PRP Records

Probable Primes Top 10000

(295149 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 ?
12512^865238+214759260463Enzo Doria11/2023
12522^865048+1882411260406Enzo Doria12/2016
12532^864899-113871260361Enzo Doria10/2014
1254(16*10^260256-91)/3260257Robert Price11/2022
1255(7*10^260198-61)/9260198Erik Branger11/2011
12562^864298-2788421260180Enzo Doria12/2015
12572^864039-2791357260102Enzo Doria01/2016
12582^863621-113833259976Enzo Doria10/2014
125910^259945-11259945Mischa Rodermond04/2023
1260(28*10^259897+113)/3259898Robert Price06/2023
12612^862837+75767259740Enzo Doria05/2016
12622^862637-31259680Jorge Menendez05/2019
12632^862088+1874941259515Enzo Doria06/2016
12642^861987-134557259484Hans Havermann10/2018
1265(14*10^259431-143)/3259432Robert Price05/2023
12662^861516-1854029259343Enzo Doria09/2015
12672^860975-1853977259180Enzo Doria09/2015
12683^543128+16259138Robert Price04/2020
12692^860625-1858843259074Enzo Doria10/2015
12702^860110+77689258919Enzo Doria05/2016
12712^859600+1880371258766Enzo Doria10/2016
12722^859433+494711258716Makoto Morimoto10/2013
1274(2^859433-44)/(2^2*3)258715Makoto Morimoto08/2019
1273(2^859431-11)/3258715Stefano Morozzi08/2022
1275(13*10^258710-43)/3258711Robert Price08/2023
1276(2^859433+39899)/(73*3907*46301)258705Makoto Morimoto10/2016
12772^859240+1875271258658Enzo Doria06/2016
1278Tau(971^15738)258571Nik Lygeros / Olivier Rozier05/2015
12792^858812+30421258529Enzo Doria03/2024
1280(23*10^258494-47)/3258495Robert Price09/2023
1281(144^119671+1)/145258292Paul Bourdelais08/2019
12822^857608+105258166Stefano Morozzi05/2021
1283(11*2^857159-13)/15258031Renaud Lifchitz08/2011
12842^857016-633113257988Enzo Doria12/2013
12852^855732-113969257602Enzo Doria10/2014
1286(5*10^257431+91)/3257432Robert Price08/2023
12872^853682-3911256984Enzo Doria05/2014
128811^246668-90256879Enzo Doria12/2012
12892^853181+30287256834Enzo Doria03/2024
12905*2^852698+3256689Jon Grantham07/2023
1291(23*10^256654+7)/3256655Robert Price05/2023
12922^851904-113939256449Enzo Doria10/2014
12932^851725-851725^2256395Henri Lifchitz03/2019
129411^246167-90256357Enzo Doria12/2012
1295(85*10^256301-1)/3256303Robert Price12/2022
1296(10^256187+7)/63443/148782853256175Alfred Reich10/2021
12972^850700-569049256087Enzo Doria11/2013
12982^850675+153256079Stefano Morozzi05/2021
129921^193601-20^193601255983Jean-Louis Charton02/2015
1300(37^163193+1)/38255918Paul Bourdelais07/2019
1301(14*10^255805-83)/3255806Robert Price11/2022
13022^849316+25861255670Enzo Doria12/2023
13032^849177-114025255628Enzo Doria12/2014
13042*10^255442-21255443Robert Price08/2023
13052^848502-3173255425Yves Minet07/2016
13062^848178-140291255328Enzo Doria01/2014
13077*10^255167+87255168Robert Price11/2022
13082^847622-2441255160Yves Minet02/2016
13092^847291+182843255061Enzo Doria11/2016
13102^847174+1879429255025Enzo Doria09/2016
13112^846881+215837254937Enzo Doria12/2023
131224*29^174239+13361254809Curtis Bright04/2015
131322*10^254639+7254641Robert Price10/2022
13142^845633-933075254561Paul Bourdelais11/2021
13152^845610-1868591254554Enzo Doria04/2016
13162^845484+81931254517Enzo Doria08/2016
13172^845402-114761254492Enzo Doria05/2015
131898*10^254173-9254175Robert Price05/2023
13192^844334-2792441254170Enzo Doria02/2016
13202*10^254162+69254163Robert Price08/2023
1321(4*10^254107+11)/3254108Tyler Busby02/2023
132211^243796-90253888Enzo Doria12/2012
1323(10^253891+7)/44777/79843/16940711253875Alfred Reich10/2021
132430^171733-29^171733253671Jean-Louis Charton10/2018
13252^842325+25907253566Enzo Doria11/2023
13262^842209+1876037253531Enzo Doria07/2016
13272^842123-59197253505Enzo Doria10/2015
1328(8*10^253313-53)/9253313Serge Batalov11/2022
1329(28*10^253210+191)/3253211Robert Price07/2023
13302^840797-3253106Paul Bourdelais06/2019
13312^840716-2969253081Yves Minet05/2016
13322^840358-462491252973Enzo Doria08/2015
