PRP Records

Probable Primes Top 10000

(301429 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 ?
250156*10^195032-3195034Robert Price03/2020
250211^187185-90194934Enzo Doria09/2012
25032^647545-25194931Boyan Hu12/2024
25042^647468+220141194908Enzo Doria03/2024
2505(86*10^194818-437)/9194819Robert Price03/2021
25067^230492-230492^7194789Henri Lifchitz07/2024
25072^647068+77281194787Enzo Doria05/2016
25082*10^194716-93194717Robert Price12/2021
250915^165559-14^165559194713Jean-Louis Charton03/2011
2510F(931517)194676Henri Lifchitz09/2008
25114*10^194668+49194669Robert Price01/2019
25122^646589+1179407194643Enzo Doria06/2016
25132^646289-114621194553Enzo Doria05/2015
25142^646236-39659194537Enzo Doria09/2015
2515(16*10^194536+53)/3194537Robert Price03/2019
25162^646161-59833194514Enzo Doria11/2015
2517(17*10^194502+31)/3194503Robert Price01/2019
2518(19*10^194428+287)/9194429Robert Price10/2021
25192*10^194413+3194414Robert Price07/2015
25202^645360-1848599194273Enzo Doria08/2015
252122470^44641+44641^22470194260Norbert Schneider08/2023
2522(112*10^194150-1)/3194152Serge Batalov12/2014
2523Phi(293127,10)194041Makoto Kamada12/2023
25242*10^193981-43193982Robert Price04/2018
25252^644382+75169193979Enzo Doria04/2016
25262^644304-1861409193955Enzo Doria11/2015
2527(29*10^193950-23)/3193951Robert Price03/2022
25285*10^193907-9193908Robert Price05/2015
25292^644043+1876703193877Enzo Doria07/2016
25302*10^193841-63193842Robert Price01/2022
25312^643735+1879733193784Enzo Doria09/2016
2532(5^277183+1)/6193742Paul Bourdelais07/2010
25339*10^193712+71193713Robert Price08/2020
25342^643216-286565193628Enzo Doria07/2015
25352^643204+215011193624Enzo Doria11/2023
253610^193566+1126339193567Patrick De Geest09/2022
253810^193566-10000000001193566Robert Price04/2021
253710^193566-454041193566Patrick De Geest08/2021
25402^642888-24965193529Enzo Doria09/2013
25392^642889+25367193529Enzo Doria11/2023
25412^642448-114825193397Enzo Doria05/2015
25422^642437-1856623193393Enzo Doria10/2015
25432^642039-59797193273Enzo Doria11/2015
25442^641987+39193258Jon Grantham08/2023
254510^193230+513861193231Patrick De Geest07/2018
254610^193230-8001193230Robert Price03/2018
2547(62*10^193225-233)/9193226Robert Price02/2022
25482^641692-286349193169Enzo Doria07/2015
25492^641690-24737193168Enzo Doria09/2013
255022268^44421+44421^22268193129Norbert Schneider06/2023
25512^641514+1876549193115Enzo Doria07/2016
25522^640888-2785619192927Enzo Doria10/2015
25532^640874-2783741192923Enzo Doria09/2015
255410^192922+192207192923Patrick De Geest08/2021
255510^192922-7001192922Robert Price04/2021
25562^640854+25192917Stefano Morozzi05/2021
255734*10^192868-9192870Robert Price06/2020
2558(46*10^192841+683)/9192842Robert Price03/2019
25592^640181+467192714Lelio R Paula08/2013
25602^640072+27541192681Enzo Doria01/2024
2561(10^192700)/(192700^10)192648Henri Lifchitz05/2025
25622^639536-1850249192520Enzo Doria08/2015
256340714<>40712<>...<>1086421357911<>...<>40711<>40713192464Hans Havermann12/2019
25645*10^192422-43192423Robert Price01/2019
