PRP Records

Probable Primes Top 10000

(294627 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 ?
12512^845633-933075254561Paul Bourdelais11/2021
12522^845610-1868591254554Enzo Doria04/2016
12532^845484+81931254517Enzo Doria08/2016
12542^845402-114761254492Enzo Doria05/2015
125598*10^254173-9254175Robert Price05/2023
12562^844334-2792441254170Enzo Doria02/2016
12572*10^254162+69254163Robert Price08/2023
1258(4*10^254107+11)/3254108Tyler Busby02/2023
125911^243796-90253888Enzo Doria12/2012
1260(10^253891+7)/44777/79843/16940711253875Alfred Reich10/2021
126130^171733-29^171733253671Jean-Louis Charton10/2018
12622^842325+25907253566Enzo Doria11/2023
12632^842209+1876037253531Enzo Doria07/2016
12642^842123-59197253505Enzo Doria10/2015
1265(8*10^253313-53)/9253313Serge Batalov11/2022
1266(28*10^253210+191)/3253211Robert Price07/2023
12672^840797-3253106Paul Bourdelais06/2019
12682^840716-2969253081Yves Minet05/2016
12692^840358-462491252973Enzo Doria08/2015
12702^840310+1878379252959Enzo Doria08/2016
12712^840203-21252927Stefano Morozzi07/2022
127211^242579-60252620Enzo Doria10/2012
127345^152659+2252378Robert Price09/2015
1274(95^127583+1)/96252322Paul Bourdelais07/2019
12757*10^252209-17252210Robert Price12/2022
12762^837725+1869377252181Enzo Doria05/2016
12772^837536-311039252124Enzo Doria06/2015
127821^190632-2252058Robert Price07/2015
12792^837242+1873297252035Enzo Doria06/2016
12802^836656-2787929251859Enzo Doria11/2015
12812^836548+219061251827Enzo Doria02/2024
12822^836380+1875541251776Enzo Doria07/2016
1283(359^98327-1)/358251233Alexander Zhirkov11/2017
1284tau(41^28288)250924Nik Lygeros / Olivier Rozier10/2013
1285(28*10^250655+113)/3250656Robert Price06/2023
12862^832511-461197250611Enzo Doria07/2015
12872^832505+1881137250609Enzo Doria11/2016
12882^832363+583295250567Enzo Doria12/2016
12892^832244-403635250531Enzo Doria01/2014
1290(14*10^250336-41)/9250337Serge Batalov01/2023
12912^831528+24811250315Enzo Doria11/2023
12922^831157+1880657250204Enzo Doria11/2016
12932^831088-7200899250183Enzo Doria01/2015
12942^830956-1349250143Yves Minet07/2015
12952^830037+282317249867Enzo Doria09/2016
12962^829589-113653249732Enzo Doria09/2014
1297(4*10^249550-7)/3249551Serge Batalov01/2023
1298(103*10^249399+17)/3249401Robert Price04/2023
12992^828281-3193249338Yves Minet08/2016
1300(2^828140-19)/3249295Stefano Morozzi08/2022
13012^828064-2785619249273Enzo Doria10/2015
13022^827602+60409249134Enzo Doria03/2016
13032^827306+212419249044Enzo Doria09/2023
130410^249010+348861249011Patrick De Geest04/2016
130510^249010-21249010Serge Batalov12/2014
13062^826733+1882907248872Enzo Doria12/2016
13072^825800+22441248591Enzo Doria10/2023
13082^825682+1876549248556Enzo Doria07/2016
13092^824991-114121248348Enzo Doria12/2014
13102^824642-362727248242Enzo Doria12/2013
13112^824565-114265248219Enzo Doria01/2015
1312(73*10^248145-1)/9248146Robert Price01/2015
13132^823321+219407247845Enzo Doria02/2024
1314(2^823337+1)/(3*362268281)247841Gord Palameta08/2018
1315(13*10^247793-43)/3247794Robert Price08/2023
1316(2^822971-1)/6583769/28211445881/21255852651726486149207247700Robert Kinser09/2016
13172^822296+76501247536Enzo Doria05/2016
13182^821590-114167247324Enzo Doria12/2014
13192^821512-2790659247300Enzo Doria12/2015
1320(21996^57121-1)/(21996^239-1)247002Ryan Propper11/2023
13212^820356+7246952Jon Grantham08/2023
13222^820077+382847246868Enzo Doria11/2016
13232^820001+81269246845Enzo Doria07/2016
13242^819463-59197246683Enzo Doria10/2015
13252^819296+80581246633Enzo Doria07/2016
13262^818764+21573246473Enzo Doria11/2023
13272^817852+215491246198Enzo Doria11/2023
13282^817160-350369245990Enzo Doria06/2015
13292^816039-19245653Stefano Morozzi07/2022
13302^816029+219407245650Enzo Doria02/2024
1331(71*10^245558-17)/9245559Serge Batalov01/2023
13325*3^514648+2^514648245551Jon Grantham08/2023
133388093#+(653879#)/(88093#)245374Makoto Morimoto11/2017
