PRP Records

Probable Primes Top 10000

(294687 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(4*10^183657+41)/9183657Serge Batalov11/2022
22527*10^183596+39183597Robert Price01/2023
22532^609846-1834251183582Enzo Doria07/2015
225410^183546+1547323183547Patrick De Geest02/2021
225610^183546-800000001183546Robert Price09/2020
225510^183546-584297183546Patrick De Geest02/2021
22577*10^183511+39183512Robert Price01/2023
2258(23*10^183477-71)/3183478Robert Price07/2020
225911^176176-240183469Enzo Doria11/2012
2260(41^113749+1)/42183451Paul Bourdelais11/2017
22616*10^183429+53183430Robert Price05/2020
2262(28*10^183403+191)/3183404Robert Price02/2020
2263(101^91463+1)/102183320Paul Bourdelais11/2017
22642^608965-113989183317Enzo Doria10/2014
2265A005165(43592)183312Serge Batalov07/2017
2266(61*10^183294+119)/9183295Robert Price05/2019
22672^608814-461261183272Enzo Doria06/2015
2268(163*10^183227-1)/9183229Serge Batalov12/2014
22692^608541-608541^2183190Henri Lifchitz02/2018
22702^608293+143807183115Enzo Doria10/2016
22712^608164-462419183076Enzo Doria08/2015
22722^607950-1862303183012Enzo Doria12/2015
22735*3^383376+2^383376182918Jon Grantham08/2023
2274(46*10^182896+683)/9182897Robert Price03/2019
2275(2*10^182787+73)/3182787Robert Price09/2020
22762^607101+1871987182756Enzo Doria05/2016
22772^606869-69175182686Enzo Doria11/2015
22788*10^182671+71182672Robert Price05/2022
2279(23*10^182666-71)/3182667Robert Price07/2020
22803*10^182614-11182615Robert Price07/2018
22812^606560-357182593Enzo Doria05/2014
228266*10^182420+7182422Robert Price07/2020
22832^605687+1866983182330Enzo Doria03/2016
22842^605655-114445182321Enzo Doria02/2015
228594*10^182291-3182293Robert Price05/2020
2286(20^140053+1)/21182212Paul Bourdelais04/2010
2287(14*10^182177-221)/9182178Robert Price04/2018
22882^605174-112751182176Enzo Doria06/2014
22892^604761+1874507182052Enzo Doria06/2016
22902^604705+1871957182035Enzo Doria05/2016
2291(14*10^182000+229)/9182001Robert Price03/2018
2292(10^181996+41)/3181996Robert Price12/2017
2293(17*10^181979+91)/9181980Robert Price02/2022
2294(5*10^181950-101)/3181951Robert Price04/2018
22952^603915+75233181797Enzo Doria04/2016
229639470^39537+39537^39470181723Norbert Schneider12/2022
2297(10^181710+7)/563747/2019847181698Alfred Reich08/2021
22987*10^181594-57181595Robert Price06/2020
22998*10^181580+29181581Robert Price11/2021
2300(83*10^181544+61)/9181545Serge Batalov01/2023
2301(2*10^181457+7)/9181457Rytis Slatkevicius01/2023
23023*10^181445+23181446Robert Price03/2022
2303(194*10^181369-11)/3181371Robert Price09/2020
230411^174145-360181354Enzo Doria10/2012
23052^602351-396765181326Enzo Doria08/2013
23066*10^181306+17181307Robert Price04/2019
2307(286*10^181220-1)/3181222Robert Price11/2020
23082^601957-113833181208Enzo Doria09/2014
230966^99581-65^99581181193Robert Price09/2013
231010^181182+383973181183Patrick De Geest04/2016
231110^181182-21181182Serge Batalov12/2014
2312(797*10^181171-41)/9181173Robert Price04/2022
23132^601722+74209181137Enzo Doria08/2023
