PRP Records

Probable Primes Top 10000

(301081 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 ?
25012^632156+78391190298Enzo Doria06/2016
250297*10^190295-3190297Robert Price05/2020
25032^632082-1851971190276Enzo Doria08/2015
25042^632020+1880311190257Enzo Doria09/2016
2505(5*10^190242-77)/9190242Robert Price04/2021
25067*10^190210+13190211Robert Price03/2021
25072^631637-462373190142Enzo Doria08/2015
25082*10^190126-21190127Robert Price09/2020
2509(28*10^190105+191)/3190106Robert Price02/2020
25102*10^190093+33190094Robert Price11/2021
2511(68*10^190053-113)/9190054Robert Price03/2021
25122^631183+213413190006Enzo Doria09/2023
25132^631122-39251189987Enzo Doria08/2015
2514(26*10^189928-89)/9189929Robert Price06/2018
25152^630839-97189902Yves Minet07/2017
251699*10^189876-7189878Robert Price07/2020
251741147^41147+30^30189867Henri Lifchitz09/2024
25182^630359+1788953189757Enzo Doria05/2016
25192^630228+1871971189718Enzo Doria05/2016
25202^630108+781189682Lelio R Paula08/2013
25212^629870-1867811189610Enzo Doria04/2016
2522(359^74189-1)/358189558Alexander Zhirkov11/2017
25232^629326+2792929189447Enzo Doria02/2016
25244*10^189401+13189402Robert Price02/2021
2525(10^189385-61)/3189385Serge Batalov12/2014
25262^629036+1874011189359Enzo Doria06/2016
25272^628930+80779189327Enzo Doria07/2016
2528(134*10^189309-11)/3189311Robert Price01/2022
25299*10^189306-11189307Mischa Rodermond04/2023
25303^396740-396740^3189294Henri Lifchitz07/2024
25312^628582+1179439189223Enzo Doria06/2016
2532(44*10^188999-503)/9189000Robert Price12/2018
2533(16*10^188823+167)/3188824Robert Price06/2019
2534(10^188796+7)/4967/71933188788Alfred Reich08/2021
25352^627037-2785843188757Enzo Doria10/2015
2536(10^188566+7)/311640753181661188552Alfred Reich04/2022
2537(16*10^188457+161)/3188458Robert Price02/2019
2538L(901657)188436Renaud Lifchitz11/2008
2539(19*10^188375+137)/3188376Robert Price03/2022
25402^625651+74213188340Enzo Doria04/2016
25412^625584-460919188320Enzo Doria06/2015
2542(8*10^188308-71)/9188308Serge Batalov11/2022
25435^269399-3^269399-1188302Jon Grantham08/2023
2544(14*10^188218+139)/9188219Robert Price11/2021
254540760^40821-40821^40760188195Norbert Schneider07/2024
2546(10^188164+359)/9188164Serge Batalov12/2014
25472^624481-113611187988Enzo Doria08/2014
2548(2^624389+125582)/2187960Stefano Morozzi09/2019
2549(2^624389+166982)/2187960Stefano Morozzi09/2019
2550(2^624389+179886)/2187960Stefano Morozzi09/2019
2551(2^624387+64466)/2187959Stefano Morozzi09/2019
2552(2^624378+112990)/2187957Stefano Morozzi09/2019
2553(2^624380+161986)/2187957Stefano Morozzi09/2019
2555(2^624376+55762)/2187956Stefano Morozzi09/2019
2554(2^624377+169506)/2187956Stefano Morozzi09/2019
2556(2^624355+80178)/2187950Stefano Morozzi09/2019
2557(2^624351+61350)/2187949Stefano Morozzi09/2019
2558(2^624341+63462)/2187946Stefano Morozzi09/2019
2559(2^624344+135990)/2187946Stefano Morozzi09/2019
2560(2^624344+183898)/2187946Stefano Morozzi09/2019
2562(2^624340+126982)/2187945Stefano Morozzi09/2019