13332^840310+1878379252959Enzo Doria08/2016
13342^840203-21252927Stefano Morozzi07/2022
133511^242579-60252620Enzo Doria10/2012
133645^152659+2252378Robert Price09/2015
1337(95^127583+1)/96252322Paul Bourdelais07/2019
13387*10^252209-17252210Robert Price12/2022
13392^837725+1869377252181Enzo Doria05/2016
13402^837536-311039252124Enzo Doria06/2015
134121^190632-2252058Robert Price07/2015
13422^837242+1873297252035Enzo Doria06/2016
13432^836656-2787929251859Enzo Doria11/2015
13442^836548+219061251827Enzo Doria02/2024
13452^836380+1875541251776Enzo Doria07/2016
1346(359^98327-1)/358251233Alexander Zhirkov11/2017
1347tau(41^28288)250924Nik Lygeros / Olivier Rozier10/2013
1348(28*10^250655+113)/3250656Robert Price06/2023
13492^832511-461197250611Enzo Doria07/2015
13502^832505+1881137250609Enzo Doria11/2016
13512^832363+583295250567Enzo Doria12/2016
13522^832244-403635250531Enzo Doria01/2014
1353(14*10^250336-41)/9250337Serge Batalov01/2023
13542^831528+24811250315Enzo Doria11/2023
13552^831157+1880657250204Enzo Doria11/2016
13562^831088-7200899250183Enzo Doria01/2015
13572^830956-1349250143Yves Minet07/2015
13582^830699+220583250066Enzo Doria03/2024
13592^830037+282317249867Enzo Doria09/2016
13602^829589-113653249732Enzo Doria09/2014
1361(4*10^249550-7)/3249551Serge Batalov01/2023
1362(103*10^249399+17)/3249401Robert Price04/2023
13632^828281-3193249338Yves Minet08/2016
1364(2^828140-19)/3249295Stefano Morozzi08/2022
13652^828064-2785619249273Enzo Doria10/2015
13662^827602+60409249134Enzo Doria03/2016
13672^827306+212419249044Enzo Doria09/2023
136810^249010+348861249011Patrick De Geest04/2016
136910^249010-21249010Serge Batalov12/2014
13702^826733+1882907248872Enzo Doria12/2016
13712^825800+22441248591Enzo Doria10/2023
13722^825682+1876549248556Enzo Doria07/2016
13732^824991-114121248348Enzo Doria12/2014
13742^824642-362727248242Enzo Doria12/2013
13752^824565-114265248219Enzo Doria01/2015
1376(73*10^248145-1)/9248146Robert Price01/2015
13772^823321+219407247845Enzo Doria02/2024
1378(2^823337+1)/(3*362268281)247841Gord Palameta08/2018
1379(13*10^247793-43)/3247794Robert Price08/2023
1380(2^822971-1)/6583769/28211445881/21255852651726486149207247700Robert Kinser09/2016
13812^822296+76501247536Enzo Doria05/2016
13822^821590-114167247324Enzo Doria12/2014
13832^821512-2790659247300Enzo Doria12/2015
1384(21996^57121-1)/(21996^239-1)247002Ryan Propper11/2023
13852^820356+7246952Jon Grantham08/2023
13862^820077+382847246868Enzo Doria11/2016
13872^820001+81269246845Enzo Doria07/2016
13882^819463-59197246683Enzo Doria10/2015
13892^819296+80581246633Enzo Doria07/2016
13902^818764+21573246473Enzo Doria11/2023
13912^817852+215491246198Enzo Doria11/2023
13922^817160-350369245990Enzo Doria06/2015
13932^816039-19245653Stefano Morozzi07/2022
13942^816029+219407245650Enzo Doria02/2024
1395(71*10^245558-17)/9245559Serge Batalov01/2023
13965*3^514648+2^514648245551Jon Grantham08/2023
139788093#+(653879#)/(88093#)245374Makoto Morimoto11/2017
13982^815111-113857245373Enzo Doria10/2014
1399(34555^54289-1)/(34555^233-1)245334Ryan Propper11/2023
14002^814914-4001245314Yves Minet05/2017
1401846^83761-845^83761245200Jean-Louis Charton12/2012
14022^814356-2790449245146Enzo Doria12/2015
14032^814276-459029245122Enzo Doria04/2015
14042^814023+180923245046Enzo Doria07/2016
14052^813496+216751244887Enzo Doria12/2023
1406(3^513059-2^513059)/(1026119*5430216457)244776Mike Oakes03/2017
14073^513007+16244767Robert Price04/2020
14082^811882+27289244401Enzo Doria12/2023
14092^811842-113675244389Enzo Doria09/2014
14102^811132-2787929244176Enzo Doria11/2015
14112^809746-2790971243758Enzo Doria01/2016
1412(14*10^243724-197)/3243725Robert Price03/2023
14132^808767-3295243464Yves Minet12/2016
14142^808621-113809243420Enzo Doria09/2014
14152^808199+29693243293Enzo Doria03/2024
14162^807724+1879621243150Enzo Doria09/2016
14172^807417+217787243057Enzo Doria01/2024
