PRP Records

Probable Primes Top 10000

(295503 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 ?
100169478^20987+20987^69478300281Hans Havermann07/2021
100264088^48393+48393^64088300239Hans Havermann07/2021
100364605^44146+44146^64605300084Hans Havermann08/2021
10042^996845+29027300081Enzo Doria02/2024
10057^355039-6^355039300043Jean-Louis Charton05/2011
100667594^27465+27465^67594300035Hans Havermann06/2021
100710^300000+287389300001Patrick De Geest10/2019
100810^300000-83657300000Patrick De Geest10/2019
100970599^17756+17756^70599300000Hans Havermann06/2021
1010numbpart(72526161452)299999Serge Batalov04/2017
10112^996182-114431299881Enzo Doria02/2015
10123*2^996126+5299865Jon Grantham07/2023
10132^996034-17299837Stefano Morozzi07/2022
1014(19*10^299640+77)/3299641Robert Price03/2023
10152^995214-2788361299590Enzo Doria12/2015
10162^994791-114319299462Enzo Doria01/2015
10172^994490-1863791299372Enzo Doria01/2016
10182^993322+1885729299020Enzo Doria03/2017
1019(36395^65536+36393^65536)/2298913Kellen Shenton04/2022
10202^992711-2788807298836Enzo Doria12/2015
10212^992525-114199298780Enzo Doria12/2014
1022(7^353501-3^353501)/4298743Jon Grantham08/2023
10232^992329+1884707298721Enzo Doria02/2017
10242^992052+215491298638Enzo Doria11/2023
10252^991968-23298613Stefano Morozzi07/2022
10262^991715-19298536Stefano Morozzi07/2022
1027(10^298414+7)/191/823/56921/1334467298398Alfred Reich10/2021
10282^989562+25297888Stefano Morozzi05/2021
10292^988580+214051297593Enzo Doria10/2023
10302^988537+218837297580Enzo Doria03/2024
1031(19*10^297497+77)/3297498Robert Price03/2023
1032(2*10^297488-23)/3297488Robert Price10/2022
1033(2^986191+1)/3296873Vincent Diepeveen06/2008
10342^985217-114553296580Enzo Doria03/2015
1035(76^157649-1)/75296507Paul Bourdelais07/2019
10362^984650+21529296410Enzo Doria08/2023
10372^984131-1828009296253Enzo Doria01/2015
10382^983620+60451296100Phil Moore03/2008
10392^982721-2683295829Yves Minet02/2016
1040(23*10^295581+7)/3295582Robert Price05/2023
10412^981298-2788421295401Enzo Doria12/2015
10422^981163-2790967295360Enzo Doria12/2015
10432^981016-15295316Stefano Morozzi07/2022
10448*10^295160-13295161Robert Price08/2023
10452^979594+1865839294888Enzo Doria02/2016
10462^979502+221029294860Enzo Doria03/2024
10472*10^294527-91294528Robert Price02/2023
1048(49363^63001-1)/(49363^251-1)294511Ryan Propper11/2023
104910^294475+49294476Robert Price02/2023
1050(11*10^294308+91)/3294309Robert Price03/2023
10512^976760+1885021294035Enzo Doria02/2017
10523*2^976518+5293962Jon Grantham07/2023
10532^975798+218599293745Enzo Doria01/2024
10542^974441+1878407293336Enzo Doria08/2016
10552^974180+1876831293258Enzo Doria07/2016
10562^974170+453319293255Enzo Doria01/2017
1057(211^126023-1)/210292911Anonymous05/2024
10582^972744-114419292826Enzo Doria03/2015
105911^281143+6292781Paul Bourdelais03/2021
1060(4*10^292619-91)/3292620Robert Price12/2022
1061E(69468)/13247122135292549Sergey Batalov10/2023
1062CopelandErdos(292447)292447Mark Rodenkirch12/2015
10633*10^292344-97292345Robert Price01/2023
10642^970911+1873373292274Enzo Doria07/2016
10652^970670+383059292201Enzo Doria12/2016
10662^970141-100363292042Enzo Doria02/2014
10672^969945+1874717291983Enzo Doria06/2016
10682^969384+1880701291814Enzo Doria10/2016
1069(13*10^291721-43)/3291722Robert Price08/2023
1070(3^611333-2^611333)/(99035947*87109884549431)291659Mike Oakes02/2017
10713*2^963892+5290161Jon Grantham07/2023
1072(151*10^289877-1)/3289879Robert Price07/2023
10732^962194+60139289650Enzo Doria02/2016
10742^959307-1861507288781Enzo Doria11/2015
1075(17*10^288692+31)/3288693Robert Price04/2023
107614^251797-3288592Paul Bourdelais12/2020
1077(8745^73441-1)/(8745^271-1)288419Ryan Propper11/2023
1078(2*10^288371-23)/3288371Robert Price10/2022
1079(31*10^288238-1)/3288240Robert Price02/2023
1080(7^341063-2^341063)/5288231Jon Grantham08/2023
10812^957372+283531288198Enzo Doria02/2017
10822^957192-1864049288144Enzo Doria01/2016