2561(2^624338+196110)/2187945Stefano Morozzi09/2019
2563(2^624337+105162)/2187944Stefano Morozzi09/2019
2564(2^624333+44594)/2187943Stefano Morozzi09/2019
2565(2^624321+88742)/2187940Stefano Morozzi09/2019
2566(2^624324+135178)/2187940Stefano Morozzi09/2019
2567(2^624317+14186)/2187938Stefano Morozzi09/2019
2568(2^624313+24450)/2187937Stefano Morozzi09/2019
2569(2^624309+184590)/2187936Stefano Morozzi09/2019
2571(2^624307+152658)/2187935Stefano Morozzi09/2019
2570(2^624307+185978)/2187935Stefano Morozzi09/2019
2572(2^624303+40814)/2187934Stefano Morozzi09/2019
2573(2^624304+99238)/2187934Stefano Morozzi09/2019
25742^624077-112723187866Enzo Doria07/2014
25752^624008+1874941187846Enzo Doria06/2016
25762^623870+78679187804Enzo Doria05/2016
25772^623714-114035187757Enzo Doria11/2014
25782^623651-1834251187738Enzo Doria07/2015
2579(7*10^187645+53)/3187646Robert Price05/2018
258021650^43269+43269^21650187591Norbert Schneider02/2023
25812^623146+1879609187586Enzo Doria09/2016
2582(401*10^187512+13)/9187514Robert Price09/2021
2583(5*10^187471+91)/3187472Robert Price04/2018
25842^622500+81931187392Enzo Doria08/2016
2585(13*10^187382-157)/9187383Robert Price05/2021
25862^622300-1861739187331Enzo Doria12/2015
2587(22*10^187317-91)/3187318Robert Price02/2022
2588(38*10^187281+349)/9187282Robert Price10/2018
25892^622052+76771187257Enzo Doria05/2016
25902^622005-24091187243Enzo Doria08/2013
25917*10^187205-57187206Robert Price06/2020
25922^621879-351787187205Enzo Doria07/2015
2593(5*10^187168-53)/3187169Robert Price09/2020
2594(23*10^187164-143)/3187165Robert Price12/2019
25952^621700+79411187151Enzo Doria06/2016
25962^621597+39187120Jon Grantham08/2023
2597(7*10^187101+131)/3187102Robert Price06/2020
2598(2*10^187062-71)/3187062Robert Price12/2017
2599V(1118570)187013Serge Batalov07/2024
26002^620929-113203186919Enzo Doria07/2014
260110^186842+168223186843Patrick De Geest07/2018
260210^186842-8001186842Robert Price03/2018
2603V(1117640)/13411681/26823361/575709775681/989889277441186814Serge Batalov07/2024
26042^620347-1777186744Lelio R Paula07/2013
2605(11*10^186659+133)/9186660Robert Price04/2022
260611^179143-4170186559Enzo Doria12/2012
2607(5^266863+1)/6186529Paul Bourdelais07/2010
26082*10^186517+33186518Robert Price11/2021
26092^619297-2792353186427Enzo Doria02/2016
2610(49*10^186409+383)/9186410Robert Price04/2019
26112^618940-460139186320Enzo Doria06/2015
26122^618046+74179186051Enzo Doria04/2016
26133*10^186019+11186020Robert Price07/2018
2614(16*10^185978-19)/3185979Robert Price02/2019
2615(22*10^185950-7)/3185951Robert Price12/2022
26162*10^185930-3185931Robert Price07/2015
2617(82^97151+1)/83185928Paul Bourdelais10/2017
26184*10^185905+91185906Robert Price08/2018
2619(34*10^185902-601)/9185903Robert Price07/2022
2620(19*10^185873+131)/3185874Robert Price06/2020
2621(37*10^185811+377)/9185812Robert Price11/2018
26222^617250+9385185811Lelio R Paula07/2013
26232^617130+9185775Stefano Morozzi05/2021
262439^116749+2185756Robert Price04/2015
26252^616924-39719185713Enzo Doria09/2015