25652^639110-2792441192392Enzo Doria02/2016
2566(241^80761-1)/240192372Anonymous04/2024
25672^638955-29827192345Enzo Doria08/2015
256815^163539+14192337Alfred Reich10/2023
25692^638713-2784223192272Enzo Doria10/2015
2570(10^192216+7)/149192214Alfred Reich07/2021
25712^638490-113507192205Enzo Doria08/2014
25722^638189-39943192115Enzo Doria09/2015
25732^638110+1877119192091Enzo Doria07/2016
2574MillsLike(2,1,4,12,4,22,12,114,4,138,142,2956,6388,5248,17532,96930,83782,1464,897448,300832)+82440192083Sergey Batalov05/2024
2575MillsLike(2,1,4,12,4,22,12,114,4,138,142,2956,6388,5248,17532,96930,83782,1464,897448,300832)192083Sergey Batalov05/2024
25762^638066-2785211192078Enzo Doria10/2015
2577(35*10^191973-341)/9191974Robert Price08/2021
2578(112*10^191900+17)/3191902Robert Price03/2020
25792^637475-115309191900Enzo Doria07/2015
2580(68*10^191754-113)/9191755Robert Price03/2021
25812^636930-11191736Stefano Morozzi07/2022
2582(47*10^191732+259)/9191733Robert Price03/2022
258341459^41522-41522^41459191733Norbert Schneider04/2025
25842^636661+1876577191655Enzo Doria07/2016
2585(9^200807-2^200807)/7191618Jon Grantham07/2023
2586(34^125101-1)/33191589Paul Bourdelais11/2017
2587fibonacci(916540)-2191546Jon Grantham08/2023
25882^636177-1855123191509Enzo Doria09/2015
25892^636158-113627191503Enzo Doria08/2014
2590(37*25^136966+63)/4191472Curtis Bright05/2015
25912^636035+79823191466Enzo Doria06/2016
25922^636011-1860847191459Enzo Doria11/2015
25932^635926-1860611191433Enzo Doria11/2015
25943*2^635755+5191382Jon Grantham07/2023
25953*10^191152-7191153Robert Price08/2015
25962^634883-1865677191119Enzo Doria02/2016
25972^634801+1871957191095Enzo Doria05/2016
2598(77*10^191080+157)/9191081Robert Price05/2022
2599(35*10^191073+1)/9191074Serge Batalov07/2010
26009*10^191018-41191019Robert Price08/2020
26012^634470-59861190995Enzo Doria11/2015
26022^634368-29519190964Enzo Doria08/2015
2603(19*10^190935+11)/3190936Robert Price07/2023
26042^634188-350609190910Enzo Doria06/2015
2605(65*10^190899+493)/9190900Robert Price08/2021
2606(62*10^190795-413)/9190796Robert Price09/2021
2607(26*10^190789-131)/3190790Robert Price10/2019
2608(13*10^190732-61)/3190733Robert Price11/2018
26093*2^633524+5190711Jon Grantham07/2023
2610(7*10^190683+143)/3190684Robert Price03/2018
26112^633088-113879190579Enzo Doria10/2014
26122^633064+1874911190572Enzo Doria06/2016
26135*3^399402+2^399402190564Jon Grantham08/2023
2614(43*10^190547+83)/9190548Robert Price11/2018
261599*10^190543+7190545Robert Price05/2021
2616(299*10^190533+1)/3190535Robert Price04/2020
2617(1744*10^190519-1747)/3190522Robert Price12/2020
26182^632815-15190497Stefano Morozzi07/2022
26192^632795-351205190491Enzo Doria06/2015
262041171^41272+41272^41171190454Norbert Schneider05/2023
2621(16*10^190420-19)/3190421Robert Price02/2019
2622(43*10^190351+101)/9190352Robert Price11/2018
26232^632156+78391190298Enzo Doria06/2016
262497*10^190295-3190297Robert Price05/2020
26252^632082-1851971190276Enzo Doria08/2015
26262^632020+1880311190257Enzo Doria09/2016