13342^815111-113857245373Enzo Doria10/2014
1335(34555^54289-1)/(34555^233-1)245334Ryan Propper11/2023
13362^814914-4001245314Yves Minet05/2017
1337846^83761-845^83761245200Jean-Louis Charton12/2012
13382^814356-2790449245146Enzo Doria12/2015
13392^814276-459029245122Enzo Doria04/2015
13402^814023+180923245046Enzo Doria07/2016
13412^813496+216751244887Enzo Doria12/2023
1342(3^513059-2^513059)/(1026119*5430216457)244776Mike Oakes03/2017
13433^513007+16244767Robert Price04/2020
13442^811882+27289244401Enzo Doria12/2023
13452^811842-113675244389Enzo Doria09/2014
13462^811132-2787929244176Enzo Doria11/2015
13472^809746-2790971243758Enzo Doria01/2016
1348(14*10^243724-197)/3243725Robert Price03/2023
13492^808767-3295243464Yves Minet12/2016
13502^808621-113809243420Enzo Doria09/2014
13512^808199+29693243293Enzo Doria03/2024
13522^807724+1879621243150Enzo Doria09/2016
13532^807417+217787243057Enzo Doria01/2024
1354(23*10^242909+91)/3242910Robert Price03/2023
13552^806708+20371242844Enzo Doria08/2023
13562*10^242822-91242823Robert Price02/2023
135720^186554-3242713Paul Bourdelais12/2020
13582^805843-113611242583Enzo Doria08/2014
13592^805745-459763242554Enzo Doria05/2015
13602^805353+782687242436Enzo Doria11/2016
1361(19*10^242362-7)/3242363Robert Price12/2023
13622^804725+28229242247Enzo Doria01/2024
13636^311257+5242206Paul Bourdelais02/2021
13642^804277-417933242112Enzo Doria01/2014
13652^803468-269039241868Enzo Doria10/2013
13662^803172+80851241779Enzo Doria07/2016
13672^803011+220073241731Enzo Doria03/2024
13683^506233-2241535Robert Price11/2013
13692^802025-25999241434Enzo Doria10/2013
1370(3^505823+3^252912+1)/7241339Serge Batalov03/2014
13712^801575+25073241299Enzo Doria11/2023
13722^801303+1872923241217Enzo Doria05/2016
13732^801105+216977241157Enzo Doria12/2023
1374(23*10^241048-143)/3241049Robert Price12/2023
13752^800579-1862947240999Enzo Doria12/2015
13762^799999+16205240824Norman Luhn09/2023
13773^504206+2240568Luke W. Richards03/2018
13782^798973-26283240515Enzo Doria10/2013
13792^798671-69487240424Enzo Doria12/2015
13802^797220+79831239988Enzo Doria06/2016
13812^796910-26001239894Enzo Doria10/2013
13822^796598+653119239800Enzo Doria12/2016
13832^796432-1859729239750Enzo Doria11/2015
13842^796002-1852211239621Enzo Doria08/2015
13852^795884+214081239585Enzo Doria10/2023
13862^795709+75767239533Enzo Doria04/2016
13872^795708+81721239532Enzo Doria08/2016
13882^795468-2786249239460Enzo Doria10/2015
13892^795442+80779239452Enzo Doria07/2016
13902^795075-1852057239342Enzo Doria08/2015
1391(86^123677+1)/87239252Paul Bourdelais01/2019
13922^794043+1875023239031Enzo Doria06/2016
13932^793347-69577238822Enzo Doria01/2016
13945*2^793288+3238805Jon Grantham07/2023
13952^792988-344429238714Enzo Doria08/2015
13962^792700-2786369238627Enzo Doria11/2015
13972^792663-1844797238616Enzo Doria06/2015
13982^792605-291943238598Enzo Doria07/2015
13992^792366+218599238526Enzo Doria01/2024
1400(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
14014*10^238163+21238164Robert Price12/2022
1402(26*10^238157-77)/3238158Robert Price03/2023
140310^237670+9237671Robert Price08/2023
14042^789373+1869377237625Enzo Doria05/2016
1405((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961237544Serge Batalov04/2015
14062^789033+218537237523Enzo Doria01/2024
14072^788942+1866409237496Enzo Doria02/2016
14082^788844-114329237466Enzo Doria01/2015
14092^788705-1859713237424Enzo Doria11/2015
141015^201475+14236953Alfred Reich10/2023
14112^786663+219173236810Enzo Doria02/2024
14122^786180+1871971236664Enzo Doria05/2016
141311^227092-90236492Enzo Doria11/2012
14142^785260+1866361236387Enzo Doria02/2016
14152^785220+1880611236375Enzo Doria10/2016
1416(2^784689-15)/7236215Stefano Morozzi08/2022
141719^184650-2236122Robert Price10/2014
141810^236059+216513236060Patrick De Geest04/2016
141910^236059-20909236059Robert Price09/2015
