PRP Records

Probable Primes Top 10000

(294627 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(61*10^183294+119)/9183295Robert Price05/2019
22522^608814-461261183272Enzo Doria06/2015
2253(163*10^183227-1)/9183229Serge Batalov12/2014
22542^608541-608541^2183190Henri Lifchitz02/2018
22552^608293+143807183115Enzo Doria10/2016
22562^608164-462419183076Enzo Doria08/2015
22572^607950-1862303183012Enzo Doria12/2015
22585*3^383376+2^383376182918Jon Grantham08/2023
2259(46*10^182896+683)/9182897Robert Price03/2019
2260(2*10^182787+73)/3182787Robert Price09/2020
22612^607101+1871987182756Enzo Doria05/2016
22622^606869-69175182686Enzo Doria11/2015
22638*10^182671+71182672Robert Price05/2022
2264(23*10^182666-71)/3182667Robert Price07/2020
22653*10^182614-11182615Robert Price07/2018
22662^606560-357182593Enzo Doria05/2014
226766*10^182420+7182422Robert Price07/2020
22682^605687+1866983182330Enzo Doria03/2016
22692^605655-114445182321Enzo Doria02/2015
227094*10^182291-3182293Robert Price05/2020
2271(20^140053+1)/21182212Paul Bourdelais04/2010
2272(14*10^182177-221)/9182178Robert Price04/2018
22732^605174-112751182176Enzo Doria06/2014
22742^604761+1874507182052Enzo Doria06/2016
22752^604705+1871957182035Enzo Doria05/2016
2276(14*10^182000+229)/9182001Robert Price03/2018
2277(10^181996+41)/3181996Robert Price12/2017
2278(17*10^181979+91)/9181980Robert Price02/2022
2279(5*10^181950-101)/3181951Robert Price04/2018
22802^603915+75233181797Enzo Doria04/2016
228139470^39537+39537^39470181723Norbert Schneider12/2022
2282(10^181710+7)/563747/2019847181698Alfred Reich08/2021
22837*10^181594-57181595Robert Price06/2020
22848*10^181580+29181581Robert Price11/2021
2285(83*10^181544+61)/9181545Serge Batalov01/2023
2286(2*10^181457+7)/9181457Rytis Slatkevicius01/2023
22873*10^181445+23181446Robert Price03/2022
2288(194*10^181369-11)/3181371Robert Price09/2020
228911^174145-360181354Enzo Doria10/2012
22902^602351-396765181326Enzo Doria08/2013
22916*10^181306+17181307Robert Price04/2019
2292(286*10^181220-1)/3181222Robert Price11/2020
22932^601957-113833181208Enzo Doria09/2014
229466^99581-65^99581181193Robert Price09/2013
229510^181182+383973181183Patrick De Geest04/2016
229610^181182-21181182Serge Batalov12/2014
2297(797*10^181171-41)/9181173Robert Price04/2022
22982^601722+74209181137Enzo Doria08/2023
2299(5*10^181127-29)/3181128Robert Price03/2018
23002^601521-29143181076Enzo Doria07/2015
23012^601442-2797811181053Enzo Doria04/2016
230244*10^181029+3181031Robert Price04/2020
23035*10^180992-9180993Robert Price05/2015
230410^180979+79477180980Patrick De Geest04/2016
230510^180979+107739180980Patrick De Geest04/2016
230610^180979-11180979Serge Batalov12/2014
23072^601023-113851180926Enzo Doria10/2014
2308(23*10^180862-143)/3180863Robert Price12/2019
23093*10^180852+29180853Robert Price05/2018
2310(277*10^180782-7)/9180784Robert Price02/2022
23112^600412+29851180743Enzo Doria03/2024
2312(8*10^180725-629)/9180725Robert Price01/2022
2313(79*10^180710-1)/3180712Robert Price02/2020