2627(5*10^190242-77)/9190242Robert Price04/2021
26287*10^190210+13190211Robert Price03/2021
26292^631637-462373190142Enzo Doria08/2015
26302*10^190126-21190127Robert Price09/2020
2631(28*10^190105+191)/3190106Robert Price02/2020
26322*10^190093+33190094Robert Price11/2021
2633(68*10^190053-113)/9190054Robert Price03/2021
26342^631183+213413190006Enzo Doria09/2023
26352^631122-39251189987Enzo Doria08/2015
2636(26*10^189928-89)/9189929Robert Price06/2018
26372^630839-97189902Yves Minet07/2017
263899*10^189876-7189878Robert Price07/2020
263941147^41147+30^30189867Henri Lifchitz09/2024
26402^630359+1788953189757Enzo Doria05/2016
26412^630228+1871971189718Enzo Doria05/2016
26422^630108+781189682Lelio R Paula08/2013
26432^629870-1867811189610Enzo Doria04/2016
2644(359^74189-1)/358189558Alexander Zhirkov11/2017
26452^629326+2792929189447Enzo Doria02/2016
26464*10^189401+13189402Robert Price02/2021
2647(10^189385-61)/3189385Serge Batalov12/2014
26482^629036+1874011189359Enzo Doria06/2016
26492^628930+80779189327Enzo Doria07/2016
2650(134*10^189309-11)/3189311Robert Price01/2022
26519*10^189306-11189307Mischa Rodermond04/2023
26523^396740-396740^3189294Henri Lifchitz07/2024
26532^628582+1179439189223Enzo Doria06/2016
2654(44*10^188999-503)/9189000Robert Price12/2018
2655(16*10^188823+167)/3188824Robert Price06/2019
2656(10^188796+7)/4967/71933188788Alfred Reich08/2021
26572^627037-2785843188757Enzo Doria10/2015
2658(10^188566+7)/311640753181661188552Alfred Reich04/2022
2659(16*10^188457+161)/3188458Robert Price02/2019
2660L(901657)188436Renaud Lifchitz11/2008
2661(19*10^188375+137)/3188376Robert Price03/2022
26622^625651+74213188340Enzo Doria04/2016
26632^625584-460919188320Enzo Doria06/2015
2664(8*10^188308-71)/9188308Serge Batalov11/2022
26655^269399-3^269399-1188302Jon Grantham08/2023
2666(14*10^188218+139)/9188219Robert Price11/2021
266740760^40821-40821^40760188195Norbert Schneider07/2024
2668(10^188164+359)/9188164Serge Batalov12/2014
26692^624481-113611187988Enzo Doria08/2014
2670(2^624389+125582)/2187960Stefano Morozzi09/2019
2671(2^624389+166982)/2187960Stefano Morozzi09/2019
2672(2^624389+179886)/2187960Stefano Morozzi09/2019
2673(2^624387+64466)/2187959Stefano Morozzi09/2019
2674(2^624378+112990)/2187957Stefano Morozzi09/2019
2675(2^624380+161986)/2187957Stefano Morozzi09/2019
2677(2^624376+55762)/2187956Stefano Morozzi09/2019
2676(2^624377+169506)/2187956Stefano Morozzi09/2019
2678(2^624355+80178)/2187950Stefano Morozzi09/2019
2679(2^624351+61350)/2187949Stefano Morozzi09/2019
2680(2^624341+63462)/2187946Stefano Morozzi09/2019
2681(2^624344+135990)/2187946Stefano Morozzi09/2019
2682(2^624344+183898)/2187946Stefano Morozzi09/2019
2684(2^624340+126982)/2187945Stefano Morozzi09/2019
2683(2^624338+196110)/2187945Stefano Morozzi09/2019
2685(2^624337+105162)/2187944Stefano Morozzi09/2019
2686(2^624333+44594)/2187943Stefano Morozzi09/2019
2687(2^624321+88742)/2187940Stefano Morozzi09/2019
2688(2^624324+135178)/2187940Stefano Morozzi09/2019
2689(2^624317+14186)/2187938Stefano Morozzi09/2019