2314(5*10^181127-29)/3181128Robert Price03/2018
23152^601521-29143181076Enzo Doria07/2015
23162^601442-2797811181053Enzo Doria04/2016
231744*10^181029+3181031Robert Price04/2020
23185*10^180992-9180993Robert Price05/2015
231910^180979+79477180980Patrick De Geest04/2016
232010^180979+107739180980Patrick De Geest04/2016
232110^180979-11180979Serge Batalov12/2014
23222^601023-113851180926Enzo Doria10/2014
2323(23*10^180862-143)/3180863Robert Price12/2019
23243*10^180852+29180853Robert Price05/2018
2325(277*10^180782-7)/9180784Robert Price02/2022
23262^600412+29851180743Enzo Doria03/2024
2327(8*10^180725-629)/9180725Robert Price01/2022
2328(79*10^180710-1)/3180712Robert Price02/2020
23292^600300-1852559180709Enzo Doria08/2015
2330(2*10^180706-77)/3180706Robert Price02/2021
2331(10^180689+71)/9180689Serge Batalov07/2015
23322^600209+76487180681Enzo Doria05/2016
23332^599999+378461180617Norman Luhn09/2023
2334(8*10^180536-269)/9180536Robert Price09/2021
23352^599702-369885180529Enzo Doria11/2013
2336Tau(643^11688)180524Nik Lygeros / Olivier Rozier05/2015
2337(2951*29^123418-3)/4180490Curtis Bright05/2015
2338(29*10^180432-17)/3180433Robert Price09/2019
23394*10^180360+93180361Robert Price08/2018
23402^599035+219323180328Enzo Doria03/2024
23412^598942+80779180300Enzo Doria07/2016
2342(38*10^180296+403)/9180297Robert Price10/2018
2343(85*10^180241+77)/9180242Robert Price07/2022
23442^598591-1844797180194Enzo Doria06/2015
2345(100^90089+1)/101180176Paul Bourdelais08/2017
23462^598301+28517180107Enzo Doria01/2024
2347(29*10^180072+691)/9180073Robert Price08/2021
2348(59*10^180038+157)/9180039Robert Price12/2021
234995*10^180019-9180021Robert Price01/2022
23506*10^179970+91179971Robert Price05/2019
2351(4*10^179963-79)/3179964Robert Price02/2018
2352(403*10^179944-43)/9179946Robert Price06/2021
2353Gamma-Prime(179849)179849Eric W. Weisstein06/2011
23542^597424-1859729179843Enzo Doria11/2015
2355Phi(180683,10)179760Maksym Voznyy09/2015
2356(10^180683-1)*9/(10^643-1)/(10^281-1)179760Robert Price07/2016
2357(3^376657-2^376657)/22301107657179701Mike Oakes04/2017
2358(29*10^179697+223)/9179698Robert Price09/2018
23592^596884+73179680Stefano Morozzi04/2021
2360(11*10^179679+13)/3179680Robert Price03/2022
2361(68*10^179656+7)/3179658Robert Price01/2020
2362(10^179643+173)/3179643Robert Price05/2021
23632^596690-461261179622Enzo Doria07/2015
23642^596684-113939179620Enzo Doria10/2014
23652^596642+39179608Jon Grantham08/2023
23662*10^179602+63179603Robert Price05/2018
236732262^39815-39815^32262179514Frank Doornink02/2024
2368(25*10^179488-403)/9179489Robert Price01/2021
23697*10^179460+99179461Robert Price05/2021
23702^596127+74333179453Enzo Doria07/2023
23713^375887-112696179344Enzo Doria07/2014
23724*10^179265-71179266Robert Price12/2018
23732*10^179193+83179194Robert Price12/2021
23742^595144-1850429179157Enzo Doria08/2015
23752^595122-5179150Stefano Morozzi07/2022
23763*10^179138+89179139Robert Price10/2018
2377(52*10^179062-133)/9179063Robert Price09/2021