23142^600300-1852559180709Enzo Doria08/2015
2315(2*10^180706-77)/3180706Robert Price02/2021
2316(10^180689+71)/9180689Serge Batalov07/2015
23172^600209+76487180681Enzo Doria05/2016
23182^599999+378461180617Norman Luhn09/2023
2319(8*10^180536-269)/9180536Robert Price09/2021
23202^599702-369885180529Enzo Doria11/2013
2321Tau(643^11688)180524Nik Lygeros / Olivier Rozier05/2015
2322(2951*29^123418-3)/4180490Curtis Bright05/2015
2323(29*10^180432-17)/3180433Robert Price09/2019
23244*10^180360+93180361Robert Price08/2018
23252^599035+219323180328Enzo Doria03/2024
23262^598942+80779180300Enzo Doria07/2016
2327(38*10^180296+403)/9180297Robert Price10/2018
2328(85*10^180241+77)/9180242Robert Price07/2022
23292^598591-1844797180194Enzo Doria06/2015
2330(100^90089+1)/101180176Paul Bourdelais08/2017
23312^598301+28517180107Enzo Doria01/2024
2332(29*10^180072+691)/9180073Robert Price08/2021
2333(59*10^180038+157)/9180039Robert Price12/2021
233495*10^180019-9180021Robert Price01/2022
23356*10^179970+91179971Robert Price05/2019
2336(4*10^179963-79)/3179964Robert Price02/2018
2337(403*10^179944-43)/9179946Robert Price06/2021
2338Gamma-Prime(179849)179849Eric W. Weisstein06/2011
23392^597424-1859729179843Enzo Doria11/2015
2340Phi(180683,10)179760Maksym Voznyy09/2015
2341(10^180683-1)*9/(10^643-1)/(10^281-1)179760Robert Price07/2016
2342(3^376657-2^376657)/22301107657179701Mike Oakes04/2017
2343(29*10^179697+223)/9179698Robert Price09/2018
23442^596884+73179680Stefano Morozzi04/2021
2345(11*10^179679+13)/3179680Robert Price03/2022
2346(68*10^179656+7)/3179658Robert Price01/2020
2347(10^179643+173)/3179643Robert Price05/2021
23482^596690-461261179622Enzo Doria07/2015
23492^596684-113939179620Enzo Doria10/2014
23502^596642+39179608Jon Grantham08/2023
23512*10^179602+63179603Robert Price05/2018
235232262^39815-39815^32262179514Frank Doornink02/2024
2353(25*10^179488-403)/9179489Robert Price01/2021
23547*10^179460+99179461Robert Price05/2021
23552^596127+74333179453Enzo Doria07/2023
23563^375887-112696179344Enzo Doria07/2014
23574*10^179265-71179266Robert Price12/2018
23582*10^179193+83179194Robert Price12/2021
23592^595144-1850429179157Enzo Doria08/2015
23602^595122-5179150Stefano Morozzi07/2022
23613*10^179138+89179139Robert Price10/2018
2362(52*10^179062-133)/9179063Robert Price09/2021
23632^594531+82253178972Enzo Doria09/2016
2364(664*10^178939-61)/9178941Robert Price09/2021
23652^594260-2787899178891Enzo Doria11/2015
2366(14*10^178822+67)/9178823Robert Price05/2022
2367(29*10^178732-119)/9178733Robert Price12/2021
23682^593631+101381178701Jorge Menendez04/2018
236910^178695+136719178696Patrick De Geest05/2016
237010^178695-71178695Serge Batalov12/2014
2371(2*10^178649-161)/3178649Robert Price12/2020
2372(691^62903-1)/690178609Michael Stocker05/2020
2373(2^148330+1)^4-2178608Cletus Emmanuel12/2003
23742^593242+28309178584Enzo Doria01/2024
23752^593222-14145178578Jorge Menendez10/2017
23767*10^178566+33178567Robert Price06/2020
23772^593178+1867219178565Enzo Doria03/2016
