PRP Records

Probable Primes Top 10000

(301421 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 ?
1251314738^9+9^314738300337Anatoly F. Selevich02/2011
12522^997689+217787300335Enzo Doria01/2024
125369478^20987+20987^69478300281Hans Havermann07/2021
125464088^48393+48393^64088300239Hans Havermann07/2021
125564605^44146+44146^64605300084Hans Havermann08/2021
12562^996845+29027300081Enzo Doria02/2024
12577^355039-6^355039300043Jean-Louis Charton05/2011
125867594^27465+27465^67594300035Hans Havermann06/2021
125910^300000+287389300001Patrick De Geest10/2019
126010^300000-83657300000Patrick De Geest10/2019
126170599^17756+17756^70599300000Hans Havermann06/2021
1262numbpart(72526161452)299999Serge Batalov04/2017
12632^996182-114431299881Enzo Doria02/2015
12643*2^996126+5299865Jon Grantham07/2023
12652^996034-17299837Stefano Morozzi07/2022
12662^995793+36587299764Enzo Doria09/2024
1267(19*10^299640+77)/3299641Robert Price03/2023
12682^995214-2788361299590Enzo Doria12/2015
12692^994791-114319299462Enzo Doria01/2015
12702^994490-1863791299372Enzo Doria01/2016
12712^993322+1885729299020Enzo Doria03/2017
12722^993227+230033298992Enzo Doria12/2024
1273(36395^65536+36393^65536)/2298913Kellen Shenton04/2022
12742^992711-2788807298836Enzo Doria12/2015
12752^992525-114199298780Enzo Doria12/2014
1276(7^353501-3^353501)/4298743Jon Grantham08/2023
12772^992329+1884707298721Enzo Doria02/2017
12782^992292+229801298710Enzo Doria12/2024
12792^992052+215491298638Enzo Doria11/2023
12802^991968-23298613Stefano Morozzi07/2022
12812^991715-19298536Stefano Morozzi07/2022
1282(10^298414+7)/191/823/56921/1334467298398Alfred Reich10/2021
12832^989562+25297888Stefano Morozzi05/2021
12842^988580+214051297593Enzo Doria10/2023
12852^988537+218837297580Enzo Doria03/2024
1286(19*10^297497+77)/3297498Robert Price03/2023
1287(2*10^297488-23)/3297488Robert Price10/2022
12882^987033+46427297127Enzo Doria05/2025
1289(2^986191+1)/3296873Vincent Diepeveen06/2008
12902^985217-114553296580Enzo Doria03/2015
1291(76^157649-1)/75296507Paul Bourdelais07/2019
12922^984650+21529296410Enzo Doria08/2023
12932^984131-1828009296253Enzo Doria01/2015
12942^983620+60451296100Phil Moore03/2008
12952^982721-2683295829Yves Minet02/2016
1296(23*10^295581+7)/3295582Robert Price05/2023
12972^981298-2788421295401Enzo Doria12/2015
12982^981163-2790967295360Enzo Doria12/2015
12992^981016-15295316Stefano Morozzi07/2022
13008*10^295160-13295161Robert Price08/2023
13012^979594+1865839294888Enzo Doria02/2016
13022^979502+221029294860Enzo Doria03/2024
13032*10^294527-91294528Robert Price02/2023
1304(49363^63001-1)/(49363^251-1)294511Ryan Propper11/2023
130510^294475+49294476Robert Price02/2023
13062^977896+234601294377Enzo Doria04/2025
1307(11*10^294308+91)/3294309Robert Price03/2023
13082^976760+1885021294035Enzo Doria02/2017
13093*2^976518+5293962Jon Grantham07/2023
13102^975798+218599293745Enzo Doria01/2024
13112^974441+1878407293336Enzo Doria08/2016
13122^974180+1876831293258Enzo Doria07/2016
13132^974170+453319293255Enzo Doria01/2017
1314(211^126023-1)/210292911Anonymous05/2024
13152^972744-114419292826Enzo Doria03/2015
131611^281143+6292781Paul Bourdelais03/2021
1317(4*10^292619-91)/3292620Robert Price12/2022
1318E(69468)/13247122135292549Sergey Batalov10/2023
1319CopelandErdos(292447)292447Mark Rodenkirch12/2015
13203*10^292344-97292345Robert Price01/2023
13212^970911+1873373292274Enzo Doria07/2016
13222^970670+383059292201Enzo Doria12/2016
13232^970141-100363292042Enzo Doria02/2014
13242^969945+1874717291983Enzo Doria06/2016
13252^969384+1880701291814Enzo Doria10/2016
1326(13*10^291721-43)/3291722Robert Price08/2023
1327(3^611333-2^611333)/(99035947*87109884549431)291659Mike Oakes02/2017
132810^(2*145126+1)-2*10^145126-1290253Robert Price03/2025
13293*2^963892+5290161Jon Grantham07/2023
1330(151*10^289877-1)/3289879Robert Price07/2023
13312^962194+60139289650Enzo Doria02/2016
13322^961409+44267289413Enzo Doria04/2025
