PRP Records

Probable Primes Top 10000

(295461 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 ?
15012^792663-1844797238616Enzo Doria06/2015
15022^792605-291943238598Enzo Doria07/2015
15032^792366+218599238526Enzo Doria01/2024
1504(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
15052^791321+30077238212Enzo Doria03/2024
15064*10^238163+21238164Robert Price12/2022
1507(26*10^238157-77)/3238158Robert Price03/2023
150810^237670+9237671Robert Price08/2023
15092^789373+1869377237625Enzo Doria05/2016
1510((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961237544Serge Batalov04/2015
15112^789033+218537237523Enzo Doria01/2024
15122^788942+1866409237496Enzo Doria02/2016
15132^788844-114329237466Enzo Doria01/2015
15142^788705-1859713237424Enzo Doria11/2015
15152^788325+224789237310Enzo Doria07/2024
151615^201475+14236953Alfred Reich10/2023
15172^786663+219173236810Enzo Doria02/2024
15182^786180+1871971236664Enzo Doria05/2016
151911^227092-90236492Enzo Doria11/2012
15202^785260+1866361236387Enzo Doria02/2016
15212^785220+1880611236375Enzo Doria10/2016
1522(2^784689-15)/7236215Stefano Morozzi08/2022
152319^184650-2236122Robert Price10/2014
152410^236059+216513236060Patrick De Geest04/2016
152510^236059-20909236059Robert Price09/2015
15262^783893-21235976Stefano Morozzi07/2022
1527(87^121487-1)/86235625Paul Bourdelais12/2018
15282^782634-113981235597Enzo Doria11/2014
15292^782423+1879733235533Enzo Doria09/2016
1530(10^(2*117707+1)+12*10^117707-1)/3235415Robert Price10/2023
15312^781682-2789543235310Enzo Doria12/2015
15322^780481+21489234949Enzo Doria05/2024
15332^780408-113453234927Enzo Doria08/2014
15347*10^234915+9234916Robert Price04/2023
15352^780368-1864829234915Enzo Doria01/2016
15362^780284+7234889Jon Grantham08/2023
15372^779593-1836559234681Enzo Doria05/2015
1538(8713#+(549391#)/(8713#))/360295171234487Makoto Morimoto11/2017
1539(5^335429+1)/6234455Paul Bourdelais08/2010
15402^778788+22201234439Enzo Doria09/2023
15412^778395-113617234321Enzo Doria08/2014
15425*2^778090+3234230Jon Grantham07/2023
1543(21430^54289-1)/(21430^233-1)234118Ryan Propper11/2023
1544(5*10^234054-101)/3234055Robert Price08/2023
154523*10^234025-7234027Robert Price10/2022
15462^777170+21489233952Enzo Doria05/2024
1547Phi(78125,5517)233857Anonymous09/2022
15485^334359-3^334359-1233707Jon Grantham08/2023
15492^776245-2792353233674Enzo Doria02/2016
15502^776060-114029233618Enzo Doria11/2014
15512^775987-2789557233596Enzo Doria12/2015
15522*10^233564-91233565Robert Price02/2023
15532^775865+21489233559Enzo Doria05/2024
15542^775672+1866721233501Enzo Doria03/2016
15552^775238+57233370Stefano Morozzi05/2021
1556(11^223999+1)/12233270Paul Bourdelais02/2010
15572^774118+1885789233033Enzo Doria04/2017
155821^176191-20^176191232964Jean-Louis Charton01/2015
15592^773723+217523232914Enzo Doria01/2024
15602^773679-113425232901Enzo Doria08/2014
1561(7*10^232620+23)/3232621Robert Price05/2023
156210^232599+192489232600Patrick De Geest12/2013
156310^232599-3232599Markus Tervooren10/2010
15642^772552-458879232562Enzo Doria04/2015
15652^772214+1874899232460Enzo Doria06/2016
15662^771994-1862771232394Enzo Doria12/2015
15672^771889+1876037232362Enzo Doria07/2016
15682^771660+1866511232293Enzo Doria02/2016
15695^332150-18188232163Enzo Doria06/2014
15702^771227+61121232163Boyan Hu05/2024
15712^770623+212543231981Enzo Doria09/2023
15723^485977-2^485977231870Mike Oakes09/2009
15732^770082-114161231818Enzo Doria01/2015
15742^769791+25523231731Enzo Doria11/2023
15757^274120-2231659Paul Bourdelais08/2023
1576(20^177967+1)/21231540Paul Bourdelais05/2013
1577(4*10^231254+23)/9231254Serge Batalov11/2022
15782^768205+22217231253Enzo Doria09/2023
15792^767622-9221231078Lelio R Paula01/2016
15802^767344+1880311230994Enzo Doria09/2016
15818*10^230921-13230922Robert Price08/2023
1582(3^483611-1)/2230741Paul Bourdelais02/2010
1583(10^230706+179)/9230706Serge Batalov12/2014
