PRP Records

Probable Primes Top 10000

(294687 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 ?
1501(29022^51529-1)/(29022^227-1)228947Ryan Propper11/2023
1502(98^114859+1)/99228709Paul Bourdelais12/2018
15035*3^479067-2^479067228574Jon Grantham08/2023
15042^758645+216011228375Enzo Doria12/2023
1505(2^758231+1)/(3*27146942976539*73236839266867)228223Gord Palameta12/2018
1506(298*10^228177-7)/3228179Robert Price02/2023
15072^757985-2790013228177Enzo Doria12/2015
150834*10^228129-9228131Robert Price05/2023
15092^757038-1862081227892Enzo Doria12/2015
15102^756839+95849227832Makoto Morimoto10/2013
1512(2^756839+6989)/756091227826Makoto Morimoto09/2016
1511(2^756839-50211)/(137*3203)227826Makoto Morimoto08/2019
15132^756773-112723227812Enzo Doria07/2014
1514524309#+616367227431Makoto Morimoto02/2016
15152^755097-114193227307Enzo Doria12/2014
15167*10^227178+39227179Robert Price01/2023
15179*10^227153-89227154Robert Price02/2023
15182^754473-2791513227120Enzo Doria01/2016
15192^754376+25227090Stefano Morozzi05/2021
15202^754138+213289227019Enzo Doria09/2023
15212^754038+25226989Stefano Morozzi05/2021
15222^753263+217133226755Enzo Doria12/2023
15237*10^226479-9226480Robert Price02/2023
15242^751426-764321226202Enzo Doria12/2013
1525(18^180181-1)/17226176Andy Steward04/2007
15262^750740-3225996Paul Bourdelais03/2012
15272^750725+60227225991Enzo Doria02/2016
15282^750525-113743225931Enzo Doria09/2014
1529(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
15302^749444-1861889225606Enzo Doria12/2015
1531tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
15322^749096+1876861225501Enzo Doria07/2016
15332^748895+26213225440Enzo Doria12/2023
1534(519643#+43033)/(23*1871*2706283)225379Makoto Morimoto08/2019
15352^748657+79607225369Enzo Doria06/2016
1536(2^746920-11)/5224845Stefano Morozzi08/2022
15372^746653-291583224765Enzo Doria07/2015
15382^746461-114043224708Enzo Doria11/2014
15392^746302+25224660Stefano Morozzi05/2021
1540(202*10^224545-1)/3224547Robert Price06/2023
1541(19*10^224533-37)/9224534Alfred Reich12/2023
15422^745674+213949224471Enzo Doria10/2023
15432^745098-350471224297Enzo Doria06/2015
15442^745039-4897224280Yves Minet03/2021
154523*10^224232-7224234Robert Price10/2022
1546(154*10^224061-1)/9224063Serge Batalov12/2014
15472^744211-1845787224030Enzo Doria07/2015
15482^743592-134579223844Hans Havermann10/2018
15492^742452+3223501Paul Bourdelais06/2019
1550234178^9+9^234178223463Anatoly F. Selevich07/2011
15512^741651-461197223260Enzo Doria07/2015
155210^223236-1001223236Robert Price10/2022
15532^741362-1845251223173Enzo Doria07/2015
15543^467546-5*2^467546223077Jon Grantham08/2023
15552^740455-1863877222900Enzo Doria12/2015
15562^740274+217519222845Enzo Doria01/2024
1557(14*10^222718-41)/9222719Serge Batalov01/2023
15582^739636-2792219222653Enzo Doria02/2016
155911^213654-180222498Enzo Doria01/2013
15602^738957-1859743222449Enzo Doria11/2015
15614*10^222253-21222254Robert Price12/2022
15622^737825+57222108Stefano Morozzi05/2021
1563(54^128189+1)/55222073Paul Bourdelais11/2018
15642^737166+220099221910Enzo Doria03/2024
1565(10^221654+179)/9221654Serge Batalov12/2014
15662^736281+79817221643Enzo Doria06/2016
156710^221631+247617221632Patrick De Geest10/2013
156810^221631-9221631Alexander Gramolin02/2011
156910^221628+7221629Alfred Reich04/2021
15702^735970-1839821221550Enzo Doria06/2015
15712^735367+60293221368Enzo Doria03/2016
157277*10^221343+3221345Robert Price11/2023
1573(202*10^221092-1)/3221094Robert Price06/2023
1574(29^151153+1)/30221045Paul Bourdelais09/2017
15752^734228+24751221025Enzo Doria10/2023
15762^733264-2784089220735Enzo Doria10/2015
15772^733114-24555220690Enzo Doria09/2013
15782^731891-636259220322Enzo Doria12/2013
157998*10^220185-9220187Robert Price05/2023
1580418319^39164+418318220161Alfred Reich11/2023
15812^731124-25539220091Enzo Doria09/2013
15822^730972-462029220045Enzo Doria07/2015
15832^730833+1868627220003Enzo Doria04/2016
