PRP Records

Probable Primes Top 10000

(295158 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(16*10^185347+89)/3185348Robert Price03/2021
22522^615622+76639185321Enzo Doria05/2016
22532^615591+1879223185312Enzo Doria08/2016
22542^615587+217013185311Enzo Doria12/2023
22552^615503+1876643185285Enzo Doria07/2016
22565^265007-4^265007185232Jean-Louis Charton02/2013
2258(4*10^185221-91)/3185222Robert Price03/2018
2257(7*10^185221+131)/3185222Robert Price06/2020
2259(62*10^185216-413)/9185217Robert Price09/2021
2260(232*10^185180+17)/3185182Robert Price04/2021
226156*10^185139-3185141Robert Price03/2020
2262(28*10^185105+47)/3185106Robert Price02/2021
22632^614783-2790097185069Enzo Doria12/2015
22642^614745-29323185057Enzo Doria07/2015
2265(((((((((((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
2266(49*10^184993-67)/9184994Robert Price03/2019
2267(5*10^184954-191)/3184955Robert Price05/2021
2268(14*10^184950+211)/9184951Robert Price04/2018
22692^614360+215221184941Enzo Doria11/2023
22702^614315+81353184928Enzo Doria08/2016
22712^614294-1849961184921Enzo Doria08/2015
22722^614266+1877809184913Enzo Doria08/2016
2273(185*10^184878-11)/3184880Robert Price10/2020
227491*10^184867-9184869Robert Price06/2021
227539803^40170-40170^39803184779Norbert Schneider05/2024
2276(14789^44521-1)/(14789^211-1)184770Ryan Propper11/2023
2277(85*10^184768+77)/9184769Robert Price07/2022
22782^613715-1860727184747Enzo Doria11/2015
2279(4*10^184730+89)/3184731Robert Price08/2021
22802*10^184723+41184724Robert Price05/2018
2281(49*10^184703+293)/9184704Robert Price03/2021
22822^613487-349987184678Enzo Doria07/2015
2283(95^93377+1)/96184672Paul Bourdelais11/2017
228414^161089-161089^14184629Serge Batalov05/2016
228540008^40109-40109^40008184588Norbert Schneider05/2024
22862^613033-114621184542Enzo Doria05/2015
22873*2^612759+5184460Jon Grantham07/2023
22882^612587+213413184408Enzo Doria09/2023
2289(9^193247+1)/10184404Paul Bourdelais02/2010
22902^612424+212341184358Enzo Doria08/2023
22912^612341-1604809184334Enzo Doria05/2015
2292(11*10^184308-161)/3184309Robert Price11/2021
2293(2^611999-1)/18464214225958267477777390354183184199Dario Alpern06/2017
2294(14*10^184150+37)/3184151Robert Price12/2018
22952^611731-4837184150Yves Minet08/2018
22963*10^184124-7184125Robert Price08/2015
22972^611644+29371184124Enzo Doria02/2024
22989*10^184122-11184123Mischa Rodermond04/2023
22992^611628-24537184119Enzo Doria08/2013
23003*10^184110+13184111Robert Price07/2018
2301(14280^44521-1)/(14280^211-1)184097Ryan Propper11/2023
2302(194*10^184093+1)/3184095Robert Price01/2022
23032^611460+71881184068Enzo Doria04/2016
23044*10^184004-63184005Robert Price10/2018
23052^611111+84083183963Boyan Hu05/2024
23062^610982-1867301183924Enzo Doria03/2016
2307(10^183917+1)/11/9952852373183906Alfred Reich02/2024
23083*10^183872-49183873Robert Price07/2018
23092^610597+1178897183809Enzo Doria05/2016
2310(8*10^183773-269)/9183773Robert Price09/2021
2311(65*10^183768-29)/9183769Robert Price01/2021
2312(17*10^183764+31)/3183765Robert Price01/2019
2313(28*10^183760-1)/9183761Serge Batalov10/2014
23142^610401+1277183750Lelio R Paula07/2013
23152^610356-1849019183736Enzo Doria08/2015
2316(63^102103+1)/64183717Paul Bourdelais10/2017
231723*10^183710-7183712Robert Price02/2020
2318(2^610289+1)/(3*528882550291)183704Gord Palameta08/2018
2319(4*10^183659+149)/9183659Robert Price04/2018
2320(4*10^183657+41)/9183657Serge Batalov11/2022
23217*10^183596+39183597Robert Price01/2023
23222^609846-1834251183582Enzo Doria07/2015
232310^183546+1547323183547Patrick De Geest02/2021
232510^183546-800000001183546Robert Price09/2020
232410^183546-584297183546Patrick De Geest02/2021
23267*10^183511+39183512Robert Price01/2023
2327(23*10^183477-71)/3183478Robert Price07/2020
232811^176176-240183469Enzo Doria11/2012
2329(41^113749+1)/42183451Paul Bourdelais11/2017
23306*10^183429+53183430Robert Price05/2020
2331(28*10^183403+191)/3183404Robert Price02/2020
2332(101^91463+1)/102183320Paul Bourdelais11/2017