15842^766309+1875257230682Enzo Doria06/2016
1585(26131^52441-1)/(26131^229-1)230629Ryan Propper11/2023
15862^765635+1879883230480Enzo Doria09/2016
158743^141090+141090230467Kellen Shenton06/2023
1588(26*10^230394-119)/3230395Robert Price07/2023
15892^764348-113697230092Enzo Doria09/2014
15902^764131+78863230027Enzo Doria05/2016
15912^763701+60197229897Enzo Doria03/2016
15924*10^229836+21229837Robert Price12/2022
15932^763362+27799229795Enzo Doria01/2024
15942^762841-25905229639Enzo Doria10/2013
15952^762659+212633229584Enzo Doria09/2023
159677*10^229211+3229213Robert Price11/2023
15972^761117-113569229120Enzo Doria08/2014
1598(29022^51529-1)/(29022^227-1)228947Ryan Propper11/2023
1599(98^114859+1)/99228709Paul Bourdelais12/2018
16005*3^479067-2^479067228574Jon Grantham08/2023
16012^758645+216011228375Enzo Doria12/2023
1602(2^758231+1)/(3*27146942976539*73236839266867)228223Gord Palameta12/2018
1603(298*10^228177-7)/3228179Robert Price02/2023
16042^757985-2790013228177Enzo Doria12/2015
160534*10^228129-9228131Robert Price05/2023
16062^757038-1862081227892Enzo Doria12/2015
16072^756839+95849227832Makoto Morimoto10/2013
1609(2^756839+6989)/756091227826Makoto Morimoto09/2016
1608(2^756839-50211)/(137*3203)227826Makoto Morimoto08/2019
16102^756773-112723227812Enzo Doria07/2014
1611524309#+616367227431Makoto Morimoto02/2016
16122^755097-114193227307Enzo Doria12/2014
16137*10^227178+39227179Robert Price01/2023
16149*10^227153-89227154Robert Price02/2023
16152^754473-2791513227120Enzo Doria01/2016
16162^754376+25227090Stefano Morozzi05/2021
16172^754138+213289227019Enzo Doria09/2023
16182^754038+25226989Stefano Morozzi05/2021
16192^753263+217133226755Enzo Doria12/2023
16207*10^226479-9226480Robert Price02/2023
16212^751655+33893226271Enzo Doria06/2024
16222^751426-764321226202Enzo Doria12/2013
1623(18^180181-1)/17226176Andy Steward04/2007
16242^750740-3225996Paul Bourdelais03/2012
16252^750725+60227225991Enzo Doria02/2016
16262^750525-113743225931Enzo Doria09/2014
1627(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
16282^749444-1861889225606Enzo Doria12/2015
1629tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
16302^749096+1876861225501Enzo Doria07/2016
16312^748895+26213225440Enzo Doria12/2023
1632(519643#+43033)/(23*1871*2706283)225379Makoto Morimoto08/2019
16332^748657+79607225369Enzo Doria06/2016
1634(2^746920-11)/5224845Stefano Morozzi08/2022
16352^746653-291583224765Enzo Doria07/2015
16362^746461-114043224708Enzo Doria11/2014
16372^746302+25224660Stefano Morozzi05/2021
1638(202*10^224545-1)/3224547Robert Price06/2023
1639(19*10^224533-37)/9224534Alfred Reich12/2023
16402^745674+213949224471Enzo Doria10/2023
16412^745098-350471224297Enzo Doria06/2015
16422^745039-4897224280Yves Minet03/2021
164323*10^224232-7224234Robert Price10/2022
1644(154*10^224061-1)/9224063Serge Batalov12/2014
16452^744211-1845787224030Enzo Doria07/2015
16462^743592-134579223844Hans Havermann10/2018
16472^742452+3223501Paul Bourdelais06/2019
1648234178^9+9^234178223463Anatoly F. Selevich07/2011
16492^741651-461197223260Enzo Doria07/2015
165010^223236-1001223236Robert Price10/2022
16512^741362-1845251223173Enzo Doria07/2015
16523^467546-5*2^467546223077Jon Grantham08/2023
16532^740455-1863877222900Enzo Doria12/2015
16542^740274+217519222845Enzo Doria01/2024
1655(14*10^222718-41)/9222719Serge Batalov01/2023
16562^739636-2792219222653Enzo Doria02/2016
165711^213654-180222498Enzo Doria01/2013
16582^738957-1859743222449Enzo Doria11/2015
16594*10^222253-21222254Robert Price12/2022
16602^737825+57222108Stefano Morozzi05/2021
1661(54^128189+1)/55222073Paul Bourdelais11/2018
16622^737166+220099221910Enzo Doria03/2024
1663(10^221654+179)/9221654Serge Batalov12/2014
16642^736281+79817221643Enzo Doria06/2016
166510^221631+247617221632Patrick De Geest10/2013
166610^221631-9221631Alexander Gramolin02/2011
166710^221628+7221629Alfred Reich04/2021
16682^735970-1839821221550Enzo Doria06/2015