15842^730645-2787133219947Enzo Doria11/2015
15852^730547-25581219917Enzo Doria09/2013
1586(113*13^197420-5)/12219916Anonymous11/2022
1587(13^197420*113-5)/12219916Eric Chen10/2023
15882^730460+82291219891Enzo Doria09/2016
1589(5*10^219847-101)/3219848Robert Price08/2023
1590(2^730339+1)/(3*27839062003*7943469324347)219831Gord Palameta12/2018
1591L(1051849)219824Renaud Lifchitz03/2009
15923*2^730149+5219798Jon Grantham07/2023
15938*10^219740-3219741Serge Batalov01/2023
159411^210961-240219694Enzo Doria01/2013
1595(26*10^219639-77)/3219640Robert Price03/2023
15962^729611-113437219635Enzo Doria08/2014
15977^259710-2219481Paul Bourdelais01/2021
1598F(1049897)219416Henri Lifchitz10/2008
1599(1488^69151-1)/1487219386Alexander Zhirkov02/2023
16002^728604+1879321219332Enzo Doria10/2016
160133^144412+2219292Robert Price04/2015
16022^728277-183313219234Hans Havermann10/2018
16032^727998-1862711219150Enzo Doria12/2015
1604(29*10^219124+91)/3219125Robert Price12/2022
16052^727729-114073219069Enzo Doria12/2014
16062^727496-1851809218999Enzo Doria08/2015
16072^727025+25907218857Enzo Doria12/2023
16082^726591+2793143218726Enzo Doria02/2016
1609(7*10^218644+17)/3218645Robert Price06/2023
16102^725534-2791931218408Enzo Doria02/2016
1611Phi(220531,10)/2686456812680882641217774Makoto Kamada10/2020
16122^722184+1877821217400Enzo Doria08/2016
1613(109*10^217360-1)/9217362Serge Batalov12/2014
16142^721721-4453217260Yves Minet03/2021
161510^216950+49216951Robert Price02/2023
1616281*499979#/46410-2702372216849Robert Smith08/2016
1617281*499979#/46410+2400766216849Robert Smith08/2016
1618tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
16192^718756-114107216368Enzo Doria12/2014
16202^717672+121216041Stefano Morozzi05/2021
16212^717305+80327215931Enzo Doria07/2016
16222^717069-59773215860Enzo Doria10/2015
162310^215802+33215803Robert Price08/2023
162430^146021-29^146021215691Jean-Louis Charton09/2018
1625277^88301-276^88301215674Jean-Louis Charton06/2012
16262^716428+215011215667Enzo Doria11/2023
1627(13*10^215592-43)/3215593Robert Price08/2023
1628227^91413-40215372Enzo Doria04/2015
1629(2^715008-21)/5215239Stefano Morozzi08/2022
16302^714717+782897215152Enzo Doria11/2016
1631tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
16322^713241+1879157214707Enzo Doria08/2016
1633(23*10^214633+91)/3214634Robert Price03/2023
163411^206081-10^206081214612Jean-Louis Charton10/2011
16352^712801-69553214575Enzo Doria01/2016
16362^712603-25357214515Enzo Doria09/2013
16372^711721-1846723214250Enzo Doria07/2015
16382^710730-396765213952Enzo Doria09/2013
1639(19*10^213934-37)/9213935Alfred Reich12/2023
1640(19*10^213730-37)/9213731Alfred Reich12/2023
1641(713^74897-1)/712213685Jinyuan Wang08/2023
16422^709773+25907213663Enzo Doria12/2023
16432^708468-114329213271Enzo Doria02/2015
16442^708293+27557213218Enzo Doria01/2024
16452^707277+28997212912Enzo Doria02/2024
1646(163*10^212779-1)/9212781Serge Batalov12/2014
16472^706838-69041212780Enzo Doria11/2015
16482^705653+25907212423Enzo Doria12/2023
164922*10^212339+7212341Robert Price10/2022
16502^704577-113871212099Enzo Doria10/2014
1651(2^704548-19)/3212090Stefano Morozzi08/2022
16522^704110-2792441211959Enzo Doria02/2016
16532^704084+28531211951Enzo Doria02/2024
16542^703943-1862947211908Enzo Doria12/2015
1655(60^119083+1)/61211746Paul Bourdelais10/2018
1656(184*10^211682-1)/3211684Robert Price12/2022
1657(10^211610-91)/9211610Serge Batalov12/2014
1658227^89797+2211565Lelio R Paula08/2012
16592^702194-3211382Paul Bourdelais03/2012
16602^702064+1874911211343Enzo Doria07/2016
16612^701968-113873211314Enzo Doria10/2014
1662(14*10^211262-41)/9211263Serge Batalov01/2023
16632^701713-113779211237Enzo Doria09/2014
16642^701616-216803211208Enzo Doria01/2024
16652^701449-25201211158Enzo Doria09/2013
16662^701403-2786977211144Enzo Doria11/2015
16672^701189-25423211079Enzo Doria09/2013
16682^701162-459161211071Enzo Doria05/2015
16692^700793+219407210960Enzo Doria03/2024
