PRP Records

Probable Primes Top 10000

(301723 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 ?
30012^607950-1862303183012Enzo Doria12/2015
30025*3^383376+2^383376182918Jon Grantham08/2023
3003(46*10^182896+683)/9182897Robert Price03/2019
3004(2*10^182787+73)/3182787Robert Price09/2020
30052^607101+1871987182756Enzo Doria05/2016
30062^606869-69175182686Enzo Doria11/2015
30078*10^182671+71182672Robert Price05/2022
3008(23*10^182666-71)/3182667Robert Price07/2020
30093*10^182614-11182615Robert Price07/2018
30102^606560-357182593Enzo Doria05/2014
301166*10^182420+7182422Robert Price07/2020
30122^605687+1866983182330Enzo Doria03/2016
30132^605655-114445182321Enzo Doria02/2015
301494*10^182291-3182293Robert Price05/2020
3015(20^140053+1)/21182212Paul Bourdelais04/2010
3016(14*10^182177-221)/9182178Robert Price04/2018
30172^605174-112751182176Enzo Doria06/2014
3018(905^61609-1)/904182154Anonymous05/2024
30192^604761+1874507182052Enzo Doria06/2016
30202^604705+1871957182035Enzo Doria05/2016
3021(14*10^182000+229)/9182001Robert Price03/2018
3022(10^181996+41)/3181996Robert Price12/2017
3023(17*10^181979+91)/9181980Robert Price02/2022
3024(10^181960+3)/7181960Jinyuan Wang11/2024
3025(5*10^181950-101)/3181951Robert Price04/2018
30262^603915+75233181797Enzo Doria04/2016
302739470^39537+39537^39470181723Norbert Schneider12/2022
3028(10^181710+7)/563747/2019847181698Alfred Reich08/2021
30297*10^181594-57181595Robert Price06/2020
30308*10^181580+29181581Robert Price11/2021
3031(83*10^181544+61)/9181545Serge Batalov01/2023
3032(2*10^181457+7)/9181457Rytis Slatkevicius01/2023
30333*10^181445+23181446Robert Price03/2022
3034(194*10^181369-11)/3181371Robert Price09/2020
303511^174145-360181354Enzo Doria10/2012
30362^602351-396765181326Enzo Doria08/2013
30376*10^181306+17181307Robert Price04/2019
3038(353^71143-1)/352181254Anonymous04/2024
3039(286*10^181220-1)/3181222Robert Price11/2020
30402^601957-113833181208Enzo Doria09/2014
304166^99581-65^99581181193Robert Price09/2013
304210^181182+383973181183Patrick De Geest04/2016
304310^181182-21181182Serge Batalov12/2014
3044(797*10^181171-41)/9181173Robert Price04/2022
30452^601722+74209181137Enzo Doria08/2023
3046(5*10^181127-29)/3181128Robert Price03/2018
30472^601521-29143181076Enzo Doria07/2015
30482^601442-2797811181053Enzo Doria04/2016
304944*10^181029+3181031Robert Price04/2020
30505*10^180992-9180993Robert Price05/2015
305110^180979+79477180980Patrick De Geest04/2016
305210^180979+107739180980Patrick De Geest04/2016
305310^180979-11180979Serge Batalov12/2014
30542^601023-113851180926Enzo Doria10/2014
3055(23*10^180862-143)/3180863Robert Price12/2019
30563*10^180852+29180853Robert Price05/2018
3057(277*10^180782-7)/9180784Robert Price02/2022
30582^600412+29851180743Enzo Doria03/2024
3059(8*10^180725-629)/9180725Robert Price01/2022
3060(79*10^180710-1)/3180712Robert Price02/2020
30612^600300-1852559180709Enzo Doria08/2015
3062(2*10^180706-77)/3180706Robert Price02/2021
3063(156^82393-1)/155180696Anonymous06/2024
