PRP Records

Probable Primes Top 10000

(296083 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 ?
17512^741362-1845251223173Enzo Doria07/2015
17523^467546-5*2^467546223077Jon Grantham08/2023
17532^740455-1863877222900Enzo Doria12/2015
17542^740274+217519222845Enzo Doria01/2024
1755(14*10^222718-41)/9222719Serge Batalov01/2023
17562^739636-2792219222653Enzo Doria02/2016
175711^213654-180222498Enzo Doria01/2013
17582^738957-1859743222449Enzo Doria11/2015
17594*10^222253-21222254Robert Price12/2022
17602^737825+57222108Stefano Morozzi05/2021
1761(54^128189+1)/55222073Paul Bourdelais11/2018
17622^737166+220099221910Enzo Doria03/2024
1763(10^221654+179)/9221654Serge Batalov12/2014
17642^736281+79817221643Enzo Doria06/2016
176510^221631+247617221632Patrick De Geest10/2013
176610^221631-9221631Alexander Gramolin02/2011
176710^221628+7221629Alfred Reich04/2021
17682^735970-1839821221550Enzo Doria06/2015
17692^735367+60293221368Enzo Doria03/2016
177077*10^221343+3221345Robert Price11/2023
1771(241^92821-1)/240221099Anonymous04/2024
1772(202*10^221092-1)/3221094Robert Price06/2023
1773(29^151153+1)/30221045Paul Bourdelais09/2017
17742^734228+24751221025Enzo Doria10/2023
1775(28*10^220800+173)/3220801Robert Price07/2024
17762^733264-2784089220735Enzo Doria10/2015
17772^733114-24555220690Enzo Doria09/2013
17782^731891-636259220322Enzo Doria12/2013
177998*10^220185-9220187Robert Price05/2023
1780418319^39164+418318220161Alfred Reich11/2023
17812^731124-25539220091Enzo Doria09/2013
17822^730972-462029220045Enzo Doria07/2015
17832^730833+1868627220003Enzo Doria04/2016
17842^730645-2787133219947Enzo Doria11/2015
17852^730547-25581219917Enzo Doria09/2013
1786(113*13^197420-5)/12219916Anonymous11/2022
1787(13^197420*113-5)/12219916Eric Chen10/2023
17882^730460+82291219891Enzo Doria09/2016
1789(5*10^219847-101)/3219848Robert Price08/2023
1790(2^730339+1)/(3*27839062003*7943469324347)219831Gord Palameta12/2018
1791L(1051849)219824Renaud Lifchitz03/2009
17923*2^730149+5219798Jon Grantham07/2023
17938*10^219740-3219741Serge Batalov01/2023
179411^210961-240219694Enzo Doria01/2013
1795(26*10^219639-77)/3219640Robert Price03/2023
17962^729611-113437219635Enzo Doria08/2014
17977^259710-2219481Paul Bourdelais01/2021
1798F(1049897)219416Henri Lifchitz10/2008
1799(1488^69151-1)/1487219386Alexander Zhirkov02/2023
18002^728604+1879321219332Enzo Doria10/2016
180133^144412+2219292Robert Price04/2015
18022^728277-183313219234Hans Havermann10/2018
18032^727998-1862711219150Enzo Doria12/2015
1804(29*10^219124+91)/3219125Robert Price12/2022
18052^727729-114073219069Enzo Doria12/2014
18062^727496-1851809218999Enzo Doria08/2015
18072^727025+25907218857Enzo Doria12/2023
18082^726591+2793143218726Enzo Doria02/2016
1809(7*10^218644+17)/3218645Robert Price06/2023
18102^725534-2791931218408Enzo Doria02/2016
1811Phi(220531,10)/2686456812680882641217774Makoto Kamada10/2020
18122^722184+1877821217400Enzo Doria08/2016
1813(109*10^217360-1)/9217362Serge Batalov12/2014
18142^721721-4453217260Yves Minet03/2021
181510^216950+49216951Robert Price02/2023
1816281*499979#/46410-2702372216849Robert Smith08/2016
1817281*499979#/46410+2400766216849Robert Smith08/2016
1818tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
18192^718756-114107216368Enzo Doria12/2014
18202^717672+121216041Stefano Morozzi05/2021
18212^717305+80327215931Enzo Doria07/2016
18222^717069-59773215860Enzo Doria10/2015
182310^215802+33215803Robert Price08/2023
182430^146021-29^146021215691Jean-Louis Charton09/2018
1825277^88301-276^88301215674Jean-Louis Charton06/2012
18262^716428+215011215667Enzo Doria11/2023
1827(13*10^215592-43)/3215593Robert Price08/2023
1828227^91413-40215372Enzo Doria04/2015
1829(2^715008-21)/5215239Stefano Morozzi08/2022
18302^714717+782897215152Enzo Doria11/2016
1831tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
18322^713241+1879157214707Enzo Doria08/2016
1833(23*10^214633+91)/3214634Robert Price03/2023
