PRP Records

Probable Primes Top 10000

(295158 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
15012^780368-1864829234915Enzo Doria01/2016
15022^780284+7234889Jon Grantham08/2023
15032^779593-1836559234681Enzo Doria05/2015
1504(8713#+(549391#)/(8713#))/360295171234487Makoto Morimoto11/2017
1505(5^335429+1)/6234455Paul Bourdelais08/2010
15062^778788+22201234439Enzo Doria09/2023
15072^778395-113617234321Enzo Doria08/2014
15085*2^778090+3234230Jon Grantham07/2023
1509(21430^54289-1)/(21430^233-1)234118Ryan Propper11/2023
1510(5*10^234054-101)/3234055Robert Price08/2023
151123*10^234025-7234027Robert Price10/2022
15122^777170+21489233952Enzo Doria05/2024
1513Phi(78125,5517)233857Anonymous09/2022
15145^334359-3^334359-1233707Jon Grantham08/2023
15152^776245-2792353233674Enzo Doria02/2016
15162^776060-114029233618Enzo Doria11/2014
15172^775987-2789557233596Enzo Doria12/2015
15182*10^233564-91233565Robert Price02/2023
15192^775865+21489233559Enzo Doria05/2024
15202^775672+1866721233501Enzo Doria03/2016
15212^775238+57233370Stefano Morozzi05/2021
1522(11^223999+1)/12233270Paul Bourdelais02/2010
15232^774118+1885789233033Enzo Doria04/2017
152421^176191-20^176191232964Jean-Louis Charton01/2015
15252^773723+217523232914Enzo Doria01/2024
15262^773679-113425232901Enzo Doria08/2014
1527(7*10^232620+23)/3232621Robert Price05/2023
152810^232599+192489232600Patrick De Geest12/2013
152910^232599-3232599Markus Tervooren10/2010
15302^772552-458879232562Enzo Doria04/2015
15312^772214+1874899232460Enzo Doria06/2016
15322^771994-1862771232394Enzo Doria12/2015
15332^771889+1876037232362Enzo Doria07/2016
15342^771660+1866511232293Enzo Doria02/2016
15355^332150-18188232163Enzo Doria06/2014
15362^771227+61121232163Boyan Hu05/2024
15372^770623+212543231981Enzo Doria09/2023
15383^485977-2^485977231870Mike Oakes09/2009
15392^770082-114161231818Enzo Doria01/2015
15402^769791+25523231731Enzo Doria11/2023
15417^274120-2231659Paul Bourdelais08/2023
1542(20^177967+1)/21231540Paul Bourdelais05/2013
1543(4*10^231254+23)/9231254Serge Batalov11/2022
15442^768205+22217231253Enzo Doria09/2023
15452^767622-9221231078Lelio R Paula01/2016
15462^767344+1880311230994Enzo Doria09/2016
15478*10^230921-13230922Robert Price08/2023
1548(3^483611-1)/2230741Paul Bourdelais02/2010
1549(10^230706+179)/9230706Serge Batalov12/2014
15502^766309+1875257230682Enzo Doria06/2016
1551(26131^52441-1)/(26131^229-1)230629Ryan Propper11/2023
15522^765635+1879883230480Enzo Doria09/2016
155343^141090+141090230467Kellen Shenton06/2023
1554(26*10^230394-119)/3230395Robert Price07/2023
15552^764348-113697230092Enzo Doria09/2014
15562^764131+78863230027Enzo Doria05/2016
15572^763701+60197229897Enzo Doria03/2016
15584*10^229836+21229837Robert Price12/2022
15592^763362+27799229795Enzo Doria01/2024
15602^762841-25905229639Enzo Doria10/2013
15612^762659+212633229584Enzo Doria09/2023
156277*10^229211+3229213Robert Price11/2023
15632^761117-113569229120Enzo Doria08/2014
1564(29022^51529-1)/(29022^227-1)228947Ryan Propper11/2023
1565(98^114859+1)/99228709Paul Bourdelais12/2018
15665*3^479067-2^479067228574Jon Grantham08/2023
15672^758645+216011228375Enzo Doria12/2023
1568(2^758231+1)/(3*27146942976539*73236839266867)228223Gord Palameta12/2018
1569(298*10^228177-7)/3228179Robert Price02/2023
15702^757985-2790013228177Enzo Doria12/2015
157134*10^228129-9228131Robert Price05/2023
15722^757038-1862081227892Enzo Doria12/2015
15732^756839+95849227832Makoto Morimoto10/2013
1575(2^756839+6989)/756091227826Makoto Morimoto09/2016
1574(2^756839-50211)/(137*3203)227826Makoto Morimoto08/2019
15762^756773-112723227812Enzo Doria07/2014
1577524309#+616367227431Makoto Morimoto02/2016
15782^755097-114193227307Enzo Doria12/2014
15797*10^227178+39227179Robert Price01/2023
15809*10^227153-89227154Robert Price02/2023
15812^754473-2791513227120Enzo Doria01/2016
15822^754376+25227090Stefano Morozzi05/2021
15832^754138+213289227019Enzo Doria09/2023
