PRP Records

Probable Primes Top 10000

(294113 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 ?
12512^802025-25999241434Enzo Doria10/2013
1252(3^505823+3^252912+1)/7241339Serge Batalov03/2014
12532^801575+25073241299Enzo Doria11/2023
12542^801303+1872923241217Enzo Doria05/2016
1255(23*10^241048-143)/3241049Robert Price12/2023
12562^800579-1862947240999Enzo Doria12/2015
12572^799999+16205240824Norman Luhn09/2023
12583^504206+2240568Luke W. Richards03/2018
12592^798973-26283240515Enzo Doria10/2013
12602^798671-69487240424Enzo Doria12/2015
12612^797220+79831239988Enzo Doria06/2016
12622^796910-26001239894Enzo Doria10/2013
12632^796598+653119239800Enzo Doria12/2016
12642^796432-1859729239750Enzo Doria11/2015
12652^796002-1852211239621Enzo Doria08/2015
12662^795884+214081239585Enzo Doria10/2023
12672^795709+75767239533Enzo Doria04/2016
12682^795708+81721239532Enzo Doria08/2016
12692^795468-2786249239460Enzo Doria10/2015
12702^795442+80779239452Enzo Doria07/2016
12712^795075-1852057239342Enzo Doria08/2015
1272(86^123677+1)/87239252Paul Bourdelais01/2019
12732^794043+1875023239031Enzo Doria06/2016
12742^793347-69577238822Enzo Doria01/2016
12755*2^793288+3238805Jon Grantham07/2023
12762^792988-344429238714Enzo Doria08/2015
12772^792700-2786369238627Enzo Doria11/2015
12782^792663-1844797238616Enzo Doria06/2015
12792^792605-291943238598Enzo Doria07/2015
1280(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
12814*10^238163+21238164Robert Price12/2022
1282(26*10^238157-77)/3238158Robert Price03/2023
128310^237670+9237671Robert Price08/2023
12842^789373+1869377237625Enzo Doria05/2016
1285((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961237544Serge Batalov04/2015
12862^788942+1866409237496Enzo Doria02/2016
12872^788844-114329237466Enzo Doria01/2015
12882^788705-1859713237424Enzo Doria11/2015
128915^201475+14236953Alfred Reich10/2023
12902^786180+1871971236664Enzo Doria05/2016
129111^227092-90236492Enzo Doria11/2012
12922^785260+1866361236387Enzo Doria02/2016
12932^785220+1880611236375Enzo Doria10/2016
1294(2^784689-15)/7236215Stefano Morozzi08/2022
129519^184650-2236122Robert Price10/2014
129610^236059+216513236060Patrick De Geest04/2016
129710^236059-20909236059Robert Price09/2015
12982^783893-21235976Stefano Morozzi07/2022
1299(87^121487-1)/86235625Paul Bourdelais12/2018
13002^782634-113981235597Enzo Doria11/2014
13012^782423+1879733235533Enzo Doria09/2016
1302(10^(2*117707+1)+12*10^117707-1)/3235415Robert Price10/2023
13032^781682-2789543235310Enzo Doria12/2015
13042^780408-113453234927Enzo Doria08/2014
13057*10^234915+9234916Robert Price04/2023
13062^780368-1864829234915Enzo Doria01/2016
13072^780284+7234889Jon Grantham08/2023
13082^779593-1836559234681Enzo Doria05/2015
1309(8713#+(549391#)/(8713#))/360295171234487Makoto Morimoto11/2017
1310(5^335429+1)/6234455Paul Bourdelais08/2010
13112^778788+22201234439Enzo Doria09/2023
13122^778395-113617234321Enzo Doria08/2014
13135*2^778090+3234230Jon Grantham07/2023
1314(21430^54289-1)/(21430^233-1)234118Ryan Propper11/2023
1315(5*10^234054-101)/3234055Robert Price08/2023
131623*10^234025-7234027Robert Price10/2022
1317Phi(78125,5517)233857Anonymous09/2022
13185^334359-3^334359-1233707Jon Grantham08/2023
13192^776245-2792353233674Enzo Doria02/2016
13202^776060-114029233618Enzo Doria11/2014
13212^775987-2789557233596Enzo Doria12/2015
13222*10^233564-91233565Robert Price02/2023
13232^775672+1866721233501Enzo Doria03/2016
13242^775238+57233370Stefano Morozzi05/2021
1325(11^223999+1)/12233270Paul Bourdelais02/2010
13262^774118+1885789233033Enzo Doria04/2017
132721^176191-20^176191232964Jean-Louis Charton01/2015
13282^773679-113425232901Enzo Doria08/2014
1329(7*10^232620+23)/3232621Robert Price05/2023
133010^232599+192489232600Patrick De Geest12/2013
133110^232599-3232599Markus Tervooren10/2010
13322^772552-458879232562Enzo Doria04/2015
13332^772214+1874899232460Enzo Doria06/2016