16692^735367+60293221368Enzo Doria03/2016
167077*10^221343+3221345Robert Price11/2023
1671(241^92821-1)/240221099Anonymous04/2024
1672(202*10^221092-1)/3221094Robert Price06/2023
1673(29^151153+1)/30221045Paul Bourdelais09/2017
16742^734228+24751221025Enzo Doria10/2023
1675(28*10^220800+173)/3220801Robert Price07/2024
16762^733264-2784089220735Enzo Doria10/2015
16772^733114-24555220690Enzo Doria09/2013
16782^731891-636259220322Enzo Doria12/2013
167998*10^220185-9220187Robert Price05/2023
1680418319^39164+418318220161Alfred Reich11/2023
16812^731124-25539220091Enzo Doria09/2013
16822^730972-462029220045Enzo Doria07/2015
16832^730833+1868627220003Enzo Doria04/2016
16842^730645-2787133219947Enzo Doria11/2015
16852^730547-25581219917Enzo Doria09/2013
1686(113*13^197420-5)/12219916Anonymous11/2022
1687(13^197420*113-5)/12219916Eric Chen10/2023
16882^730460+82291219891Enzo Doria09/2016
1689(5*10^219847-101)/3219848Robert Price08/2023
1690(2^730339+1)/(3*27839062003*7943469324347)219831Gord Palameta12/2018
1691L(1051849)219824Renaud Lifchitz03/2009
16923*2^730149+5219798Jon Grantham07/2023
16938*10^219740-3219741Serge Batalov01/2023
169411^210961-240219694Enzo Doria01/2013
1695(26*10^219639-77)/3219640Robert Price03/2023
16962^729611-113437219635Enzo Doria08/2014
16977^259710-2219481Paul Bourdelais01/2021
1698F(1049897)219416Henri Lifchitz10/2008
1699(1488^69151-1)/1487219386Alexander Zhirkov02/2023
17002^728604+1879321219332Enzo Doria10/2016
170133^144412+2219292Robert Price04/2015
17022^728277-183313219234Hans Havermann10/2018
17032^727998-1862711219150Enzo Doria12/2015
1704(29*10^219124+91)/3219125Robert Price12/2022
17052^727729-114073219069Enzo Doria12/2014
17062^727496-1851809218999Enzo Doria08/2015
17072^727025+25907218857Enzo Doria12/2023
17082^726591+2793143218726Enzo Doria02/2016
1709(7*10^218644+17)/3218645Robert Price06/2023
17102^725534-2791931218408Enzo Doria02/2016
1711Phi(220531,10)/2686456812680882641217774Makoto Kamada10/2020
17122^722184+1877821217400Enzo Doria08/2016
1713(109*10^217360-1)/9217362Serge Batalov12/2014
17142^721721-4453217260Yves Minet03/2021
171510^216950+49216951Robert Price02/2023
1716281*499979#/46410-2702372216849Robert Smith08/2016
1717281*499979#/46410+2400766216849Robert Smith08/2016
1718tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
17192^718756-114107216368Enzo Doria12/2014
17202^717672+121216041Stefano Morozzi05/2021
17212^717305+80327215931Enzo Doria07/2016
17222^717069-59773215860Enzo Doria10/2015
172310^215802+33215803Robert Price08/2023
172430^146021-29^146021215691Jean-Louis Charton09/2018
1725277^88301-276^88301215674Jean-Louis Charton06/2012
17262^716428+215011215667Enzo Doria11/2023
1727(13*10^215592-43)/3215593Robert Price08/2023
1728227^91413-40215372Enzo Doria04/2015
1729(2^715008-21)/5215239Stefano Morozzi08/2022
17302^714717+782897215152Enzo Doria11/2016
1731tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
17322^713241+1879157214707Enzo Doria08/2016
1733(23*10^214633+91)/3214634Robert Price03/2023
173411^206081-10^206081214612Jean-Louis Charton10/2011
17352^712801-69553214575Enzo Doria01/2016
17362^712603-25357214515Enzo Doria09/2013
17372^711721-1846723214250Enzo Doria07/2015
17382^710730-396765213952Enzo Doria09/2013
1739(19*10^213934-37)/9213935Alfred Reich12/2023
1740(19*10^213730-37)/9213731Alfred Reich12/2023
1741(713^74897-1)/712213685Jinyuan Wang08/2023
17422^709773+25907213663Enzo Doria12/2023
17432^708468-114329213271Enzo Doria02/2015
17442^708293+27557213218Enzo Doria01/2024
17452^707277+28997212912Enzo Doria02/2024
1746(163*10^212779-1)/9212781Serge Batalov12/2014
17472^706838-69041212780Enzo Doria11/2015
17482^705653+25907212423Enzo Doria12/2023
174922*10^212339+7212341Robert Price10/2022
17502^704577-113871212099Enzo Doria10/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 19 2024 15:29 (Time in France)

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