PRP Records

Probable Primes Top 10000

(295148 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 ?
2251(62*10^185216-413)/9185217Robert Price09/2021
2252(232*10^185180+17)/3185182Robert Price04/2021
225356*10^185139-3185141Robert Price03/2020
2254(28*10^185105+47)/3185106Robert Price02/2021
22552^614783-2790097185069Enzo Doria12/2015
22562^614745-29323185057Enzo Doria07/2015
2257(((((((((((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
2258(49*10^184993-67)/9184994Robert Price03/2019
2259(5*10^184954-191)/3184955Robert Price05/2021
2260(14*10^184950+211)/9184951Robert Price04/2018
22612^614360+215221184941Enzo Doria11/2023
22622^614315+81353184928Enzo Doria08/2016
22632^614294-1849961184921Enzo Doria08/2015
22642^614266+1877809184913Enzo Doria08/2016
2265(185*10^184878-11)/3184880Robert Price10/2020
226691*10^184867-9184869Robert Price06/2021
226739803^40170-40170^39803184779Norbert Schneider05/2024
2268(14789^44521-1)/(14789^211-1)184770Ryan Propper11/2023
2269(85*10^184768+77)/9184769Robert Price07/2022
22702^613715-1860727184747Enzo Doria11/2015
2271(4*10^184730+89)/3184731Robert Price08/2021
22722*10^184723+41184724Robert Price05/2018
2273(49*10^184703+293)/9184704Robert Price03/2021
22742^613487-349987184678Enzo Doria07/2015
2275(95^93377+1)/96184672Paul Bourdelais11/2017
227614^161089-161089^14184629Serge Batalov05/2016
227740008^40109-40109^40008184588Norbert Schneider05/2024
22782^613033-114621184542Enzo Doria05/2015
22793*2^612759+5184460Jon Grantham07/2023
22802^612587+213413184408Enzo Doria09/2023
2281(9^193247+1)/10184404Paul Bourdelais02/2010
22822^612424+212341184358Enzo Doria08/2023
22832^612341-1604809184334Enzo Doria05/2015
2284(11*10^184308-161)/3184309Robert Price11/2021
2285(2^611999-1)/18464214225958267477777390354183184199Dario Alpern06/2017
2286(14*10^184150+37)/3184151Robert Price12/2018
22872^611731-4837184150Yves Minet08/2018
22883*10^184124-7184125Robert Price08/2015
22892^611644+29371184124Enzo Doria02/2024
22909*10^184122-11184123Mischa Rodermond04/2023
22912^611628-24537184119Enzo Doria08/2013
22923*10^184110+13184111Robert Price07/2018
2293(14280^44521-1)/(14280^211-1)184097Ryan Propper11/2023
2294(194*10^184093+1)/3184095Robert Price01/2022
22952^611460+71881184068Enzo Doria04/2016
22964*10^184004-63184005Robert Price10/2018
22972^611111+84083183963Boyan Hu05/2024
22982^610982-1867301183924Enzo Doria03/2016
2299(10^183917+1)/11/9952852373183906Alfred Reich02/2024
23003*10^183872-49183873Robert Price07/2018
23012^610597+1178897183809Enzo Doria05/2016
2302(8*10^183773-269)/9183773Robert Price09/2021
2303(65*10^183768-29)/9183769Robert Price01/2021
2304(17*10^183764+31)/3183765Robert Price01/2019
2305(28*10^183760-1)/9183761Serge Batalov10/2014
23062^610401+1277183750Lelio R Paula07/2013
23072^610356-1849019183736Enzo Doria08/2015
2308(63^102103+1)/64183717Paul Bourdelais10/2017
230923*10^183710-7183712Robert Price02/2020
2310(2^610289+1)/(3*528882550291)183704Gord Palameta08/2018
2311(4*10^183659+149)/9183659Robert Price04/2018
2312(4*10^183657+41)/9183657Serge Batalov11/2022
23137*10^183596+39183597Robert Price01/2023
23142^609846-1834251183582Enzo Doria07/2015
231510^183546+1547323183547Patrick De Geest02/2021
231710^183546-800000001183546Robert Price09/2020
231610^183546-584297183546Patrick De Geest02/2021
23187*10^183511+39183512Robert Price01/2023
2319(23*10^183477-71)/3183478Robert Price07/2020
232011^176176-240183469Enzo Doria11/2012
2321(41^113749+1)/42183451Paul Bourdelais11/2017
23226*10^183429+53183430Robert Price05/2020
2323(28*10^183403+191)/3183404Robert Price02/2020
2324(101^91463+1)/102183320Paul Bourdelais11/2017
23252^608965-113989183317Enzo Doria10/2014
2326A005165(43592)183312Serge Batalov07/2017
2327(61*10^183294+119)/9183295Robert Price05/2019
23282^608814-461261183272Enzo Doria06/2015
2329(163*10^183227-1)/9183229Serge Batalov12/2014
23302^608541-608541^2183190Henri Lifchitz02/2018
23312^608293+143807183115Enzo Doria10/2016
23322^608164-462419183076Enzo Doria08/2015