183411^206081-10^206081214612Jean-Louis Charton10/2011
18352^712801-69553214575Enzo Doria01/2016
18362^712603-25357214515Enzo Doria09/2013
18372^711721-1846723214250Enzo Doria07/2015
18382^710730-396765213952Enzo Doria09/2013
1839(19*10^213934-37)/9213935Alfred Reich12/2023
1840(19*10^213730-37)/9213731Alfred Reich12/2023
1841(713^74897-1)/712213685Jinyuan Wang08/2023
18422^709773+25907213663Enzo Doria12/2023
18432^708468-114329213271Enzo Doria02/2015
18442^708293+27557213218Enzo Doria01/2024
18452^707277+28997212912Enzo Doria02/2024
1846(163*10^212779-1)/9212781Serge Batalov12/2014
18472^706838-69041212780Enzo Doria11/2015
18482^705653+25907212423Enzo Doria12/2023
184922*10^212339+7212341Robert Price10/2022
18502^704577-113871212099Enzo Doria10/2014
1851(2^704548-19)/3212090Stefano Morozzi08/2022
18522^704110-2792441211959Enzo Doria02/2016
18532^704084+28531211951Enzo Doria02/2024
18542^703943-1862947211908Enzo Doria12/2015
1855(60^119083+1)/61211746Paul Bourdelais10/2018
1856(184*10^211682-1)/3211684Robert Price12/2022
1857(10^211610-91)/9211610Serge Batalov12/2014
1858227^89797+2211565Lelio R Paula08/2012
18592^702194-3211382Paul Bourdelais03/2012
18602^702064+1874911211343Enzo Doria07/2016
18612^701968-113873211314Enzo Doria10/2014
1862(14*10^211262-41)/9211263Serge Batalov01/2023
18632^701713-113779211237Enzo Doria09/2014
18642^701616-216803211208Enzo Doria01/2024
18652^701449-25201211158Enzo Doria09/2013
18662^701403-2786977211144Enzo Doria11/2015
18672^701189-25423211079Enzo Doria09/2013
18682^701162-459161211071Enzo Doria05/2015
18692^700793+219407210960Enzo Doria03/2024
1870(24^152783-1)/23210872Paul Bourdelais04/2018
18712^700400+9385210842Lelio R Paula01/2014
18722^700304-17210813Stefano Morozzi07/2022
18732^700131+1874693210761Enzo Doria06/2016
1874(2^700095+225414)/2210750Stefano Morozzi04/2020
1875(2^700090+278254)/2210748Stefano Morozzi04/2020
1876(2^700075+303666)/2210744Stefano Morozzi04/2020
1877(2^700073+75882)/2210743Stefano Morozzi04/2020
1878(2^700074+328890)/2210743Stefano Morozzi04/2020
1879(2^700052+79162)/2210737Stefano Morozzi04/2020
1880(2^700052+304458)/2210737Stefano Morozzi04/2020
1881(2^700048+376578)/2210736Stefano Morozzi04/2020
188211^202357-1140210734Enzo Doria12/2012
1883(2^700021+25874)/2210728Stefano Morozzi04/2020
1884(2^700018+377518)/2210727Stefano Morozzi04/2020
18852^699999+300729210721Norman Luhn09/2023
1886(238*10^210712-1)/3210714Robert Price09/2023
18872^699740+25210643Stefano Morozzi05/2021
1888(23*10^210525-143)/3210526Robert Price12/2023
18892^698929-2788423210399Enzo Doria11/2015
1890(5^300893+4^300893)/9210315Jean-Louis Charton11/2011
18912^698316+1878601210215Enzo Doria08/2016
189234*10^210097-9210099Robert Price05/2023
1893(19*10^210011-49)/3210012Robert Price06/2023
18946*10^209846-91209847Robert Price05/2023
18952^697036+1878751209829Enzo Doria08/2016
18962^696813+28607209762Enzo Doria02/2024
1897(238*10^209715-1)/3209717Robert Price09/2023
18986^269407+5209640Paul Bourdelais02/2021
1899(2^696343-1)/11141489/36009913139329209600Tony Prest / Never Odd Or Even02/2014
19002^696254-115151209594Enzo Doria06/2015
1901(35^135623+1)/36209410Paul Bourdelais07/2018
19027*10^209161+39209162Robert Price01/2023
19032^694633+1887257209106Enzo Doria05/2017
1904fibonacci(999790)-4208944Jon Grantham08/2023
19052^693959+180923208903Enzo Doria07/2016
1906(2^693747-11)/3208839Stefano Morozzi08/2022
19072^693462-1847561208753Enzo Doria07/2015
19082^690890-59981207979Enzo Doria11/2015
1909(38^131591+1)/39207884Paul Bourdelais07/2018
19103*2^690484+5207857Jon Grantham07/2023
19112^690163+1877063207760Enzo Doria07/2016
19127^245608-2207563Paul Bourdelais01/2021
1913(67*10^207556+23)/9207557Serge Batalov01/2023
19142^689286-29381207496Enzo Doria08/2015
19152^689122-114521207447Enzo Doria04/2015
19169*10^207254-89207255Robert Price02/2023
19172^688373+6077207221Enzo Doria02/2016
19182^688201+1875527207170Enzo Doria07/2016
