-37197960Robert Price11/2021
2983(29*10^197941-41)/3197942Tyler Busby03/2024
2984(232*10^197897+17)/3197899Robert Price04/2021
2985(4*10^197778+173)/3197779Robert Price02/2018
29862^656964+6561197766Henri Lifchitz01/2025
29872^656763+211373197706Enzo Doria08/2023
298878*10^197702-7197704Robert Price10/2020
2989(17*10^197640-23)/3197641Robert Price03/2021
2990(29*10^197629-77)/3197630Robert Price02/2020
29912^656462+1874419197615Enzo Doria06/2016
2992(89^101363+1)/90197595Paul Bourdelais11/2017
29932^656172+229051197528Enzo Doria11/2024
29942^655893-344563197444Enzo Doria07/2015
29952^655875+71333197439Enzo Doria04/2016
29962^655845-9197430Robert Price01/2017
2997(299*10^197426+1)/3197428Robert Price04/2020
29982^655682-1849121197380Enzo Doria08/2015
29994*10^197268-89197269Robert Price11/2018
3000(11*10^197198-89)/3197199Robert Price05/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 15 2026 19:12 (Time in France)

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