23782^594531+82253178972Enzo Doria09/2016
2379(664*10^178939-61)/9178941Robert Price09/2021
23802^594260-2787899178891Enzo Doria11/2015
2381(14*10^178822+67)/9178823Robert Price05/2022
2382(29*10^178732-119)/9178733Robert Price12/2021
23832^593631+101381178701Jorge Menendez04/2018
238410^178695+136719178696Patrick De Geest05/2016
238510^178695-71178695Serge Batalov12/2014
2386(2*10^178649-161)/3178649Robert Price12/2020
2387(691^62903-1)/690178609Michael Stocker05/2020
2388(2^148330+1)^4-2178608Cletus Emmanuel12/2003
23892^593242+28309178584Enzo Doria01/2024
23902^593222-14145178578Jorge Menendez10/2017
23917*10^178566+33178567Robert Price06/2020
23922^593178+1867219178565Enzo Doria03/2016
23932^593152+22441178557Enzo Doria09/2023
2394(38*10^178456+151)/9178457Robert Price03/2022
2395(302*10^178369+13)/9178371Robert Price02/2020
2396(26*10^178296-113)/3178297Robert Price06/2020
2397(18^142031-1)/17178287Paul Bourdelais03/2010
2398(13*10^178233+137)/3178234Robert Price06/2021
2399(5*10^178206+91)/3178207Robert Price04/2018
24002^591872-291929178172Enzo Doria07/2015
24012^591682-286871178115Enzo Doria07/2015
2402(7^210761-5^210761)/2178114Jon Grantham08/2023
24034*10^178091+9178092Robert Price05/2015
2404410747#+478483178007Makoto Morimoto02/2016
24053*10^177872+73177873Robert Price08/2018
24062^590762-396765177838Enzo Doria08/2013
2407(136*10^177754-1)/9177756Serge Batalov12/2014
2408ReverseConsecutiveIntegerPrime(37765)177719Eric W. Weisstein04/2010
2409Smr(37765)177719Eric W. Weisstein12/2021
2410(266*10^177577-11)/3177579Robert Price04/2020
2411(11*10^177466-113)/3177467Robert Price10/2018
24123*10^177373-97177374Robert Price07/2018
24132^589204+1881151177369Enzo Doria11/2016
24142^589132-69479177347Enzo Doria01/2016
2415(101*10^177302-17)/3177304Robert Price02/2020
24162^588912-113519177281Enzo Doria08/2014
2417(682*10^177266-7)/9177268Robert Price08/2021
241815^150706+2177245Robert Price06/2015
2419(31208^39601-1)/(31208^199-1)177084Ryan Propper11/2023
24202^588194-1861001177065Enzo Doria11/2015
24215*10^177016-37177017Robert Price11/2021
2422fibonacci(846926)-4176997Jon Grantham08/2023
2423(23*10^176964-47)/3176965Robert Price09/2019
242420530^41031+41031^20530176942Norbert Schneider07/2022
2425(19*10^176932+521)/9176933Robert Price05/2018
2426(8*10^176908+43)/3176909Robert Price06/2018
2427(85*10^176900+203)/9176901Robert Price09/2020
24282^587560-113699176874Enzo Doria09/2014
242920596^40995+40995^20596176844Norbert Schneider07/2022
2430(101*10^176815-17)/3176817Robert Price02/2020
2431(25*10^176715-37)/3176716Robert Price10/2019
24325^252763-12862176674Enzo Doria05/2014
243338442^38531+38531^38442176658Norbert Schneider09/2022
24342^586829+23961176654Enzo Doria10/2023
24352^586804+81721176646Enzo Doria08/2016
2436(10^176584+77)/3176584Robert Price01/2018
24372^586570+1874419176576Enzo Doria06/2016
2438(157*10^176482-1)/3176484Robert Price01/2022
24395*2^586202+3176466Jon Grantham07/2023
244027122^39799-39799^27122176442Frank Doornink01/2024