23782^593152+22441178557Enzo Doria09/2023
2379(38*10^178456+151)/9178457Robert Price03/2022
2380(302*10^178369+13)/9178371Robert Price02/2020
2381(26*10^178296-113)/3178297Robert Price06/2020
2382(18^142031-1)/17178287Paul Bourdelais03/2010
2383(13*10^178233+137)/3178234Robert Price06/2021
2384(5*10^178206+91)/3178207Robert Price04/2018
23852^591872-291929178172Enzo Doria07/2015
23862^591682-286871178115Enzo Doria07/2015
2387(7^210761-5^210761)/2178114Jon Grantham08/2023
23884*10^178091+9178092Robert Price05/2015
2389410747#+478483178007Makoto Morimoto02/2016
23903*10^177872+73177873Robert Price08/2018
23912^590762-396765177838Enzo Doria08/2013
2392(136*10^177754-1)/9177756Serge Batalov12/2014
2393ReverseConsecutiveIntegerPrime(37765)177719Eric W. Weisstein04/2010
2394Smr(37765)177719Eric W. Weisstein12/2021
2395(266*10^177577-11)/3177579Robert Price04/2020
2396(11*10^177466-113)/3177467Robert Price10/2018
23973*10^177373-97177374Robert Price07/2018
23982^589204+1881151177369Enzo Doria11/2016
23992^589132-69479177347Enzo Doria01/2016
2400(101*10^177302-17)/3177304Robert Price02/2020
24012^588912-113519177281Enzo Doria08/2014
2402(682*10^177266-7)/9177268Robert Price08/2021
240315^150706+2177245Robert Price06/2015
2404(31208^39601-1)/(31208^199-1)177084Ryan Propper11/2023
24052^588194-1861001177065Enzo Doria11/2015
24065*10^177016-37177017Robert Price11/2021
2407fibonacci(846926)-4176997Jon Grantham08/2023
2408(23*10^176964-47)/3176965Robert Price09/2019
240920530^41031+41031^20530176942Norbert Schneider07/2022
2410(19*10^176932+521)/9176933Robert Price05/2018
2411(8*10^176908+43)/3176909Robert Price06/2018
2412(85*10^176900+203)/9176901Robert Price09/2020
24132^587560-113699176874Enzo Doria09/2014
241420596^40995+40995^20596176844Norbert Schneider07/2022
2415(101*10^176815-17)/3176817Robert Price02/2020
2416(25*10^176715-37)/3176716Robert Price10/2019
24175^252763-12862176674Enzo Doria05/2014
241838442^38531+38531^38442176658Norbert Schneider09/2022
24192^586829+23961176654Enzo Doria10/2023
24202^586804+81721176646Enzo Doria08/2016
2421(10^176584+77)/3176584Robert Price01/2018
24222^586570+1874419176576Enzo Doria06/2016
2423(157*10^176482-1)/3176484Robert Price01/2022
24245*2^586202+3176466Jon Grantham07/2023
242527122^39799-39799^27122176442Frank Doornink01/2024
24262^585994-3311176402Yves Minet12/2014
24278*10^176383-81176384Robert Price02/2021
2428(23*10^176357+61)/3176358Robert Price01/2022
24292^585832-112799176354Enzo Doria07/2014
2430fibonacci(843383)+4176257Jon Grantham08/2023
2431(29*10^176240+49)/3176241Robert Price09/2021
2432(2^585387-11)/3176219Stefano Morozzi08/2022
24332^585336-461039176204Enzo Doria06/2015
2434(25*10^176164+143)/3176165Robert Price08/2020
24352^585095-1848127176132Enzo Doria08/2015
2436(5*10^176101-311)/9176101Robert Price12/2021
24376*10^176092+77176093Robert Price06/2020
24382^584950-115451176088Enzo Doria07/2015
2439(646*10^176044+11)/9176046Robert Price10/2021
2440(7^208283-5^208283)/2176020Jon Grantham08/2023