14202^783893-21235976Stefano Morozzi07/2022
1421(87^121487-1)/86235625Paul Bourdelais12/2018
14222^782634-113981235597Enzo Doria11/2014
14232^782423+1879733235533Enzo Doria09/2016
1424(10^(2*117707+1)+12*10^117707-1)/3235415Robert Price10/2023
14252^781682-2789543235310Enzo Doria12/2015
14262^780408-113453234927Enzo Doria08/2014
14277*10^234915+9234916Robert Price04/2023
14282^780368-1864829234915Enzo Doria01/2016
14292^780284+7234889Jon Grantham08/2023
14302^779593-1836559234681Enzo Doria05/2015
1431(8713#+(549391#)/(8713#))/360295171234487Makoto Morimoto11/2017
1432(5^335429+1)/6234455Paul Bourdelais08/2010
14332^778788+22201234439Enzo Doria09/2023
14342^778395-113617234321Enzo Doria08/2014
14355*2^778090+3234230Jon Grantham07/2023
1436(21430^54289-1)/(21430^233-1)234118Ryan Propper11/2023
1437(5*10^234054-101)/3234055Robert Price08/2023
143823*10^234025-7234027Robert Price10/2022
1439Phi(78125,5517)233857Anonymous09/2022
14405^334359-3^334359-1233707Jon Grantham08/2023
14412^776245-2792353233674Enzo Doria02/2016
14422^776060-114029233618Enzo Doria11/2014
14432^775987-2789557233596Enzo Doria12/2015
14442*10^233564-91233565Robert Price02/2023
14452^775672+1866721233501Enzo Doria03/2016
14462^775238+57233370Stefano Morozzi05/2021
1447(11^223999+1)/12233270Paul Bourdelais02/2010
14482^774118+1885789233033Enzo Doria04/2017
144921^176191-20^176191232964Jean-Louis Charton01/2015
14502^773723+217523232914Enzo Doria01/2024
14512^773679-113425232901Enzo Doria08/2014
1452(7*10^232620+23)/3232621Robert Price05/2023
145310^232599+192489232600Patrick De Geest12/2013
145410^232599-3232599Markus Tervooren10/2010
14552^772552-458879232562Enzo Doria04/2015
14562^772214+1874899232460Enzo Doria06/2016
14572^771994-1862771232394Enzo Doria12/2015
14582^771889+1876037232362Enzo Doria07/2016
14592^771660+1866511232293Enzo Doria02/2016
14605^332150-18188232163Enzo Doria06/2014
14612^770623+212543231981Enzo Doria09/2023
14623^485977-2^485977231870Mike Oakes09/2009
14632^770082-114161231818Enzo Doria01/2015
14642^769791+25523231731Enzo Doria11/2023
14657^274120-2231659Paul Bourdelais08/2023
1466(20^177967+1)/21231540Paul Bourdelais05/2013
1467(4*10^231254+23)/9231254Serge Batalov11/2022
14682^768205+22217231253Enzo Doria09/2023
14692^767622-9221231078Lelio R Paula01/2016
14702^767344+1880311230994Enzo Doria09/2016
14718*10^230921-13230922Robert Price08/2023
1472(3^483611-1)/2230741Paul Bourdelais02/2010
1473(10^230706+179)/9230706Serge Batalov12/2014
14742^766309+1875257230682Enzo Doria06/2016
1475(26131^52441-1)/(26131^229-1)230629Ryan Propper11/2023
14762^765635+1879883230480Enzo Doria09/2016
147743^141090+141090230467Kellen Shenton06/2023
1478(26*10^230394-119)/3230395Robert Price07/2023
14792^764348-113697230092Enzo Doria09/2014
14802^764131+78863230027Enzo Doria05/2016
14812^763701+60197229897Enzo Doria03/2016
14824*10^229836+21229837Robert Price12/2022
14832^763362+27799229795Enzo Doria01/2024
14842^762841-25905229639Enzo Doria10/2013
14852^762659+212633229584Enzo Doria09/2023
148677*10^229211+3229213Robert Price11/2023
14872^761117-113569229120Enzo Doria08/2014
1488(29022^51529-1)/(29022^227-1)228947Ryan Propper11/2023
1489(98^114859+1)/99228709Paul Bourdelais12/2018
14905*3^479067-2^479067228574Jon Grantham08/2023
14912^758645+216011228375Enzo Doria12/2023
1492(2^758231+1)/(3*27146942976539*73236839266867)228223Gord Palameta12/2018
1493(298*10^228177-7)/3228179Robert Price02/2023
14942^757985-2790013228177Enzo Doria12/2015
149534*10^228129-9228131Robert Price05/2023
14962^757038-1862081227892Enzo Doria12/2015
14972^756839+95849227832Makoto Morimoto10/2013
1499(2^756839+6989)/756091227826Makoto Morimoto09/2016
1498(2^756839-50211)/(137*3203)227826Makoto Morimoto08/2019
15002^756773-112723227812Enzo Doria07/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 12 2024 13:37 (Time in France)

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