15842^754038+25226989Stefano Morozzi05/2021
15852^753263+217133226755Enzo Doria12/2023
15867*10^226479-9226480Robert Price02/2023
15872^751426-764321226202Enzo Doria12/2013
1588(18^180181-1)/17226176Andy Steward04/2007
15892^750740-3225996Paul Bourdelais03/2012
15902^750725+60227225991Enzo Doria02/2016
15912^750525-113743225931Enzo Doria09/2014
1592(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
15932^749444-1861889225606Enzo Doria12/2015
1594tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
15952^749096+1876861225501Enzo Doria07/2016
15962^748895+26213225440Enzo Doria12/2023
1597(519643#+43033)/(23*1871*2706283)225379Makoto Morimoto08/2019
15982^748657+79607225369Enzo Doria06/2016
1599(2^746920-11)/5224845Stefano Morozzi08/2022
16002^746653-291583224765Enzo Doria07/2015
16012^746461-114043224708Enzo Doria11/2014
16022^746302+25224660Stefano Morozzi05/2021
1603(202*10^224545-1)/3224547Robert Price06/2023
1604(19*10^224533-37)/9224534Alfred Reich12/2023
16052^745674+213949224471Enzo Doria10/2023
16062^745098-350471224297Enzo Doria06/2015
16072^745039-4897224280Yves Minet03/2021
160823*10^224232-7224234Robert Price10/2022
1609(154*10^224061-1)/9224063Serge Batalov12/2014
16102^744211-1845787224030Enzo Doria07/2015
16112^743592-134579223844Hans Havermann10/2018
16122^742452+3223501Paul Bourdelais06/2019
1613234178^9+9^234178223463Anatoly F. Selevich07/2011
16142^741651-461197223260Enzo Doria07/2015
161510^223236-1001223236Robert Price10/2022
16162^741362-1845251223173Enzo Doria07/2015
16173^467546-5*2^467546223077Jon Grantham08/2023
16182^740455-1863877222900Enzo Doria12/2015
16192^740274+217519222845Enzo Doria01/2024
1620(14*10^222718-41)/9222719Serge Batalov01/2023
16212^739636-2792219222653Enzo Doria02/2016
162211^213654-180222498Enzo Doria01/2013
16232^738957-1859743222449Enzo Doria11/2015
16244*10^222253-21222254Robert Price12/2022
16252^737825+57222108Stefano Morozzi05/2021
1626(54^128189+1)/55222073Paul Bourdelais11/2018
16272^737166+220099221910Enzo Doria03/2024
1628(10^221654+179)/9221654Serge Batalov12/2014
16292^736281+79817221643Enzo Doria06/2016
163010^221631+247617221632Patrick De Geest10/2013
163110^221631-9221631Alexander Gramolin02/2011
163210^221628+7221629Alfred Reich04/2021
16332^735970-1839821221550Enzo Doria06/2015
16342^735367+60293221368Enzo Doria03/2016
163577*10^221343+3221345Robert Price11/2023
1636(241^92821-1)/240221099Anonymous04/2024
1637(202*10^221092-1)/3221094Robert Price06/2023
1638(29^151153+1)/30221045Paul Bourdelais09/2017
16392^734228+24751221025Enzo Doria10/2023
16402^733264-2784089220735Enzo Doria10/2015
16412^733114-24555220690Enzo Doria09/2013
16422^731891-636259220322Enzo Doria12/2013
164398*10^220185-9220187Robert Price05/2023
1644418319^39164+418318220161Alfred Reich11/2023
16452^731124-25539220091Enzo Doria09/2013
16462^730972-462029220045Enzo Doria07/2015
16472^730833+1868627220003Enzo Doria04/2016
16482^730645-2787133219947Enzo Doria11/2015
16492^730547-25581219917Enzo Doria09/2013
1650(113*13^197420-5)/12219916Anonymous11/2022
1651(13^197420*113-5)/12219916Eric Chen10/2023
16522^730460+82291219891Enzo Doria09/2016
1653(5*10^219847-101)/3219848Robert Price08/2023
1654(2^730339+1)/(3*27839062003*7943469324347)219831Gord Palameta12/2018
1655L(1051849)219824Renaud Lifchitz03/2009
16563*2^730149+5219798Jon Grantham07/2023
16578*10^219740-3219741Serge Batalov01/2023
165811^210961-240219694Enzo Doria01/2013
1659(26*10^219639-77)/3219640Robert Price03/2023
16602^729611-113437219635Enzo Doria08/2014
16617^259710-2219481Paul Bourdelais01/2021
1662F(1049897)219416Henri Lifchitz10/2008
1663(1488^69151-1)/1487219386Alexander Zhirkov02/2023
16642^728604+1879321219332Enzo Doria10/2016
166533^144412+2219292Robert Price04/2015
16662^728277-183313219234Hans Havermann10/2018
16672^727998-1862711219150Enzo Doria12/2015
1668(29*10^219124+91)/3219125Robert Price12/2022
16692^727729-114073219069Enzo Doria12/2014