3064(10^180689+71)/9180689Serge Batalov07/2015
30652^600209+76487180681Enzo Doria05/2016
30662^599999+378461180618Norman Luhn09/2023
3067(8*10^180536-269)/9180536Robert Price09/2021
30682^599702-369885180529Enzo Doria11/2013
3069Tau(643^11688)180524Nik Lygeros / Olivier Rozier05/2015
3070(2951*29^123418-3)/4180490Curtis Bright05/2015
3071(29*10^180432-17)/3180433Robert Price09/2019
30724*10^180360+93180361Robert Price08/2018
30732^599035+219323180328Enzo Doria03/2024
30742^598942+80779180300Enzo Doria07/2016
3075(38*10^180296+403)/9180297Robert Price10/2018
3076(85*10^180241+77)/9180242Robert Price07/2022
30772^598591-1844797180194Enzo Doria06/2015
3078(100^90089+1)/101180176Paul Bourdelais08/2017
30792^598301+28517180107Enzo Doria01/2024
3080(29*10^180072+691)/9180073Robert Price08/2021
3081(59*10^180038+157)/9180039Robert Price12/2021
308295*10^180019-9180021Robert Price01/2022
30836*10^179970+91179971Robert Price05/2019
3084(4*10^179963-79)/3179964Robert Price02/2018
3085(403*10^179944-43)/9179946Robert Price06/2021
3086Gamma-Prime(179849)179849Eric W. Weisstein06/2011
30872^597424-1859729179843Enzo Doria11/2015
3088Phi(180683,10)179760Maksym Voznyy09/2015
3089(10^180683-1)*9/(10^643-1)/(10^281-1)179760Robert Price07/2016
3090(3^376657-2^376657)/22301107657179701Mike Oakes04/2017
3091(29*10^179697+223)/9179698Robert Price09/2018
3092U(1289697)179687Serge Batalov07/2024
30942^596884+73179680Stefano Morozzi04/2021
3093(11*10^179679+13)/3179680Robert Price03/2022
3095(68*10^179656+7)/3179658Robert Price01/2020
3096(10^179643+173)/3179643Robert Price05/2021
30972^596690-461261179622Enzo Doria07/2015
30982^596684-113939179620Enzo Doria10/2014
30992^596642+39179608Jon Grantham08/2023
31002*10^179602+63179603Robert Price05/2018
310132262^39815-39815^32262179514Frank Doornink02/2024
3102(25*10^179488-403)/9179489Robert Price01/2021
31037*10^179460+99179461Robert Price05/2021
31042^596127+74333179453Enzo Doria07/2023
31053^375887-112696179344Enzo Doria07/2014
31064*10^179265-71179266Robert Price12/2018
31072*10^179193+83179194Robert Price12/2021
31082^595144-1850429179157Enzo Doria08/2015
31092^595122-5179150Stefano Morozzi07/2022
31103*10^179138+89179139Robert Price10/2018
3111(52*10^179062-133)/9179063Robert Price09/2021
31122^594531+82253178972Enzo Doria09/2016
3113(664*10^178939-61)/9178941Robert Price09/2021
31142^594260-2787899178891Enzo Doria11/2015
3115(14*10^178822+67)/9178823Robert Price05/2022
3116(29*10^178732-119)/9178733Robert Price12/2021
31172^593631+101381178701Jorge Menendez04/2018
311810^178695+136719178696Patrick De Geest05/2016
311910^178695-71178695Serge Batalov12/2014
3120(2*10^178649-161)/3178649Robert Price12/2020
3121(691^62903-1)/690178609Michael Stocker05/2020
3122(2^148330+1)^4-2178608Cletus Emmanuel12/2003
31232^593242+28309178584Enzo Doria01/2024
31242^593222-14145178578Jorge Menendez10/2017
31257*10^178566+33178567Robert Price06/2020
31262^593178+1867219178565Enzo Doria03/2016
31272^593152+22441178557Enzo Doria09/2023
3128(38*10^178456+151)/9178457Robert Price03/2022