13332^959307-1861507288781Enzo Doria11/2015
1334(17*10^288692+31)/3288693Robert Price04/2023
133514^251797-3288592Paul Bourdelais12/2020
1336(8745^73441-1)/(8745^271-1)288419Ryan Propper11/2023
1337(2*10^288371-23)/3288371Robert Price10/2022
1338(31*10^288238-1)/3288240Robert Price02/2023
1339(7^341063-2^341063)/5288231Jon Grantham08/2023
13402^957372+283531288198Enzo Doria02/2017
13412^957192-1864049288144Enzo Doria01/2016
1342(95774^58081-1)/(95774^241-1)288116Ryan Propper11/2023
13432^956446+1875199287919Enzo Doria06/2016
13442^956283+219143287870Enzo Doria02/2024
13457*10^287854+39287855Robert Price01/2023
13462^956082+28309287810Enzo Doria02/2024
1347(17^233689+1)/18287542Paul Bourdelais09/2013
13482^955178+1883587287538Enzo Doria12/2016
13492^954127-954127^2287221Henri Lifchitz01/2021
13502^954001+1875257287183Enzo Doria07/2016
13512*10^287175-49287176Robert Price05/2023
1352(22*10^287085-19)/3287086Robert Price07/2023
13532^953667+38573287083Enzo Doria11/2024
13542^953488+22411287029Enzo Doria09/2023
1355(23891^65536+1)/2286932Serge Batalov03/2018
13565*3^601336-2^601336286911Jon Grantham08/2023
13572^952268+1878601286662Enzo Doria09/2016
13582^950801+81557286220Enzo Doria08/2016
13592^949403+217523285799Enzo Doria01/2024
136022845^65536+22844^65536285658Kellen Shenton03/2021
1361(19*10^285615+53)/9285616Rytis Slatkevicius12/2024
1362(11*2^948635-13)/15285568Renaud Lifchitz11/2011
1363(54^164839+1)/55285565Paul Bourdelais07/2019
13642^948510+782569285530Enzo Doria10/2016
13652^948374-114137285490Enzo Doria01/2015
13662^947739+1872923285298Enzo Doria06/2016
13672^946274+218407284857Enzo Doria03/2024
13687*10^284751+9284752Robert Price04/2023
13692^944561-21284342Stefano Morozzi07/2022
1370(4*10^284330-31)/9284330Serge Batalov11/2022
1371(32*10^283826-23)/9283827Serge Batalov01/2023
13722^942533+82067283731Enzo Doria09/2016
13732^941469+39283411Jon Grantham08/2023
1374(10^283342-31)/3283342Robert Price03/2023
13752^940950+1874989283255Enzo Doria06/2016
13762^940426-2786141283097Enzo Doria11/2015
13772^940155+226973283015Enzo Doria09/2024
1378(2*10^282948-11)/9282948Serge Batalov11/2022
13792^939881-114115282933Enzo Doria12/2014
1380(14*10^282673-143)/3282674Robert Price05/2023
138110^282493+632551282494Patrick De Geest02/2017
138310^282493-9^282493282493Jean-Louis Charton03/2007
138210^282493-132327282493Patrick De Geest02/2017
13843^591827-2^591827282374Mike Oakes08/2009
1385Tau(509^18946)282048Nik Lygeros / Olivier Rozier05/2015
13862^936716-1835519281980Enzo Doria04/2015
13872^936588+79411281942Enzo Doria06/2016
13882^936047+1877423281779Enzo Doria08/2016
13892^935713+1869377281678Enzo Doria05/2016
13902^933082+1877059280886Enzo Doria08/2016
1391(5*10^280710+1)/3280711Serge Batalov10/2014
13922^932443+225893280694Enzo Doria08/2024
13932^932064+26521280580Enzo Doria12/2023
13942^931976+25280553Stefano Morozzi05/2021
1395(42^172663+1)/43280274Paul Bourdelais07/2019
1396(10^279978+11)/3279978Serge Batalov07/2015
13972^929524-1864829279815Enzo Doria01/2016
13982^929329+22697279756Enzo Doria09/2023
13992^929152+60181279703Enzo Doria02/2016
14002^928621-2787883279543Enzo Doria11/2015
1401(2^927763+lucasV(-1,2,927763)+1)/2279285Mike Oakes04/2017
14023*10^279271+77279272Robert Price06/2024
14032^927429+1882277279184Enzo Doria12/2016
14042^926766-11278985Stefano Morozzi07/2022
1405(71^150697-1)/70278978Paul Bourdelais07/2019
1406(33^183661-1)/32278891Paul Bourdelais12/2018
1407(166*10^278633-7)/3278635Robert Price02/2023
1408(2^925391+lucasV(-1,2,925391)+1)/2278571Mike Oakes03/2017
14092^925330-1301278553Yves Minet06/2015
1410(299*10^278546+1)/3278548Robert Price01/2023
14112^925299+216053278543Enzo Doria11/2023
1412(21^210599+1)/22278457Paul Bourdelais08/2013
1413(266*10^278325+1)/3278327Robert Price01/2023
14142^923261-69175277930Enzo Doria11/2015
1415757^96487-756^96487277796Jean-Louis Charton12/2012
14162^922301+57277641Stefano Morozzi05/2021
14177*10^277478-39277479Robert Price07/2023