23332^607950-1862303183012Enzo Doria12/2015
23345*3^383376+2^383376182918Jon Grantham08/2023
2335(46*10^182896+683)/9182897Robert Price03/2019
2336(2*10^182787+73)/3182787Robert Price09/2020
23372^607101+1871987182756Enzo Doria05/2016
23382^606869-69175182686Enzo Doria11/2015
23398*10^182671+71182672Robert Price05/2022
2340(23*10^182666-71)/3182667Robert Price07/2020
23413*10^182614-11182615Robert Price07/2018
23422^606560-357182593Enzo Doria05/2014
234366*10^182420+7182422Robert Price07/2020
23442^605687+1866983182330Enzo Doria03/2016
23452^605655-114445182321Enzo Doria02/2015
234694*10^182291-3182293Robert Price05/2020
2347(20^140053+1)/21182212Paul Bourdelais04/2010
2348(14*10^182177-221)/9182178Robert Price04/2018
23492^605174-112751182176Enzo Doria06/2014
2350(905^61609-1)/904182154Anonymous05/2024
23512^604761+1874507182052Enzo Doria06/2016
23522^604705+1871957182035Enzo Doria05/2016
2353(14*10^182000+229)/9182001Robert Price03/2018
2354(10^181996+41)/3181996Robert Price12/2017
2355(17*10^181979+91)/9181980Robert Price02/2022
2356(5*10^181950-101)/3181951Robert Price04/2018
23572^603915+75233181797Enzo Doria04/2016
235839470^39537+39537^39470181723Norbert Schneider12/2022
2359(10^181710+7)/563747/2019847181698Alfred Reich08/2021
23607*10^181594-57181595Robert Price06/2020
23618*10^181580+29181581Robert Price11/2021
2362(83*10^181544+61)/9181545Serge Batalov01/2023
2363(2*10^181457+7)/9181457Rytis Slatkevicius01/2023
23643*10^181445+23181446Robert Price03/2022
2365(194*10^181369-11)/3181371Robert Price09/2020
236611^174145-360181354Enzo Doria10/2012
23672^602351-396765181326Enzo Doria08/2013
23686*10^181306+17181307Robert Price04/2019
2369(353^71143-1)/352181254Anonymous04/2024
2370(286*10^181220-1)/3181222Robert Price11/2020
23712^601957-113833181208Enzo Doria09/2014
237266^99581-65^99581181193Robert Price09/2013
237310^181182+383973181183Patrick De Geest04/2016
237410^181182-21181182Serge Batalov12/2014
2375(797*10^181171-41)/9181173Robert Price04/2022
23762^601722+74209181137Enzo Doria08/2023
2377(5*10^181127-29)/3181128Robert Price03/2018
23782^601521-29143181076Enzo Doria07/2015
23792^601442-2797811181053Enzo Doria04/2016
238044*10^181029+3181031Robert Price04/2020
23815*10^180992-9180993Robert Price05/2015
238210^180979+79477180980Patrick De Geest04/2016
238310^180979+107739180980Patrick De Geest04/2016
238410^180979-11180979Serge Batalov12/2014
23852^601023-113851180926Enzo Doria10/2014
2386(23*10^180862-143)/3180863Robert Price12/2019
23873*10^180852+29180853Robert Price05/2018
2388(277*10^180782-7)/9180784Robert Price02/2022
23892^600412+29851180743Enzo Doria03/2024
2390(8*10^180725-629)/9180725Robert Price01/2022
2391(79*10^180710-1)/3180712Robert Price02/2020
23922^600300-1852559180709Enzo Doria08/2015
2393(2*10^180706-77)/3180706Robert Price02/2021
2394(10^180689+71)/9180689Serge Batalov07/2015
23952^600209+76487180681Enzo Doria05/2016
23962^599999+378461180618Norman Luhn09/2023
2397(8*10^180536-269)/9180536Robert Price09/2021
23982^599702-369885180529Enzo Doria11/2013
2399Tau(643^11688)180524Nik Lygeros / Olivier Rozier05/2015
2400(2951*29^123418-3)/4180490Curtis Bright05/2015
2401(29*10^180432-17)/3180433Robert Price09/2019
24024*10^180360+93180361Robert Price08/2018
24032^599035+219323180328Enzo Doria03/2024
24042^598942+80779180300Enzo Doria07/2016
2405(38*10^180296+403)/9180297Robert Price10/2018
2406(85*10^180241+77)/9180242Robert Price07/2022
24072^598591-1844797180194Enzo Doria06/2015
2408(100^90089+1)/101180176Paul Bourdelais08/2017
24092^598301+28517180107Enzo Doria01/2024
2410(29*10^180072+691)/9180073Robert Price08/2021
2411(59*10^180038+157)/9180039Robert Price12/2021
241295*10^180019-9180021Robert Price01/2022
24136*10^179970+91179971Robert Price05/2019
2414(4*10^179963-79)/3179964Robert Price02/2018
2415(403*10^179944-43)/9179946Robert Price06/2021
2416Gamma-Prime(179849)179849Eric W. Weisstein06/2011
24172^597424-1859729179843Enzo Doria11/2015
2418Phi(180683,10)179760Maksym Voznyy09/2015