3129(302*10^178369+13)/9178371Robert Price02/2020
3130(26*10^178296-113)/3178297Robert Price06/2020
3131(18^142031-1)/17178287Paul Bourdelais03/2010
3132(13*10^178233+137)/3178234Robert Price06/2021
3133(5*10^178206+91)/3178207Robert Price04/2018
31342^591872-291929178172Enzo Doria07/2015
31352^591682-286871178115Enzo Doria07/2015
3136(7^210761-5^210761)/2178114Jon Grantham08/2023
31374*10^178091+9178092Robert Price05/2015
31382^591435+335931178040Enzo Doria09/2024
3139410747#+478483178007Makoto Morimoto02/2016
31403*10^177872+73177873Robert Price08/2018
31412^590762-396765177838Enzo Doria08/2013
3142(136*10^177754-1)/9177756Serge Batalov12/2014
3143ReverseConsecutiveIntegerPrime(37765)177719Eric W. Weisstein04/2010
3144Smr(37765)177719Eric W. Weisstein12/2021
3145598^128^209+209^128^598177594Henri Lifchitz03/2025
3146(266*10^177577-11)/3177579Robert Price04/2020
3147(11*10^177466-113)/3177467Robert Price10/2018
31483*10^177373-97177374Robert Price07/2018
31492^589204+1881151177369Enzo Doria11/2016
31502^589132-69479177347Enzo Doria01/2016
3151(3^371666)/(371666^3)177314Henri Lifchitz05/2025
3152(101*10^177302-17)/3177304Robert Price02/2020
31532^588912-113519177281Enzo Doria08/2014
3154(682*10^177266-7)/9177268Robert Price08/2021
315515^150706+2177245Robert Price06/2015
31562^588403+335931177127Enzo Doria09/2024
3157(31208^39601-1)/(31208^199-1)177084Ryan Propper11/2023
31582^588194-1861001177065Enzo Doria11/2015
31595*10^177016-37177017Robert Price11/2021
3160fibonacci(846926)-4176997Jon Grantham08/2023
3161(23*10^176964-47)/3176965Robert Price09/2019
316220530^41031+41031^20530176942Norbert Schneider07/2022
3163(19*10^176932+521)/9176933Robert Price05/2018
3164(8*10^176908+43)/3176909Robert Price06/2018
3165(85*10^176900+203)/9176901Robert Price09/2020
31662^587560-113699176874Enzo Doria09/2014
316720596^40995+40995^20596176844Norbert Schneider07/2022
3168(101*10^176815-17)/3176817Robert Price02/2020
3169(25*10^176715-37)/3176716Robert Price10/2019
31705^252763-12862176674Enzo Doria05/2014
317138442^38531+38531^38442176658Norbert Schneider09/2022
31722^586829+23961176654Enzo Doria10/2023
31732^586804+81721176646Enzo Doria08/2016
3174(10^176584+77)/3176584Robert Price01/2018
31752^586570+1874419176576Enzo Doria06/2016
3176(157*10^176482-1)/3176484Robert Price01/2022
31775*2^586202+3176466Jon Grantham07/2023
317827122^39799-39799^27122176442Frank Doornink01/2024
31792^585994-3311176402Yves Minet12/2014
31808*10^176383-81176384Robert Price02/2021
3181(23*10^176357+61)/3176358Robert Price01/2022
31822^585832-112799176354Enzo Doria07/2014
3183fibonacci(843383)+4176257Jon Grantham08/2023
3184(29*10^176240+49)/3176241Robert Price09/2021
3185(2^585387-11)/3176219Stefano Morozzi08/2022
31862^585336-461039176204Enzo Doria06/2015
3187(25*10^176164+143)/3176165Robert Price08/2020
31882^585095-1848127176132Enzo Doria08/2015
3189(5*10^176101-311)/9176101Robert Price12/2021
31906*10^176092+77176093Robert Price06/2020
31912^584950-115451176088Enzo Doria07/2015