23332^608965-113989183317Enzo Doria10/2014
2334A005165(43592)183312Serge Batalov07/2017
2335(61*10^183294+119)/9183295Robert Price05/2019
23362^608814-461261183272Enzo Doria06/2015
2337(163*10^183227-1)/9183229Serge Batalov12/2014
23382^608541-608541^2183190Henri Lifchitz02/2018
23392^608293+143807183115Enzo Doria10/2016
23402^608164-462419183076Enzo Doria08/2015
23412^607950-1862303183012Enzo Doria12/2015
23425*3^383376+2^383376182918Jon Grantham08/2023
2343(46*10^182896+683)/9182897Robert Price03/2019
2344(2*10^182787+73)/3182787Robert Price09/2020
23452^607101+1871987182756Enzo Doria05/2016
23462^606869-69175182686Enzo Doria11/2015
23478*10^182671+71182672Robert Price05/2022
2348(23*10^182666-71)/3182667Robert Price07/2020
23493*10^182614-11182615Robert Price07/2018
23502^606560-357182593Enzo Doria05/2014
235166*10^182420+7182422Robert Price07/2020
23522^605687+1866983182330Enzo Doria03/2016
23532^605655-114445182321Enzo Doria02/2015
235494*10^182291-3182293Robert Price05/2020
2355(20^140053+1)/21182212Paul Bourdelais04/2010
2356(14*10^182177-221)/9182178Robert Price04/2018
23572^605174-112751182176Enzo Doria06/2014
2358(905^61609-1)/904182154Anonymous05/2024
23592^604761+1874507182052Enzo Doria06/2016
23602^604705+1871957182035Enzo Doria05/2016
2361(14*10^182000+229)/9182001Robert Price03/2018
2362(10^181996+41)/3181996Robert Price12/2017
2363(17*10^181979+91)/9181980Robert Price02/2022
2364(5*10^181950-101)/3181951Robert Price04/2018
23652^603915+75233181797Enzo Doria04/2016
236639470^39537+39537^39470181723Norbert Schneider12/2022
2367(10^181710+7)/563747/2019847181698Alfred Reich08/2021
23687*10^181594-57181595Robert Price06/2020
23698*10^181580+29181581Robert Price11/2021
2370(83*10^181544+61)/9181545Serge Batalov01/2023
2371(2*10^181457+7)/9181457Rytis Slatkevicius01/2023
23723*10^181445+23181446Robert Price03/2022
2373(194*10^181369-11)/3181371Robert Price09/2020
237411^174145-360181354Enzo Doria10/2012
23752^602351-396765181326Enzo Doria08/2013
23766*10^181306+17181307Robert Price04/2019
2377(353^71143-1)/352181254Anonymous04/2024
2378(286*10^181220-1)/3181222Robert Price11/2020
23792^601957-113833181208Enzo Doria09/2014
238066^99581-65^99581181193Robert Price09/2013
238110^181182+383973181183Patrick De Geest04/2016
238210^181182-21181182Serge Batalov12/2014
2383(797*10^181171-41)/9181173Robert Price04/2022
23842^601722+74209181137Enzo Doria08/2023
2385(5*10^181127-29)/3181128Robert Price03/2018
23862^601521-29143181076Enzo Doria07/2015
23872^601442-2797811181053Enzo Doria04/2016
238844*10^181029+3181031Robert Price04/2020
23895*10^180992-9180993Robert Price05/2015
239010^180979+79477180980Patrick De Geest04/2016
239110^180979+107739180980Patrick De Geest04/2016
239210^180979-11180979Serge Batalov12/2014
23932^601023-113851180926Enzo Doria10/2014
2394(23*10^180862-143)/3180863Robert Price12/2019
23953*10^180852+29180853Robert Price05/2018
2396(277*10^180782-7)/9180784Robert Price02/2022
23972^600412+29851180743Enzo Doria03/2024
2398(8*10^180725-629)/9180725Robert Price01/2022
2399(79*10^180710-1)/3180712Robert Price02/2020
24002^600300-1852559180709Enzo Doria08/2015
2401(2*10^180706-77)/3180706Robert Price02/2021
2402(10^180689+71)/9180689Serge Batalov07/2015
24032^600209+76487180681Enzo Doria05/2016
24042^599999+378461180618Norman Luhn09/2023
2405(8*10^180536-269)/9180536Robert Price09/2021
24062^599702-369885180529Enzo Doria11/2013
2407Tau(643^11688)180524Nik Lygeros / Olivier Rozier05/2015
2408(2951*29^123418-3)/4180490Curtis Bright05/2015
2409(29*10^180432-17)/3180433Robert Price09/2019
24104*10^180360+93180361Robert Price08/2018
24112^599035+219323180328Enzo Doria03/2024
24122^598942+80779180300Enzo Doria07/2016
2413(38*10^180296+403)/9180297Robert Price10/2018
2414(85*10^180241+77)/9180242Robert Price07/2022
24152^598591-1844797180194Enzo Doria06/2015
2416(100^90089+1)/101180176Paul Bourdelais08/2017
24172^598301+28517180107Enzo Doria01/2024
2418(29*10^180072+691)/9180073Robert Price08/2021
2419(59*10^180038+157)/9180039Robert Price12/2021