13342^771994-1862771232394Enzo Doria12/2015
13352^771889+1876037232362Enzo Doria07/2016
13362^771660+1866511232293Enzo Doria02/2016
13375^332150-18188232163Enzo Doria06/2014
13382^770623+212543231981Enzo Doria09/2023
13393^485977-2^485977231870Mike Oakes09/2009
13402^770082-114161231818Enzo Doria01/2015
13412^769791+25523231731Enzo Doria11/2023
13427^274120-2231659Paul Bourdelais08/2023
1343(20^177967+1)/21231540Paul Bourdelais05/2013
1344(4*10^231254+23)/9231254Serge Batalov11/2022
13452^768205+22217231253Enzo Doria09/2023
13462^767622-9221231078Lelio R Paula01/2016
13472^767344+1880311230994Enzo Doria09/2016
13488*10^230921-13230922Robert Price08/2023
1349(3^483611-1)/2230741Paul Bourdelais02/2010
1350(10^230706+179)/9230706Serge Batalov12/2014
13512^766309+1875257230682Enzo Doria06/2016
1352(26131^52441-1)/(26131^229-1)230629Ryan Propper11/2023
13532^765635+1879883230480Enzo Doria09/2016
135443^141090+141090230467Kellen Shenton06/2023
1355(26*10^230394-119)/3230395Robert Price07/2023
13562^764348-113697230092Enzo Doria09/2014
13572^764131+78863230027Enzo Doria05/2016
13582^763701+60197229897Enzo Doria03/2016
13594*10^229836+21229837Robert Price12/2022
13602^762841-25905229639Enzo Doria10/2013
13612^762659+212633229584Enzo Doria09/2023
136277*10^229211+3229213Robert Price11/2023
13632^761117-113569229120Enzo Doria08/2014
1364(29022^51529-1)/(29022^227-1)228947Ryan Propper11/2023
1365(98^114859+1)/99228709Paul Bourdelais12/2018
13665*3^479067-2^479067228574Jon Grantham08/2023
1367(2^758231+1)/(3*27146942976539*73236839266867)228223Gord Palameta12/2018
1368(298*10^228177-7)/3228179Robert Price02/2023
13692^757985-2790013228177Enzo Doria12/2015
137034*10^228129-9228131Robert Price05/2023
13712^757038-1862081227892Enzo Doria12/2015
13722^756839+95849227832Makoto Morimoto10/2013
1374(2^756839+6989)/756091227826Makoto Morimoto09/2016
1373(2^756839-50211)/(137*3203)227826Makoto Morimoto08/2019
13752^756773-112723227812Enzo Doria07/2014
1376524309#+616367227431Makoto Morimoto02/2016
13772^755097-114193227307Enzo Doria12/2014
13787*10^227178+39227179Robert Price01/2023
13799*10^227153-89227154Robert Price02/2023
13802^754473-2791513227120Enzo Doria01/2016
13812^754376+25227090Stefano Morozzi05/2021
13822^754138+213289227019Enzo Doria09/2023
13832^754038+25226989Stefano Morozzi05/2021
13847*10^226479-9226480Robert Price02/2023
13852^751426-764321226202Enzo Doria12/2013
1386(18^180181-1)/17226176Andy Steward04/2007
13872^750740-3225996Paul Bourdelais03/2012
13882^750725+60227225991Enzo Doria02/2016
13892^750525-113743225931Enzo Doria09/2014
1390(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
13912^749444-1861889225606Enzo Doria12/2015
1392tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
13932^749096+1876861225501Enzo Doria07/2016
1394(519643#+43033)/(23*1871*2706283)225379Makoto Morimoto08/2019
13952^748657+79607225369Enzo Doria06/2016
1396(2^746920-11)/5224845Stefano Morozzi08/2022
13972^746653-291583224765Enzo Doria07/2015
13982^746461-114043224708Enzo Doria11/2014
13992^746302+25224660Stefano Morozzi05/2021
1400(202*10^224545-1)/3224547Robert Price06/2023
14012^745674+213949224471Enzo Doria10/2023
14022^745098-350471224297Enzo Doria06/2015
14032^745039-4897224280Yves Minet03/2021
140423*10^224232-7224234Robert Price10/2022
1405(154*10^224061-1)/9224063Serge Batalov12/2014
14062^744211-1845787224030Enzo Doria07/2015
14072^743592-134579223844Hans Havermann10/2018
14082^742452+3223501Paul Bourdelais06/2019
1409234178^9+9^234178223463Anatoly F. Selevich07/2011
14102^741651-461197223260Enzo Doria07/2015
141110^223236-1001223236Robert Price10/2022
14122^741362-1845251223173Enzo Doria07/2015
14133^467546-5*2^467546223077Jon Grantham08/2023
14142^740455-1863877222900Enzo Doria12/2015
1415(14*10^222718-41)/9222719Serge Batalov01/2023
14162^739636-2792219222653Enzo Doria02/2016
141711^213654-180222498Enzo Doria01/2013
14182^738957-1859743222449Enzo Doria11/2015