3192(646*10^176044+11)/9176046Robert Price10/2021
3193(7^208283-5^208283)/2176020Jon Grantham08/2023
31942^584671-3697176004Yves Minet03/2017
3195(13*10^175965-37)/3175966Robert Price01/2019
319631728^39089-39089^31728175957Frank Doornink01/2024
31972*10^175860-87175861Robert Price04/2018
319827009^39670-39670^27009175798Frank Doornink01/2024
3199(86*10^175774-221)/9175775Robert Price09/2019
32002^583614+216037175686Enzo Doria11/2023
32019*10^175654+47175655Robert Price01/2022
320225430^39869-39869^25430175637Frank Doornink01/2024
320310^175608+2971175609Mike Oakes05/2010
320410^175608-55829175608Patrick De Geest09/2013
32052^583051+1879793175516Enzo Doria09/2016
3206(76*10^175514+491)/9175515Robert Price10/2021
32082^582860-23829175459Enzo Doria08/2013
3207(200^76253-1)/199175459Anonymous06/2024
3209(8*10^175428-53)/9175428Serge Batalov11/2022
3210(28*10^175417-67)/3175418Robert Price10/2020
32112^582670-23913175402Enzo Doria08/2013
32122^582573-29563175372Enzo Doria08/2015
32132^582435-1862767175331Enzo Doria12/2015
321410^175295-40000001175295Robert Price07/2022
321531093^39018-39018^31093175295Frank Doornink01/2024
3216(11*10^175250-149)/3175251Robert Price09/2018
3217(29*10^175236+31)/3175237Robert Price04/2021
32182^582072-1848599175222Enzo Doria08/2015
3219(404267#+465)/(3^4*5^2*31)175208Makoto Morimoto06/2019
3220Phi(262767,10)/259613797175168Makoto Kamada12/2022
3221(2^581871-15)/7175160Stefano Morozzi08/2022
3222(5*10^175117-311)/9175117Robert Price12/2021
322331193^38966-38966^31193175116Frank Doornink01/2024
32242^581695+225893175108Enzo Doria08/2024
322510^175093-89175093Riley Fisher10/2023
3226(220221^32768+1)/2175075Serge Batalov03/2018
32272^581560+1874911175068Enzo Doria06/2016
3228(25*10^174987-97)/9174988Robert Price01/2022
3229(75^93307-1)/74174955Paul Bourdelais09/2017
323026446^39555-39555^26446174927Frank Doornink03/2024
323131522^38883-38883^31522174920Frank Doornink01/2024
3232(27398^39601-1)/(27398^199-1)174855Ryan Propper11/2023
3233(861^59557-1)/860174798Jinyuan Wang11/2023
323431492^38859-38859^31492174796Frank Doornink01/2024
3235(47*10^174790+493)/9174791Robert Price03/2019
32362^580528-114035174757Enzo Doria11/2014
3237(19*10^174754+737)/9174755Robert Price07/2018
3238V(1045270)/4181081/12543241/81333115129561174730Serge Batalov07/2024
3239(35*10^174704-377)/9174705Robert Price07/2018
3241(49*10^174681+293)/9174682Robert Price03/2021
32406*10^174681+11174682Robert Price07/2022
32423*10^174665-97174666Robert Price07/2018
32432^580046-459161174612Enzo Doria05/2015
32442^579992-39779174595Enzo Doria09/2015
324525613^39582-39582^25613174496Frank Doornink02/2024
3246(29*10^174481-149)/3174482Robert Price08/2022
3247(4*10^174423+101)/3174424Robert Price11/2021
3248(2^579371-17)/3174408Stefano Morozzi08/2022
3249(2*10^174301-71)/3174301Robert Price12/2017
325014^152048+3174267Paul Bourdelais12/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 10 2025 14:11 (Time in France)

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