1083(95774^58081-1)/(95774^241-1)288116Ryan Propper11/2023
10842^956446+1875199287919Enzo Doria06/2016
10852^956283+219143287870Enzo Doria02/2024
10867*10^287854+39287855Robert Price01/2023
10872^956082+28309287810Enzo Doria02/2024
1088(17^233689+1)/18287542Paul Bourdelais09/2013
10892^955178+1883587287538Enzo Doria12/2016
10902^954127-954127^2287221Henri Lifchitz01/2021
10912^954001+1875257287183Enzo Doria07/2016
10922*10^287175-49287176Robert Price05/2023
1093(22*10^287085-19)/3287086Robert Price07/2023
10942^953488+22411287029Enzo Doria09/2023
1095(23891^65536+1)/2286932Serge Batalov03/2018
10965*3^601336-2^601336286911Jon Grantham08/2023
10972^952268+1878601286662Enzo Doria09/2016
10982^950801+81557286220Enzo Doria08/2016
10992^949403+217523285799Enzo Doria01/2024
110022845^65536+22844^65536285658Kellen Shenton03/2021
1101(11*2^948635-13)/15285568Renaud Lifchitz11/2011
1102(54^164839+1)/55285565Paul Bourdelais07/2019
11032^948510+782569285530Enzo Doria10/2016
11042^948374-114137285490Enzo Doria01/2015
11052^947739+1872923285298Enzo Doria06/2016
11062^946274+218407284857Enzo Doria03/2024
11077*10^284751+9284752Robert Price04/2023
11082^944561-21284342Stefano Morozzi07/2022
1109(4*10^284330-31)/9284330Serge Batalov11/2022
1110(32*10^283826-23)/9283827Serge Batalov01/2023
11112^942533+82067283731Enzo Doria09/2016
11122^941469+39283411Jon Grantham08/2023
1113(10^283342-31)/3283342Robert Price03/2023
11142^940950+1874989283255Enzo Doria06/2016
11152^940426-2786141283097Enzo Doria11/2015
1116(2*10^282948-11)/9282948Serge Batalov11/2022
11172^939881-114115282933Enzo Doria12/2014
1118(14*10^282673-143)/3282674Robert Price05/2023
111910^282493+632551282494Patrick De Geest02/2017
112110^282493-9^282493282493Jean-Louis Charton03/2007
112010^282493-132327282493Patrick De Geest02/2017
11223^591827-2^591827282374Mike Oakes08/2009
1123Tau(509^18946)282048Nik Lygeros / Olivier Rozier05/2015
11242^936716-1835519281980Enzo Doria04/2015
11252^936588+79411281942Enzo Doria06/2016
11262^936047+1877423281779Enzo Doria08/2016
11272^935713+1869377281678Enzo Doria05/2016
11282^933082+1877059280886Enzo Doria08/2016
1129(5*10^280710+1)/3280711Serge Batalov10/2014
11302^932064+26521280580Enzo Doria12/2023
11312^931976+25280553Stefano Morozzi05/2021
1132(42^172663+1)/43280274Paul Bourdelais07/2019
1133(10^279978+11)/3279978Serge Batalov07/2015
11342^929524-1864829279815Enzo Doria01/2016
11352^929329+22697279756Enzo Doria09/2023
11362^929152+60181279703Enzo Doria02/2016
11372^928621-2787883279543Enzo Doria11/2015
1138(2^927763+lucasV(-1,2,927763)+1)/2279285Mike Oakes04/2017
11393*10^279271+77279272Robert Price06/2024
11402^927429+1882277279184Enzo Doria12/2016
11412^926766-11278985Stefano Morozzi07/2022
1142(71^150697-1)/70278978Paul Bourdelais07/2019
1143(33^183661-1)/32278891Paul Bourdelais12/2018
1144(166*10^278633-7)/3278635Robert Price02/2023
1145(2^925391+lucasV(-1,2,925391)+1)/2278571Mike Oakes03/2017
11462^925330-1301278553Yves Minet06/2015
1147(299*10^278546+1)/3278548Robert Price01/2023
11482^925299+216053278543Enzo Doria11/2023
1149(21^210599+1)/22278457Paul Bourdelais08/2013
1150(266*10^278325+1)/3278327Robert Price01/2023
11512^923261-69175277930Enzo Doria11/2015
1152757^96487-756^96487277796Jean-Louis Charton12/2012
11532^922301+57277641Stefano Morozzi05/2021
11547*10^277478-39277479Robert Price07/2023
1155((((((((((((((291487327^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2277369Serge Batalov07/2016
1156(5^396413-1)/4277081Paul Bourdelais06/2010
11572^920318+2792299277044Enzo Doria02/2016
1158(16*10^276537-31)/3276538Robert Price03/2023
11592^918596-2786939276525Enzo Doria11/2015
11602^917910+28369276319Enzo Doria01/2024
1161(6737^72361-1)/(6737^269-1)276002Ryan Propper11/2023
11622^916639+60563275936Enzo Doria04/2016
1163(2*10^275922+1)/3275922Serge Batalov11/2022
11642^916385-2786383275860Enzo Doria11/2015
11652^915928+82081275722Enzo Doria09/2016
1166(4*10^275671+11)/3275672Tyler Busby02/2023