24412^584671-3697176004Yves Minet03/2017
2442(13*10^175965-37)/3175966Robert Price01/2019
244331728^39089-39089^31728175957Frank Doornink01/2024
24442*10^175860-87175861Robert Price04/2018
244527009^39670-39670^27009175798Frank Doornink01/2024
2446(86*10^175774-221)/9175775Robert Price09/2019
24472^583614+216037175686Enzo Doria11/2023
24489*10^175654+47175655Robert Price01/2022
244925430^39869-39869^25430175637Frank Doornink01/2024
245010^175608+2971175609Mike Oakes05/2010
245110^175608-55829175608Patrick De Geest09/2013
24522^583051+1879793175516Enzo Doria09/2016
2453(76*10^175514+491)/9175515Robert Price10/2021
24542^582860-23829175459Enzo Doria08/2013
2455(8*10^175428-53)/9175428Serge Batalov11/2022
2456(28*10^175417-67)/3175418Robert Price10/2020
24572^582670-23913175402Enzo Doria08/2013
24582^582573-29563175372Enzo Doria08/2015
24592^582435-1862767175331Enzo Doria12/2015
246010^175295-40000001175295Robert Price07/2022
246131093^39018-39018^31093175295Frank Doornink01/2024
2462(11*10^175250-149)/3175251Robert Price09/2018
2463(29*10^175236+31)/3175237Robert Price04/2021
24642^582072-1848599175222Enzo Doria08/2015
2465(404267#+465)/(3^4*5^2*31)175208Makoto Morimoto06/2019
2466Phi(262767,10)/259613797175168Makoto Kamada12/2022
2467(2^581871-15)/7175160Stefano Morozzi08/2022
2468(5*10^175117-311)/9175117Robert Price12/2021
246931193^38966-38966^31193175116Frank Doornink01/2024
247010^175093-89175093Riley Fisher10/2023
2471(220221^32768+1)/2175075Serge Batalov03/2018
24722^581560+1874911175068Enzo Doria06/2016
2473(25*10^174987-97)/9174988Robert Price01/2022
2474(75^93307-1)/74174955Paul Bourdelais09/2017
247531522^38883-38883^31522174920Frank Doornink01/2024
2476(27398^39601-1)/(27398^199-1)174855Ryan Propper11/2023
2477(861^59557-1)/860174798Jinyuan Wang11/2023
247831492^38859-38859^31492174796Frank Doornink01/2024
2479(47*10^174790+493)/9174791Robert Price03/2019
24802^580528-114035174757Enzo Doria11/2014
2481(19*10^174754+737)/9174755Robert Price07/2018
2482(35*10^174704-377)/9174705Robert Price07/2018
2483(49*10^174681+293)/9174682Robert Price03/2021
24846*10^174681+11174682Robert Price07/2022
24853*10^174665-97174666Robert Price07/2018
24862^580046-459161174612Enzo Doria05/2015
24872^579992-39779174595Enzo Doria09/2015
248825613^39582-39582^25613174496Frank Doornink02/2024
2489(29*10^174481-149)/3174482Robert Price08/2022
2490(4*10^174423+101)/3174424Robert Price11/2021
2491(2^579371-17)/3174408Stefano Morozzi08/2022
2492(2*10^174301-71)/3174301Robert Price12/2017
249314^152048+3174267Paul Bourdelais12/2020
2494(2^578696+1)/257174203Lelio R Paula09/2015
24952^578656-1851809174193Enzo Doria08/2015
24962^578583-113917174171Enzo Doria10/2014
24972^578434-83174126Yves Minet07/2017
249815^148048-2174118Robert Price06/2015
24995*10^174101+81174102Robert Price03/2019
25002^578346+2794249174100Enzo Doria03/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 12 2024 13:37 (Time in France)

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