242095*10^180019-9180021Robert Price01/2022
24216*10^179970+91179971Robert Price05/2019
2422(4*10^179963-79)/3179964Robert Price02/2018
2423(403*10^179944-43)/9179946Robert Price06/2021
2424Gamma-Prime(179849)179849Eric W. Weisstein06/2011
24252^597424-1859729179843Enzo Doria11/2015
2426Phi(180683,10)179760Maksym Voznyy09/2015
2427(10^180683-1)*9/(10^643-1)/(10^281-1)179760Robert Price07/2016
2428(3^376657-2^376657)/22301107657179701Mike Oakes04/2017
2429(29*10^179697+223)/9179698Robert Price09/2018
24302^596884+73179680Stefano Morozzi04/2021
2431(11*10^179679+13)/3179680Robert Price03/2022
2432(68*10^179656+7)/3179658Robert Price01/2020
2433(10^179643+173)/3179643Robert Price05/2021
24342^596690-461261179622Enzo Doria07/2015
24352^596684-113939179620Enzo Doria10/2014
24362^596642+39179608Jon Grantham08/2023
24372*10^179602+63179603Robert Price05/2018
243832262^39815-39815^32262179514Frank Doornink02/2024
2439(25*10^179488-403)/9179489Robert Price01/2021
24407*10^179460+99179461Robert Price05/2021
24412^596127+74333179453Enzo Doria07/2023
24423^375887-112696179344Enzo Doria07/2014
24434*10^179265-71179266Robert Price12/2018
24442*10^179193+83179194Robert Price12/2021
24452^595144-1850429179157Enzo Doria08/2015
24462^595122-5179150Stefano Morozzi07/2022
24473*10^179138+89179139Robert Price10/2018
2448(52*10^179062-133)/9179063Robert Price09/2021
24492^594531+82253178972Enzo Doria09/2016
2450(664*10^178939-61)/9178941Robert Price09/2021
24512^594260-2787899178891Enzo Doria11/2015
2452(14*10^178822+67)/9178823Robert Price05/2022
2453(29*10^178732-119)/9178733Robert Price12/2021
24542^593631+101381178701Jorge Menendez04/2018
245510^178695+136719178696Patrick De Geest05/2016
245610^178695-71178695Serge Batalov12/2014
2457(2*10^178649-161)/3178649Robert Price12/2020
2458(691^62903-1)/690178609Michael Stocker05/2020
2459(2^148330+1)^4-2178608Cletus Emmanuel12/2003
24602^593242+28309178584Enzo Doria01/2024
24612^593222-14145178578Jorge Menendez10/2017
24627*10^178566+33178567Robert Price06/2020
24632^593178+1867219178565Enzo Doria03/2016
24642^593152+22441178557Enzo Doria09/2023
2465(38*10^178456+151)/9178457Robert Price03/2022
2466(302*10^178369+13)/9178371Robert Price02/2020
2467(26*10^178296-113)/3178297Robert Price06/2020
2468(18^142031-1)/17178287Paul Bourdelais03/2010
2469(13*10^178233+137)/3178234Robert Price06/2021
2470(5*10^178206+91)/3178207Robert Price04/2018
24712^591872-291929178172Enzo Doria07/2015
24722^591682-286871178115Enzo Doria07/2015
2473(7^210761-5^210761)/2178114Jon Grantham08/2023
24744*10^178091+9178092Robert Price05/2015
2475410747#+478483178007Makoto Morimoto02/2016
24763*10^177872+73177873Robert Price08/2018
24772^590762-396765177838Enzo Doria08/2013
2478(136*10^177754-1)/9177756Serge Batalov12/2014
2479ReverseConsecutiveIntegerPrime(37765)177719Eric W. Weisstein04/2010
2480Smr(37765)177719Eric W. Weisstein12/2021
2481(266*10^177577-11)/3177579Robert Price04/2020
2482(11*10^177466-113)/3177467Robert Price10/2018
24833*10^177373-97177374Robert Price07/2018
24842^589204+1881151177369Enzo Doria11/2016
24852^589132-69479177347Enzo Doria01/2016
2486(101*10^177302-17)/3177304Robert Price02/2020
24872^588912-113519177281Enzo Doria08/2014
2488(682*10^177266-7)/9177268Robert Price08/2021
248915^150706+2177245Robert Price06/2015
2490(31208^39601-1)/(31208^199-1)177084Ryan Propper11/2023
24912^588194-1861001177065Enzo Doria11/2015
24925*10^177016-37177017Robert Price11/2021
2493fibonacci(846926)-4176997Jon Grantham08/2023
2494(23*10^176964-47)/3176965Robert Price09/2019
249520530^41031+41031^20530176942Norbert Schneider07/2022
2496(19*10^176932+521)/9176933Robert Price05/2018
2497(8*10^176908+43)/3176909Robert Price06/2018
2498(85*10^176900+203)/9176901Robert Price09/2020
24992^587560-113699176874Enzo Doria09/2014
250020596^40995+40995^20596176844Norbert Schneider07/2022


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 27 2024 13:30 (Time in France)

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