1418(23*10^242909+91)/3242910Robert Price03/2023
14192^806708+20371242844Enzo Doria08/2023
14202*10^242822-91242823Robert Price02/2023
142120^186554-3242713Paul Bourdelais12/2020
14222^805843-113611242583Enzo Doria08/2014
14232^805745-459763242554Enzo Doria05/2015
14242^805353+782687242436Enzo Doria11/2016
1425(19*10^242362-7)/3242363Robert Price12/2023
14262^804895+29963242298Enzo Doria03/2024
14272^804725+28229242247Enzo Doria01/2024
14286^311257+5242206Paul Bourdelais02/2021
14292^804277-417933242112Enzo Doria01/2014
14302^803468-269039241868Enzo Doria10/2013
14312^803172+80851241779Enzo Doria07/2016
14322^803011+220073241731Enzo Doria03/2024
14333^506233-2241535Robert Price11/2013
14342^802025-25999241434Enzo Doria10/2013
1435(3^505823+3^252912+1)/7241339Serge Batalov03/2014
14362^801575+25073241299Enzo Doria11/2023
14372^801303+1872923241217Enzo Doria05/2016
14382^801105+216977241157Enzo Doria12/2023
1439(23*10^241048-143)/3241049Robert Price12/2023
14402^800579-1862947240999Enzo Doria12/2015
14412^799999+16205240824Norman Luhn09/2023
14423^504206+2240568Luke W. Richards03/2018
14432^798973-26283240515Enzo Doria10/2013
14442^798671-69487240424Enzo Doria12/2015
14452^797220+79831239988Enzo Doria06/2016
14462^796910-26001239894Enzo Doria10/2013
14472^796598+653119239800Enzo Doria12/2016
14482^796432-1859729239750Enzo Doria11/2015
14492^796002-1852211239621Enzo Doria08/2015
14502^795884+214081239585Enzo Doria10/2023
14512^795709+75767239533Enzo Doria04/2016
14522^795708+81721239532Enzo Doria08/2016
14532^795468-2786249239460Enzo Doria10/2015
14542^795442+80779239452Enzo Doria07/2016
14552^795075-1852057239342Enzo Doria08/2015
1456(86^123677+1)/87239252Paul Bourdelais01/2019
14572^794043+1875023239031Enzo Doria06/2016
14582^793347-69577238822Enzo Doria01/2016
14595*2^793288+3238805Jon Grantham07/2023
14602^792988-344429238714Enzo Doria08/2015
14612^792700-2786369238627Enzo Doria11/2015
14622^792663-1844797238616Enzo Doria06/2015
14632^792605-291943238598Enzo Doria07/2015
14642^792366+218599238526Enzo Doria01/2024
1465(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
14662^791321+30077238212Enzo Doria03/2024
14674*10^238163+21238164Robert Price12/2022
1468(26*10^238157-77)/3238158Robert Price03/2023
146910^237670+9237671Robert Price08/2023
14702^789373+1869377237625Enzo Doria05/2016
1471((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961237544Serge Batalov04/2015
14722^789033+218537237523Enzo Doria01/2024
14732^788942+1866409237496Enzo Doria02/2016
14742^788844-114329237466Enzo Doria01/2015
14752^788705-1859713237424Enzo Doria11/2015
147615^201475+14236953Alfred Reich10/2023
14772^786663+219173236810Enzo Doria02/2024
14782^786180+1871971236664Enzo Doria05/2016
147911^227092-90236492Enzo Doria11/2012
14802^785260+1866361236387Enzo Doria02/2016
14812^785220+1880611236375Enzo Doria10/2016
1482(2^784689-15)/7236215Stefano Morozzi08/2022
148319^184650-2236122Robert Price10/2014
148410^236059+216513236060Patrick De Geest04/2016
148510^236059-20909236059Robert Price09/2015
14862^783893-21235976Stefano Morozzi07/2022
1487(87^121487-1)/86235625Paul Bourdelais12/2018
14882^782634-113981235597Enzo Doria11/2014
14892^782423+1879733235533Enzo Doria09/2016
1490(10^(2*117707+1)+12*10^117707-1)/3235415Robert Price10/2023
14912^781682-2789543235310Enzo Doria12/2015
14922^780481+21489234949Enzo Doria05/2024
14932^780408-113453234927Enzo Doria08/2014
14947*10^234915+9234916Robert Price04/2023
14952^780368-1864829234915Enzo Doria01/2016
14962^780284+7234889Jon Grantham08/2023
14972^779593-1836559234681Enzo Doria05/2015
1498(8713#+(549391#)/(8713#))/360295171234487Makoto Morimoto11/2017
1499(5^335429+1)/6234455Paul Bourdelais08/2010
15002^778788+22201234439Enzo Doria09/2023


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 22 2024 21:19 (Time in France)

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