2419(10^180683-1)*9/(10^643-1)/(10^281-1)179760Robert Price07/2016
2420(3^376657-2^376657)/22301107657179701Mike Oakes04/2017
2421(29*10^179697+223)/9179698Robert Price09/2018
24222^596884+73179680Stefano Morozzi04/2021
2423(11*10^179679+13)/3179680Robert Price03/2022
2424(68*10^179656+7)/3179658Robert Price01/2020
2425(10^179643+173)/3179643Robert Price05/2021
24262^596690-461261179622Enzo Doria07/2015
24272^596684-113939179620Enzo Doria10/2014
24282^596642+39179608Jon Grantham08/2023
24292*10^179602+63179603Robert Price05/2018
243032262^39815-39815^32262179514Frank Doornink02/2024
2431(25*10^179488-403)/9179489Robert Price01/2021
24327*10^179460+99179461Robert Price05/2021
24332^596127+74333179453Enzo Doria07/2023
24343^375887-112696179344Enzo Doria07/2014
24354*10^179265-71179266Robert Price12/2018
24362*10^179193+83179194Robert Price12/2021
24372^595144-1850429179157Enzo Doria08/2015
24382^595122-5179150Stefano Morozzi07/2022
24393*10^179138+89179139Robert Price10/2018
2440(52*10^179062-133)/9179063Robert Price09/2021
24412^594531+82253178972Enzo Doria09/2016
2442(664*10^178939-61)/9178941Robert Price09/2021
24432^594260-2787899178891Enzo Doria11/2015
2444(14*10^178822+67)/9178823Robert Price05/2022
2445(29*10^178732-119)/9178733Robert Price12/2021
24462^593631+101381178701Jorge Menendez04/2018
244710^178695+136719178696Patrick De Geest05/2016
244810^178695-71178695Serge Batalov12/2014
2449(2*10^178649-161)/3178649Robert Price12/2020
2450(691^62903-1)/690178609Michael Stocker05/2020
2451(2^148330+1)^4-2178608Cletus Emmanuel12/2003
24522^593242+28309178584Enzo Doria01/2024
24532^593222-14145178578Jorge Menendez10/2017
24547*10^178566+33178567Robert Price06/2020
24552^593178+1867219178565Enzo Doria03/2016
24562^593152+22441178557Enzo Doria09/2023
2457(38*10^178456+151)/9178457Robert Price03/2022
2458(302*10^178369+13)/9178371Robert Price02/2020
2459(26*10^178296-113)/3178297Robert Price06/2020
2460(18^142031-1)/17178287Paul Bourdelais03/2010
2461(13*10^178233+137)/3178234Robert Price06/2021
2462(5*10^178206+91)/3178207Robert Price04/2018
24632^591872-291929178172Enzo Doria07/2015
24642^591682-286871178115Enzo Doria07/2015
2465(7^210761-5^210761)/2178114Jon Grantham08/2023
24664*10^178091+9178092Robert Price05/2015
2467410747#+478483178007Makoto Morimoto02/2016
24683*10^177872+73177873Robert Price08/2018
24692^590762-396765177838Enzo Doria08/2013
2470(136*10^177754-1)/9177756Serge Batalov12/2014
2471ReverseConsecutiveIntegerPrime(37765)177719Eric W. Weisstein04/2010
2472Smr(37765)177719Eric W. Weisstein12/2021
2473(266*10^177577-11)/3177579Robert Price04/2020
2474(11*10^177466-113)/3177467Robert Price10/2018
24753*10^177373-97177374Robert Price07/2018
24762^589204+1881151177369Enzo Doria11/2016
24772^589132-69479177347Enzo Doria01/2016
2478(101*10^177302-17)/3177304Robert Price02/2020
24792^588912-113519177281Enzo Doria08/2014
2480(682*10^177266-7)/9177268Robert Price08/2021
248115^150706+2177245Robert Price06/2015
2482(31208^39601-1)/(31208^199-1)177084Ryan Propper11/2023
24832^588194-1861001177065Enzo Doria11/2015
24845*10^177016-37177017Robert Price11/2021
2485fibonacci(846926)-4176997Jon Grantham08/2023
2486(23*10^176964-47)/3176965Robert Price09/2019
248720530^41031+41031^20530176942Norbert Schneider07/2022
2488(19*10^176932+521)/9176933Robert Price05/2018
2489(8*10^176908+43)/3176909Robert Price06/2018
2490(85*10^176900+203)/9176901Robert Price09/2020
24912^587560-113699176874Enzo Doria09/2014
249220596^40995+40995^20596176844Norbert Schneider07/2022
2493(101*10^176815-17)/3176817Robert Price02/2020
2494(25*10^176715-37)/3176716Robert Price10/2019
24955^252763-12862176674Enzo Doria05/2014
249638442^38531+38531^38442176658Norbert Schneider09/2022
24972^586829+23961176654Enzo Doria10/2023
24982^586804+81721176646Enzo Doria08/2016
2499(10^176584+77)/3176584Robert Price01/2018
25002^586570+1874419176576Enzo Doria06/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 20 2024 09:22 (Time in France)

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