26262^616712+1867621185649Enzo Doria04/2016
2627(3^388897+2^388897)/5185551Jean-Louis Charton09/2011
26288*10^185529-67185530Robert Price08/2019
2629(5*10^185520-11)/3185521Tyler Busby02/2023
26305*2^616124+3185473Jon Grantham07/2023
26312^615916+26791185410Enzo Doria12/2023
26324*10^185355+9185356Robert Price05/2015
2633(16*10^185347+89)/3185348Robert Price03/2021
263440247^40247-56^56185327Henri Lifchitz08/2024
26352^615622+76639185321Enzo Doria05/2016
26362^615591+1879223185312Enzo Doria08/2016
26372^615587+217013185311Enzo Doria12/2023
26382^615503+1876643185285Enzo Doria07/2016
26395^265007-4^265007185232Jean-Louis Charton02/2013
2640(4*10^185221-91)/3185222Robert Price03/2018
2641(7*10^185221+131)/3185222Robert Price06/2020
2642(62*10^185216-413)/9185217Robert Price09/2021
2643(232*10^185180+17)/3185182Robert Price04/2021
264456*10^185139-3185141Robert Price03/2020
2645(28*10^185105+47)/3185106Robert Price02/2021
26462^614783-2790097185069Enzo Doria12/2015
26472^614745-29323185057Enzo Doria07/2015
2648(((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840185052Serge Batalov07/2013
2649(49*10^184993-67)/9184994Robert Price03/2019
2650(5*10^184954-191)/3184955Robert Price05/2021
2651(14*10^184950+211)/9184951Robert Price04/2018
26522^614360+215221184941Enzo Doria11/2023
26532^614315+81353184928Enzo Doria08/2016
26542^614294-1849961184921Enzo Doria08/2015
26552^614266+1877809184913Enzo Doria08/2016
2656(185*10^184878-11)/3184880Robert Price10/2020
265791*10^184867-9184869Robert Price06/2021
265839803^40170-40170^39803184779Norbert Schneider05/2024
2659(14789^44521-1)/(14789^211-1)184770Ryan Propper11/2023
2660(85*10^184768+77)/9184769Robert Price07/2022
26612^613715-1860727184747Enzo Doria11/2015
2662(4*10^184730+89)/3184731Robert Price08/2021
26632*10^184723+41184724Robert Price05/2018
2664(49*10^184703+293)/9184704Robert Price03/2021
26652^613487-349987184678Enzo Doria07/2015
2666(95^93377+1)/96184672Paul Bourdelais11/2017
266714^161089-161089^14184629Serge Batalov05/2016
266840008^40109-40109^40008184588Norbert Schneider05/2024
26692^613033-114621184542Enzo Doria05/2015
26703*2^612759+5184460Jon Grantham07/2023
26712^612587+213413184408Enzo Doria09/2023
2672(9^193247+1)/10184404Paul Bourdelais02/2010
26732^612424+212341184358Enzo Doria08/2023
26742^612341-1604809184334Enzo Doria05/2015
2675(11*10^184308-161)/3184309Robert Price11/2021
2676(2^611999-1)/18464214225958267477777390354183184199Dario Alpern06/2017
2677(14*10^184150+37)/3184151Robert Price12/2018
26782^611731-4837184150Yves Minet08/2018
26793*10^184124-7184125Robert Price08/2015
26802^611644+29371184124Enzo Doria02/2024
26819*10^184122-11184123Mischa Rodermond04/2023
26822^611628-24537184119Enzo Doria08/2013
26833*10^184110+13184111Robert Price07/2018
2684(14280^44521-1)/(14280^211-1)184097Ryan Propper11/2023
2685(194*10^184093+1)/3184095Robert Price01/2022
26862^611460+71881184068Enzo Doria04/2016
26874*10^184004-63184005Robert Price10/2018
26882^611111+84083183963Boyan Hu05/2024