1670(24^152783-1)/23210872Paul Bourdelais04/2018
16712^700400+9385210842Lelio R Paula01/2014
16722^700304-17210813Stefano Morozzi07/2022
16732^700131+1874693210761Enzo Doria06/2016
1674(2^700095+225414)/2210750Stefano Morozzi04/2020
1675(2^700090+278254)/2210748Stefano Morozzi04/2020
1676(2^700075+303666)/2210744Stefano Morozzi04/2020
1677(2^700073+75882)/2210743Stefano Morozzi04/2020
1678(2^700074+328890)/2210743Stefano Morozzi04/2020
1679(2^700052+79162)/2210737Stefano Morozzi04/2020
1680(2^700052+304458)/2210737Stefano Morozzi04/2020
1681(2^700048+376578)/2210736Stefano Morozzi04/2020
168211^202357-1140210734Enzo Doria12/2012
1683(2^700021+25874)/2210728Stefano Morozzi04/2020
1684(2^700018+377518)/2210727Stefano Morozzi04/2020
16852^699999+300729210721Norman Luhn09/2023
1686(238*10^210712-1)/3210714Robert Price09/2023
16872^699740+25210643Stefano Morozzi05/2021
1688(23*10^210525-143)/3210526Robert Price12/2023
16892^698929-2788423210399Enzo Doria11/2015
1690(5^300893+4^300893)/9210315Jean-Louis Charton11/2011
16912^698316+1878601210215Enzo Doria08/2016
169234*10^210097-9210099Robert Price05/2023
1693(19*10^210011-49)/3210012Robert Price06/2023
16946*10^209846-91209847Robert Price05/2023
16952^697036+1878751209829Enzo Doria08/2016
16962^696813+28607209762Enzo Doria02/2024
1697(238*10^209715-1)/3209717Robert Price09/2023
16986^269407+5209640Paul Bourdelais02/2021
1699(2^696343-1)/11141489/36009913139329209600Tony Prest / Never Odd Or Even02/2014
17002^696254-115151209594Enzo Doria06/2015
1701(35^135623+1)/36209410Paul Bourdelais07/2018
17027*10^209161+39209162Robert Price01/2023
17032^694633+1887257209106Enzo Doria05/2017
1704fibonacci(999790)-4208944Jon Grantham08/2023
17052^693959+180923208903Enzo Doria07/2016
1706(2^693747-11)/3208839Stefano Morozzi08/2022
17072^693462-1847561208753Enzo Doria07/2015
17082^690890-59981207979Enzo Doria11/2015
1709(38^131591+1)/39207884Paul Bourdelais07/2018
17103*2^690484+5207857Jon Grantham07/2023
17112^690163+1877063207760Enzo Doria07/2016
17127^245608-2207563Paul Bourdelais01/2021
1713(67*10^207556+23)/9207557Serge Batalov01/2023
17142^689286-29381207496Enzo Doria08/2015
17152^689122-114521207447Enzo Doria04/2015
17169*10^207254-89207255Robert Price02/2023
17172^688373+6077207221Enzo Doria02/2016
17182^688201+1875527207170Enzo Doria07/2016
1719(42^127609+1)/43207140Paul Bourdelais07/2018
17202^687938+213589207090Enzo Doria10/2023
17212^687619+81563206994Enzo Doria08/2016
17223*10^206927+37206928Robert Price08/2023
17232^687383+21803206923Enzo Doria09/2023
17242^686572-1845299206679Enzo Doria07/2015
1725(21^156217-1)/20206552Paul Bourdelais04/2010
1726(2^685739+1)/(3*87774593)206420Gord Palameta08/2018
17272^685578+3206380Paul Bourdelais04/2012
17282^685078+218599206230Enzo Doria01/2024
17292^684836-49349206157Enzo Doria10/2015
1730(73^110603-1)/72206088Paul Bourdelais06/2018
17312^684163-2790967205954Enzo Doria12/2015
1732326^81943-325^81943205941Jean-Louis Charton07/2012
1733(2^684127-1)/23765203727205933Jens K. Andersen04/2009
1734(68*10^205510+13)/9205511Serge Batalov01/2023
17354^341233-3^341233205443Jean-Louis Charton01/2006
17362^682414+215029205428Enzo Doria11/2023
1737(963^68821-1)/962205334Jinyuan Wang01/2024
1738(43*10^205183-421)/9205184Robert Price10/2023
17392^681545+467205166Lelio R Paula11/2013
17402^681306+81049205094Enzo Doria07/2016
17412^680697+1877057204911Enzo Doria07/2016
17422^680415+71783204826Enzo Doria04/2016
174310^204764-8001204764Robert Price03/2023
1744(26*10^204730-77)/3204731Robert Price03/2023
17452^679860-459995204659Enzo Doria06/2015
17462^679593+1879547204578Enzo Doria09/2016
17472^678899+220073204369Enzo Doria03/2024
17482^678753+21677204326Enzo Doria08/2023
17492^678651+1875023204295Enzo Doria07/2016
17502^678561+678561204268Henri Lifchitz05/2006


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 27 2024 11:51 (Time in France)

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