24412^585994-3311176402Yves Minet12/2014
24428*10^176383-81176384Robert Price02/2021
2443(23*10^176357+61)/3176358Robert Price01/2022
24442^585832-112799176354Enzo Doria07/2014
2445fibonacci(843383)+4176257Jon Grantham08/2023
2446(29*10^176240+49)/3176241Robert Price09/2021
2447(2^585387-11)/3176219Stefano Morozzi08/2022
24482^585336-461039176204Enzo Doria06/2015
2449(25*10^176164+143)/3176165Robert Price08/2020
24502^585095-1848127176132Enzo Doria08/2015
2451(5*10^176101-311)/9176101Robert Price12/2021
24526*10^176092+77176093Robert Price06/2020
24532^584950-115451176088Enzo Doria07/2015
2454(646*10^176044+11)/9176046Robert Price10/2021
2455(7^208283-5^208283)/2176020Jon Grantham08/2023
24562^584671-3697176004Yves Minet03/2017
2457(13*10^175965-37)/3175966Robert Price01/2019
245831728^39089-39089^31728175957Frank Doornink01/2024
24592*10^175860-87175861Robert Price04/2018
246027009^39670-39670^27009175798Frank Doornink01/2024
2461(86*10^175774-221)/9175775Robert Price09/2019
24622^583614+216037175686Enzo Doria11/2023
24639*10^175654+47175655Robert Price01/2022
246425430^39869-39869^25430175637Frank Doornink01/2024
246510^175608+2971175609Mike Oakes05/2010
246610^175608-55829175608Patrick De Geest09/2013
24672^583051+1879793175516Enzo Doria09/2016
2468(76*10^175514+491)/9175515Robert Price10/2021
24692^582860-23829175459Enzo Doria08/2013
2470(8*10^175428-53)/9175428Serge Batalov11/2022
2471(28*10^175417-67)/3175418Robert Price10/2020
24722^582670-23913175402Enzo Doria08/2013
24732^582573-29563175372Enzo Doria08/2015
24742^582435-1862767175331Enzo Doria12/2015
247510^175295-40000001175295Robert Price07/2022
247631093^39018-39018^31093175295Frank Doornink01/2024
2477(11*10^175250-149)/3175251Robert Price09/2018
2478(29*10^175236+31)/3175237Robert Price04/2021
24792^582072-1848599175222Enzo Doria08/2015
2480(404267#+465)/(3^4*5^2*31)175208Makoto Morimoto06/2019
2481Phi(262767,10)/259613797175168Makoto Kamada12/2022
2482(2^581871-15)/7175160Stefano Morozzi08/2022
2483(5*10^175117-311)/9175117Robert Price12/2021
248431193^38966-38966^31193175116Frank Doornink01/2024
248510^175093-89175093Riley Fisher10/2023
2486(220221^32768+1)/2175075Serge Batalov03/2018
24872^581560+1874911175068Enzo Doria06/2016
2488(25*10^174987-97)/9174988Robert Price01/2022
2489(75^93307-1)/74174955Paul Bourdelais09/2017
249031522^38883-38883^31522174920Frank Doornink01/2024
2491(27398^39601-1)/(27398^199-1)174855Ryan Propper11/2023
2492(861^59557-1)/860174798Jinyuan Wang11/2023
249331492^38859-38859^31492174796Frank Doornink01/2024
2494(47*10^174790+493)/9174791Robert Price03/2019
24952^580528-114035174757Enzo Doria11/2014
2496(19*10^174754+737)/9174755Robert Price07/2018
2497(35*10^174704-377)/9174705Robert Price07/2018
2498(49*10^174681+293)/9174682Robert Price03/2021
24996*10^174681+11174682Robert Price07/2022
25003*10^174665-97174666Robert Price07/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 27 2024 11:51 (Time in France)

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