2690(2^624313+24450)/2187937Stefano Morozzi09/2019
2691(2^624309+184590)/2187936Stefano Morozzi09/2019
2693(2^624307+152658)/2187935Stefano Morozzi09/2019
2692(2^624307+185978)/2187935Stefano Morozzi09/2019
2694(2^624303+40814)/2187934Stefano Morozzi09/2019
2695(2^624304+99238)/2187934Stefano Morozzi09/2019
26962^624077-112723187866Enzo Doria07/2014
26972^624008+1874941187846Enzo Doria06/2016
26982^623870+78679187804Enzo Doria05/2016
26992^623714-114035187757Enzo Doria11/2014
27002^623651-1834251187738Enzo Doria07/2015
2701(7*10^187645+53)/3187646Robert Price05/2018
270221650^43269+43269^21650187591Norbert Schneider02/2023
27032^623146+1879609187586Enzo Doria09/2016
2704(401*10^187512+13)/9187514Robert Price09/2021
2705(5*10^187471+91)/3187472Robert Price04/2018
27062^622500+81931187392Enzo Doria08/2016
2707(13*10^187382-157)/9187383Robert Price05/2021
27082^622300-1861739187331Enzo Doria12/2015
2709(22*10^187317-91)/3187318Robert Price02/2022
2710(38*10^187281+349)/9187282Robert Price10/2018
27112^622052+76771187257Enzo Doria05/2016
27122^622005-24091187243Enzo Doria08/2013
27137*10^187205-57187206Robert Price06/2020
27142^621879-351787187205Enzo Doria07/2015
2715(5*10^187168-53)/3187169Robert Price09/2020
2716(23*10^187164-143)/3187165Robert Price12/2019
27172^621700+79411187151Enzo Doria06/2016
27182^621597+39187120Jon Grantham08/2023
2719(7*10^187101+131)/3187102Robert Price06/2020
2720(2*10^187062-71)/3187062Robert Price12/2017
2721V(1118570)187013Serge Batalov07/2024
27222^620929-113203186919Enzo Doria07/2014
272310^186842+168223186843Patrick De Geest07/2018
272410^186842-8001186842Robert Price03/2018
2725V(1117640)/13411681/26823361/575709775681/989889277441186814Serge Batalov07/2024
27262^620347-1777186744Lelio R Paula07/2013
2727(11*10^186659+133)/9186660Robert Price04/2022
272811^179143-4170186559Enzo Doria12/2012
2729(13^186535)%(10^186535)186535Henri Lifchitz05/2025
2730(5^266863+1)/6186529Paul Bourdelais07/2010
27312*10^186517+33186518Robert Price11/2021
27322^619297-2792353186427Enzo Doria02/2016
2733(49*10^186409+383)/9186410Robert Price04/2019
27342^618940-460139186320Enzo Doria06/2015
27352^618046+74179186051Enzo Doria04/2016
27363*10^186019+11186020Robert Price07/2018
2737(16*10^185978-19)/3185979Robert Price02/2019
2738(22*10^185950-7)/3185951Robert Price12/2022
27392*10^185930-3185931Robert Price07/2015
2740(82^97151+1)/83185928Paul Bourdelais10/2017
27414*10^185905+91185906Robert Price08/2018
2742(34*10^185902-601)/9185903Robert Price07/2022
2743(19*10^185873+131)/3185874Robert Price06/2020
2744(37*10^185811+377)/9185812Robert Price11/2018
27452^617250+9385185811Lelio R Paula07/2013
27462^617130+9185775Stefano Morozzi05/2021
274739^116749+2185756Robert Price04/2015
27482^616924-39719185713Enzo Doria09/2015
27492^616712+1867621185649Enzo Doria04/2016
2750(3^388897+2^388897)/5185551Jean-Louis Charton09/2011


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 21 2025 13:33 (Time in France)

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