14194*10^222253-21222254Robert Price12/2022
14202^737825+57222108Stefano Morozzi05/2021
1421(54^128189+1)/55222073Paul Bourdelais11/2018
1422(10^221654+179)/9221654Serge Batalov12/2014
14232^736281+79817221643Enzo Doria06/2016
142410^221631+247617221632Patrick De Geest10/2013
142510^221631-9221631Alexander Gramolin02/2011
142610^221628+7221629Alfred Reich04/2021
14272^735970-1839821221550Enzo Doria06/2015
14282^735367+60293221368Enzo Doria03/2016
142977*10^221343+3221345Robert Price11/2023
1430(202*10^221092-1)/3221094Robert Price06/2023
1431(29^151153+1)/30221045Paul Bourdelais09/2017
14322^734228+24751221025Enzo Doria10/2023
14332^733264-2784089220735Enzo Doria10/2015
14342^733114-24555220690Enzo Doria09/2013
14352^731891-636259220322Enzo Doria12/2013
143698*10^220185-9220187Robert Price05/2023
1437418319^39164+418318220161Alfred Reich11/2023
14382^731124-25539220091Enzo Doria09/2013
14392^730972-462029220045Enzo Doria07/2015
14402^730833+1868627220003Enzo Doria04/2016
14412^730645-2787133219947Enzo Doria11/2015
14422^730547-25581219917Enzo Doria09/2013
1443(113*13^197420-5)/12219916Anonymous11/2022
1444(13^197420*113-5)/12219916Eric Chen10/2023
14452^730460+82291219891Enzo Doria09/2016
1446(5*10^219847-101)/3219848Robert Price08/2023
1447(2^730339+1)/(3*27839062003*7943469324347)219831Gord Palameta12/2018
1448L(1051849)219824Renaud Lifchitz03/2009
14493*2^730149+5219798Jon Grantham07/2023
14508*10^219740-3219741Serge Batalov01/2023
145111^210961-240219694Enzo Doria01/2013
1452(26*10^219639-77)/3219640Robert Price03/2023
14532^729611-113437219635Enzo Doria08/2014
14547^259710-2219481Paul Bourdelais01/2021
1455F(1049897)219416Henri Lifchitz10/2008
1456(1488^69151-1)/1487219386Alexander Zhirkov02/2023
14572^728604+1879321219332Enzo Doria10/2016
145833^144412+2219292Robert Price04/2015
14592^728277-183313219234Hans Havermann10/2018
14602^727998-1862711219150Enzo Doria12/2015
1461(29*10^219124+91)/3219125Robert Price12/2022
14622^727729-114073219069Enzo Doria12/2014
14632^727496-1851809218999Enzo Doria08/2015
14642^726591+2793143218726Enzo Doria02/2016
1465(7*10^218644+17)/3218645Robert Price06/2023
14662^725534-2791931218408Enzo Doria02/2016
1467Phi(220531,10)/2686456812680882641217774Makoto Kamada10/2020
14682^722184+1877821217400Enzo Doria08/2016
1469(109*10^217360-1)/9217362Serge Batalov12/2014
14702^721721-4453217260Yves Minet03/2021
147110^216950+49216951Robert Price02/2023
1472281*499979#/46410-2702372216849Robert Smith08/2016
1473281*499979#/46410+2400766216849Robert Smith08/2016
1474tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
14752^718756-114107216368Enzo Doria12/2014
14762^717672+121216041Stefano Morozzi05/2021
14772^717305+80327215931Enzo Doria07/2016
14782^717069-59773215860Enzo Doria10/2015
147910^215802+33215803Robert Price08/2023
148030^146021-29^146021215691Jean-Louis Charton09/2018
1481277^88301-276^88301215674Jean-Louis Charton06/2012
14822^716428+215011215667Enzo Doria11/2023
1483(13*10^215592-43)/3215593Robert Price08/2023
1484227^91413-40215372Enzo Doria04/2015
1485(2^715008-21)/5215239Stefano Morozzi08/2022
14862^714717+782897215152Enzo Doria11/2016
1487tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
14882^713241+1879157214707Enzo Doria08/2016
1489(23*10^214633+91)/3214634Robert Price03/2023
149011^206081-10^206081214612Jean-Louis Charton10/2011
14912^712801-69553214575Enzo Doria01/2016
14922^712603-25357214515Enzo Doria09/2013
14932^711721-1846723214250Enzo Doria07/2015
14942^710730-396765213952Enzo Doria09/2013
1495(713^74897-1)/712213685Jinyuan Wang08/2023
14962^708468-114329213271Enzo Doria02/2015
1497(163*10^212779-1)/9212781Serge Batalov12/2014
14982^706838-69041212780Enzo Doria11/2015
149922*10^212339+7212341Robert Price10/2022
15002^704577-113871212099Enzo Doria10/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 05 2023 08:12 (Time in France)

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