16702^727496-1851809218999Enzo Doria08/2015
16712^727025+25907218857Enzo Doria12/2023
16722^726591+2793143218726Enzo Doria02/2016
1673(7*10^218644+17)/3218645Robert Price06/2023
16742^725534-2791931218408Enzo Doria02/2016
1675Phi(220531,10)/2686456812680882641217774Makoto Kamada10/2020
16762^722184+1877821217400Enzo Doria08/2016
1677(109*10^217360-1)/9217362Serge Batalov12/2014
16782^721721-4453217260Yves Minet03/2021
167910^216950+49216951Robert Price02/2023
1680281*499979#/46410-2702372216849Robert Smith08/2016
1681281*499979#/46410+2400766216849Robert Smith08/2016
1682tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
16832^718756-114107216368Enzo Doria12/2014
16842^717672+121216041Stefano Morozzi05/2021
16852^717305+80327215931Enzo Doria07/2016
16862^717069-59773215860Enzo Doria10/2015
168710^215802+33215803Robert Price08/2023
168830^146021-29^146021215691Jean-Louis Charton09/2018
1689277^88301-276^88301215674Jean-Louis Charton06/2012
16902^716428+215011215667Enzo Doria11/2023
1691(13*10^215592-43)/3215593Robert Price08/2023
1692227^91413-40215372Enzo Doria04/2015
1693(2^715008-21)/5215239Stefano Morozzi08/2022
16942^714717+782897215152Enzo Doria11/2016
1695tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
16962^713241+1879157214707Enzo Doria08/2016
1697(23*10^214633+91)/3214634Robert Price03/2023
169811^206081-10^206081214612Jean-Louis Charton10/2011
16992^712801-69553214575Enzo Doria01/2016
17002^712603-25357214515Enzo Doria09/2013
17012^711721-1846723214250Enzo Doria07/2015
17022^710730-396765213952Enzo Doria09/2013
1703(19*10^213934-37)/9213935Alfred Reich12/2023
1704(19*10^213730-37)/9213731Alfred Reich12/2023
1705(713^74897-1)/712213685Jinyuan Wang08/2023
17062^709773+25907213663Enzo Doria12/2023
17072^708468-114329213271Enzo Doria02/2015
17082^708293+27557213218Enzo Doria01/2024
17092^707277+28997212912Enzo Doria02/2024
1710(163*10^212779-1)/9212781Serge Batalov12/2014
17112^706838-69041212780Enzo Doria11/2015
17122^705653+25907212423Enzo Doria12/2023
171322*10^212339+7212341Robert Price10/2022
17142^704577-113871212099Enzo Doria10/2014
1715(2^704548-19)/3212090Stefano Morozzi08/2022
17162^704110-2792441211959Enzo Doria02/2016
17172^704084+28531211951Enzo Doria02/2024
17182^703943-1862947211908Enzo Doria12/2015
1719(60^119083+1)/61211746Paul Bourdelais10/2018
1720(184*10^211682-1)/3211684Robert Price12/2022
1721(10^211610-91)/9211610Serge Batalov12/2014
1722227^89797+2211565Lelio R Paula08/2012
17232^702194-3211382Paul Bourdelais03/2012
17242^702064+1874911211343Enzo Doria07/2016
17252^701968-113873211314Enzo Doria10/2014
1726(14*10^211262-41)/9211263Serge Batalov01/2023
17272^701713-113779211237Enzo Doria09/2014
17282^701616-216803211208Enzo Doria01/2024
17292^701449-25201211158Enzo Doria09/2013
17302^701403-2786977211144Enzo Doria11/2015
17312^701189-25423211079Enzo Doria09/2013
17322^701162-459161211071Enzo Doria05/2015
17332^700793+219407210960Enzo Doria03/2024
1734(24^152783-1)/23210872Paul Bourdelais04/2018
17352^700400+9385210842Lelio R Paula01/2014
17362^700304-17210813Stefano Morozzi07/2022
17372^700131+1874693210761Enzo Doria06/2016
1738(2^700095+225414)/2210750Stefano Morozzi04/2020
1739(2^700090+278254)/2210748Stefano Morozzi04/2020
1740(2^700075+303666)/2210744Stefano Morozzi04/2020
1741(2^700073+75882)/2210743Stefano Morozzi04/2020
1742(2^700074+328890)/2210743Stefano Morozzi04/2020
1743(2^700052+79162)/2210737Stefano Morozzi04/2020
1744(2^700052+304458)/2210737Stefano Morozzi04/2020
1745(2^700048+376578)/2210736Stefano Morozzi04/2020
174611^202357-1140210734Enzo Doria12/2012
1747(2^700021+25874)/2210728Stefano Morozzi04/2020
1748(2^700018+377518)/2210727Stefano Morozzi04/2020
17492^699999+300729210721Norman Luhn09/2023
1750(238*10^210712-1)/3210714Robert Price09/2023


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 27 2024 13:30 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!