11672^915576-114137275616Enzo Doria01/2015
11682^914828+1876741275391Enzo Doria07/2016
11692^914757-2203275370Yves Minet12/2015
11707*10^275157-27275158Robert Price11/2022
11712^912744+20011274764Enzo Doria06/2023
11722^911900+1871245274510Enzo Doria05/2016
1173(16*10^274251-91)/3274252Robert Price11/2022
11742^910999+9274239Stefano Morozzi05/2021
1175(2^910869-7)/5274199Stefano Morozzi08/2022
11762^910490+283429274085Enzo Doria01/2017
11777*10^273983+39273984Robert Price01/2023
11782^909988-1862249273934Enzo Doria12/2015
11792^909297+1879157273726Enzo Doria08/2016
11802^909257-1864423273714Enzo Doria01/2016
11812^909254+31309273713Enzo Doria03/2024
11822^908739-7273558Stefano Morozzi07/2022
11832^908579-1861747273510Enzo Doria12/2015
11843*2^908005-5273338Jon Grantham07/2023
11852^907635-2791597273226Enzo Doria01/2016
11862^907059+211193273052Enzo Doria08/2023
1187(53^158341+1)/54273022Paul Bourdelais07/2019
11882^906594-113201272912Enzo Doria08/2014
11899*10^272800+91272801Robert Price05/2023
11902*10^272710-49272711Robert Price05/2023
11912*10^272403-91272404Robert Price02/2023
11922^904773+1872167272364Enzo Doria06/2016
11936^349903+5272278Paul Bourdelais02/2021
11942^904149-1862473272176Enzo Doria12/2015
1195(7*10^271757-61)/9271757Erik Branger03/2012
11962^902497+1880117271679Enzo Doria09/2016
11972^901858+77689271487Enzo Doria06/2016
11982^901372+1875301271341Enzo Doria06/2016
11992^901146+219049271272Enzo Doria02/2024
1200(8*10^271039-77)/3271040Robert Price04/2023
12012^899999+1144031270927Norman Luhn09/2023
12022*10^270802-91270803Robert Price02/2023
120323*10^270799-7270801Robert Price10/2022
12042^899121-115033270663Enzo Doria07/2015
12052^898900+883021270596Enzo Doria12/2016
12062^898762-251511270555Enzo Doria12/2013
12072^898589+47270503Lelio R Paula03/2016
1208187322*10^270343-187321270349Danilo Nitsche09/2013
120948358*10^270343-48357270348Danilo Nitsche09/2013
1210(10^270343-1)/9270343Maksym Voznyy07/2007
12112^897867-3217270285Yves Minet12/2016
12122^897849-115273270280Enzo Doria07/2015
12132^897367+26289270135Enzo Doria03/2024
12142^896616-114179269909Enzo Doria12/2014
1215(12648^66049-1)/(12648^257-1)269881Ryan Propper11/2023
1216(22*10^269517-19)/3269518Robert Price07/2023
121710^(2*134739+1)-7*10^134739-1269479Robert Price07/2023
12182^894928+583561269401Enzo Doria04/2017
12192^894673-39343269324Enzo Doria08/2015
12202^893836+23221269072Enzo Doria10/2023
12212^892718+29539268735Enzo Doria03/2024
12222^892660+213901268718Enzo Doria10/2023
1223F(1285607)268676Henri Lifchitz11/2008
12242^892234+22189268590Enzo Doria09/2023
12252^892151+24863268565Enzo Doria11/2023
12262^892112+187663268553Enzo Doria08/2016
1227(266*10^268407-17)/3268409Robert Price02/2023
1228(10^268207+1)/11268206Paul Bourdelais02/2010
12292^890957-69583268205Enzo Doria12/2015
123032841!^2+32840!^2+...+2!^2+1!^2268128Serge Batalov07/2017
12312^890122-351401267954Enzo Doria07/2015
1232(19^209359-1)/18267718Paul Bourdelais08/2010
1233(85^138647+1)/86267507Paul Bourdelais07/2019
1234(1005^89087-1)/1004267451Jinyuan Wang01/2024
1235(485^99523-1)/484267291Michael Stocker05/2020
12362^886324+77791266811Enzo Doria06/2016
12377*10^266731+87266732Robert Price11/2022
12382^886040+213901266725Enzo Doria10/2023
12392^885242+217909266485Enzo Doria01/2024
12402^884738+26809266333Enzo Doria12/2023
12412^884714+1880527266326Enzo Doria10/2016
12427*10^266024-47266025Robert Price08/2023
124311^255426+255426^11265999Serge Batalov05/2014
12442^883462-343421265949Enzo Doria07/2015
12452^883442+1875019265943Enzo Doria06/2016
12462^883333-291583265910Enzo Doria07/2015
12472^883132+30421265850Enzo Doria03/2024
124810^265566+3593037265567Paul Bourdelais08/2023
1249(2*10^265321-17)/3265321Serge Batalov11/2022
1250(16*10^265052-91)/3265053Robert Price11/2022


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 22 2024 13:34 (Time in France)

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