1418((((((((((((((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
1419(5^396413-1)/4277081Paul Bourdelais06/2010
14202^920318+2792299277044Enzo Doria02/2016
1421(16*10^276537-31)/3276538Robert Price03/2023
14222^918596-2786939276525Enzo Doria11/2015
14232^917910+28369276319Enzo Doria01/2024
14242^917328+228571276144Enzo Doria11/2024
1425(6737^72361-1)/(6737^269-1)276002Ryan Propper11/2023
14262^916639+60563275936Enzo Doria04/2016
1427(2*10^275922+1)/3275922Serge Batalov11/2022
14282^916385-2786383275860Enzo Doria11/2015
14292^915928+82081275722Enzo Doria09/2016
1430(4*10^275671+11)/3275672Tyler Busby02/2023
14312^915576-114137275616Enzo Doria01/2015
14322^914828+1876741275391Enzo Doria07/2016
14332^914757-2203275370Yves Minet12/2015
14347*10^275157-27275158Robert Price11/2022
14352^912744+20011274764Enzo Doria06/2023
14362^911900+1871245274510Enzo Doria05/2016
1437(16*10^274251-91)/3274252Robert Price11/2022
14382^910999+9274239Stefano Morozzi05/2021
1439(2^910869-7)/5274199Stefano Morozzi08/2022
14402^910490+283429274085Enzo Doria01/2017
14417*10^273983+39273984Robert Price01/2023
14422^909988-1862249273934Enzo Doria12/2015
14432^909901+378567273908Boyan Hu08/2024
14442^909297+1879157273726Enzo Doria08/2016
14452^909257-1864423273714Enzo Doria01/2016
14462^909254+31309273713Enzo Doria03/2024
14472^908739-7273558Stefano Morozzi07/2022
14482^908579-1861747273510Enzo Doria12/2015
14493*2^908005-5273338Jon Grantham07/2023
14502^907635-2791597273226Enzo Doria01/2016
14512^907059+211193273052Enzo Doria08/2023
1452(53^158341+1)/54273022Paul Bourdelais07/2019
14532^906594-113201272912Enzo Doria08/2014
14549*10^272800+91272801Robert Price05/2023
14552*10^272710-49272711Robert Price05/2023
14562*10^272403-91272404Robert Price02/2023
14572^904773+1872167272364Enzo Doria06/2016
14586^349903+5272278Paul Bourdelais02/2021
14592^904149-1862473272176Enzo Doria12/2015
14602^902926+227839271808Enzo Doria10/2024
1461(7*10^271757-61)/9271757Erik Branger03/2012
14622^902497+1880117271679Enzo Doria09/2016
14632^901858+77689271487Enzo Doria06/2016
14642^901372+1875301271341Enzo Doria06/2016
14652^901146+219049271272Enzo Doria02/2024
1466(8*10^271039-77)/3271040Robert Price04/2023
14672^899999+1144031270927Norman Luhn09/2023
14682*10^270802-91270803Robert Price02/2023
146923*10^270799-7270801Robert Price10/2022
14702^899121-115033270663Enzo Doria07/2015
14712^898900+883021270596Enzo Doria12/2016
14722^898762-251511270555Enzo Doria12/2013
14732^898589+47270503Lelio R Paula03/2016
1474187322*10^270343-187321270349Danilo Nitsche09/2013
147548358*10^270343-48357270348Danilo Nitsche09/2013
1476(10^270343-1)/9270343Maksym Voznyy07/2007
14772^897867-3217270285Yves Minet12/2016
14782^897849-115273270280Enzo Doria07/2015
14792^897367+26289270135Enzo Doria03/2024
14802^896616-114179269909Enzo Doria12/2014
1481(12648^66049-1)/(12648^257-1)269881Ryan Propper11/2023
1482(10^(2*134811+1)+6*10^134811-1)/3269623Robert Price08/2024
1483(22*10^269517-19)/3269518Robert Price07/2023
148410^(2*134739+1)-7*10^134739-1269479Robert Price07/2023
14852^894928+583561269401Enzo Doria04/2017
14862^894673-39343269324Enzo Doria08/2015
14872^893836+23221269072Enzo Doria10/2023
14882^892718+29539268735Enzo Doria03/2024
14892^892660+213901268718Enzo Doria10/2023
1490F(1285607)268676Henri Lifchitz11/2008
14912^892234+22189268590Enzo Doria09/2023
14922^892151+24863268565Enzo Doria11/2023
14932^892112+187663268553Enzo Doria08/2016
1494(266*10^268407-17)/3268409Robert Price02/2023
1495(10^268207+1)/11268206Paul Bourdelais02/2010
14962^890957-69583268205Enzo Doria12/2015
149732841!^2+32840!^2+...+2!^2+1!^2268128Serge Batalov07/2017
14982^890122-351401267954Enzo Doria07/2015
1499(19^209359-1)/18267718Paul Bourdelais08/2010
15002^888852+229051267572Enzo Doria11/2024


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 19 2025 12:52 (Time in France)

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