26892^610982-1867301183924Enzo Doria03/2016
2690(10^183917+1)/11/9952852373183906Alfred Reich02/2024
26913*10^183872-49183873Robert Price07/2018
26922^610597+1178897183809Enzo Doria05/2016
2693(8*10^183773-269)/9183773Robert Price09/2021
2694(65*10^183768-29)/9183769Robert Price01/2021
2695(17*10^183764+31)/3183765Robert Price01/2019
2696(28*10^183760-1)/9183761Serge Batalov10/2014
26972^610401+1277183750Lelio R Paula07/2013
26982^610356-1849019183736Enzo Doria08/2015
2699(63^102103+1)/64183717Paul Bourdelais10/2017
270023*10^183710-7183712Robert Price02/2020
2701(2^610289+1)/(3*528882550291)183704Gord Palameta08/2018
2702(4*10^183659+149)/9183659Robert Price04/2018
2703(4*10^183657+41)/9183657Serge Batalov11/2022
27047*10^183596+39183597Robert Price01/2023
27052^609846-1834251183582Enzo Doria07/2015
270610^183546+1547323183547Patrick De Geest02/2021
270810^183546-800000001183546Robert Price09/2020
270710^183546-584297183546Patrick De Geest02/2021
27097*10^183511+39183512Robert Price01/2023
2710(23*10^183477-71)/3183478Robert Price07/2020
271111^176176-240183469Enzo Doria11/2012
2712(41^113749+1)/42183451Paul Bourdelais11/2017
27136*10^183429+53183430Robert Price05/2020
2714(28*10^183403+191)/3183404Robert Price02/2020
2715U(1096855)183383Serge Batalov07/2024
2716(101^91463+1)/102183320Paul Bourdelais11/2017
27172^608965-113989183317Enzo Doria10/2014
2718A005165(43592)183312Serge Batalov07/2017
2719(61*10^183294+119)/9183295Robert Price05/2019
27202^608814-461261183272Enzo Doria06/2015
2721(163*10^183227-1)/9183229Serge Batalov12/2014
27222^608541-608541^2183190Henri Lifchitz02/2018
27232^608293+143807183115Enzo Doria10/2016
27242^608164-462419183076Enzo Doria08/2015
27252^607950-1862303183012Enzo Doria12/2015
27265*3^383376+2^383376182918Jon Grantham08/2023
2727(46*10^182896+683)/9182897Robert Price03/2019
2728(2*10^182787+73)/3182787Robert Price09/2020
27292^607101+1871987182756Enzo Doria05/2016
27302^606869-69175182686Enzo Doria11/2015
27318*10^182671+71182672Robert Price05/2022
2732(23*10^182666-71)/3182667Robert Price07/2020
27333*10^182614-11182615Robert Price07/2018
27342^606560-357182593Enzo Doria05/2014
273566*10^182420+7182422Robert Price07/2020
27362^605687+1866983182330Enzo Doria03/2016
27372^605655-114445182321Enzo Doria02/2015
273894*10^182291-3182293Robert Price05/2020
2739(20^140053+1)/21182212Paul Bourdelais04/2010
2740(14*10^182177-221)/9182178Robert Price04/2018
27412^605174-112751182176Enzo Doria06/2014
2742(905^61609-1)/904182154Anonymous05/2024
27432^604761+1874507182052Enzo Doria06/2016
27442^604705+1871957182035Enzo Doria05/2016
2745(14*10^182000+229)/9182001Robert Price03/2018
2746(10^181996+41)/3181996Robert Price12/2017
2747(17*10^181979+91)/9181980Robert Price02/2022
2748(10^181960+3)/7181960Jinyuan Wang11/2024
2749(5*10^181950-101)/3181951Robert Price04/2018
27502^603915+75233181797Enzo Doria04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 23 2025 20:30 (Time in France)

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