1919(42^127609+1)/43207140Paul Bourdelais07/2018
19202^687938+213589207090Enzo Doria10/2023
19212^687619+81563206994Enzo Doria08/2016
19223*10^206927+37206928Robert Price08/2023
19232^687383+21803206923Enzo Doria09/2023
1924(11*10^206688+19)/3206689Robert Price07/2024
19252^686572-1845299206679Enzo Doria07/2015
1926(21^156217-1)/20206552Paul Bourdelais04/2010
1927(2^685739+1)/(3*87774593)206420Gord Palameta08/2018
19282^685578+3206380Paul Bourdelais04/2012
19292^685078+218599206230Enzo Doria01/2024
19302^684836-49349206157Enzo Doria10/2015
1931(73^110603-1)/72206088Paul Bourdelais06/2018
19322^684163-2790967205954Enzo Doria12/2015
1933326^81943-325^81943205941Jean-Louis Charton07/2012
1934(2^684127-1)/23765203727205933Jens K. Andersen04/2009
1935(68*10^205510+13)/9205511Serge Batalov01/2023
19364^341233-3^341233205443Jean-Louis Charton01/2006
19372^682414+215029205428Enzo Doria11/2023
1938(963^68821-1)/962205334Jinyuan Wang01/2024
1939(43*10^205183-421)/9205184Robert Price10/2023
19402^681545+467205166Lelio R Paula11/2013
19412^681306+81049205094Enzo Doria07/2016
19422^680697+1877057204911Enzo Doria07/2016
19432^680415+71783204826Enzo Doria04/2016
194410^204764-8001204764Robert Price03/2023
1945(26*10^204730-77)/3204731Robert Price03/2023
19462^679860-459995204659Enzo Doria06/2015
19472^679593+1879547204578Enzo Doria09/2016
19482^678899+220073204369Enzo Doria03/2024
19492^678753+21677204326Enzo Doria08/2023
19502^678651+1875023204295Enzo Doria07/2016
19512^678561+678561204268Henri Lifchitz05/2006
19525*3^427884+2^427884204154Jon Grantham08/2023
19532^678101-114043204129Enzo Doria11/2014
19542^678028+1875631204107Enzo Doria06/2016
19552^677721+28607204015Enzo Doria01/2024
1956(19*10^203798-7)/3203799Robert Price12/2023
19572^676992-59783203795Enzo Doria10/2015
19582^676972+1866871203789Enzo Doria03/2016
19592^676815+22583203742Enzo Doria09/2023
19602^676761-9203726Robert Price01/2017
19612^676592-23203675Stefano Morozzi07/2022
19622^676563-2792407203666Enzo Doria02/2016
19632^676306-114713203589Enzo Doria04/2015
1964(2^675977-1)/(1686378749257*7171117283326998925471)203456Dario Alpern07/2015
19656*10^203365+53203366Robert Price09/2023
196610247^50678-50678^10247203250Norbert Schneider03/2022
19672^674627-25161203083Enzo Doria09/2013
19682^674603-69337203076Enzo Doria12/2015
1969(182*10^203048+1)/3203050Robert Price09/2023
19702^674459+74213203033Enzo Doria04/2016
19712^674116-458879202930Enzo Doria04/2015
19722^674076-114755202918Enzo Doria04/2015
19735^289937-4^289937202658Jean-Louis Charton03/2013
19745^289926-289926^5202650Henri Lifchitz07/2024
1975(2^673184-7)/3202649Stefano Morozzi08/2022
1976(467617#+14534)/(2^2*13*43)202603Makoto Morimoto06/2019
1977(155^92479-1)/154202558Anonymous06/2024
19782^672773+219407202525Enzo Doria03/2024
19791374^64531-64531^1374202498Henri Lifchitz10/2024
19802^672556-1835519202460Enzo Doria04/2015
1981(7*10^202267+179)/3202268Robert Price02/2023
19822^671446-351401202126Enzo Doria07/2015
19832^671373+77747202104Enzo Doria05/2016
1984(2*10^202059+7)/9202059Rytis Slatkevicius01/2023
198598*10^202021-9202023Robert Price05/2023
19862^670726-114845201909Enzo Doria05/2015
19872^670539-25045201853Enzo Doria09/2013
198810^201801-93201801Robert Price02/2023
198943284^43519-43519^43284201769Norbert Schneider08/2018
19902^670213+282317201755Enzo Doria09/2016
19912^670133+89201731Stefano Morozzi05/2021
19922^669854-113501201647Enzo Doria08/2014
19932^669718+81619201606Enzo Doria08/2016
1994(299*10^201547-17)/3201549Robert Price02/2023
1995(145*10^201504-1)/9201506Serge Batalov12/2014
19962^668938-1839821201371Enzo Doria06/2015
1997(198^87623-1)/197201239Anonymous06/2024
19982^668492+1879303201237Enzo Doria08/2016
19997*10^201140-87201141Robert Price03/2023
20006^258413-5^258413201085Jean-Louis Charton03/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 03 2024 20:14 (Time in France)

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