PRP Records

Probable Primes Top 10000

(301692 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 ?
3001(2*10^181457+7)/9181457Rytis Slatkevicius01/2023
30023*10^181445+23181446Robert Price03/2022
3003(194*10^181369-11)/3181371Robert Price09/2020
300411^174145-360181354Enzo Doria10/2012
30052^602351-396765181326Enzo Doria08/2013
30066*10^181306+17181307Robert Price04/2019
3007(353^71143-1)/352181254Anonymous04/2024
3008(286*10^181220-1)/3181222Robert Price11/2020
30092^601957-113833181208Enzo Doria09/2014
301066^99581-65^99581181193Robert Price09/2013
301110^181182+383973181183Patrick De Geest04/2016
301210^181182-21181182Serge Batalov12/2014
3013(797*10^181171-41)/9181173Robert Price04/2022
30142^601722+74209181137Enzo Doria08/2023
3015(5*10^181127-29)/3181128Robert Price03/2018
30162^601521-29143181076Enzo Doria07/2015
30172^601442-2797811181053Enzo Doria04/2016
301844*10^181029+3181031Robert Price04/2020
30195*10^180992-9180993Robert Price05/2015
302010^180979+79477180980Patrick De Geest04/2016
302110^180979+107739180980Patrick De Geest04/2016
302210^180979-11180979Serge Batalov12/2014
30232^601023-113851180926Enzo Doria10/2014
3024(23*10^180862-143)/3180863Robert Price12/2019
30253*10^180852+29180853Robert Price05/2018
3026(277*10^180782-7)/9180784Robert Price02/2022
30272^600412+29851180743Enzo Doria03/2024
3028(8*10^180725-629)/9180725Robert Price01/2022
3029(79*10^180710-1)/3180712Robert Price02/2020
30302^600300-1852559180709Enzo Doria08/2015
3031(2*10^180706-77)/3180706Robert Price02/2021
3032(156^82393-1)/155180696Anonymous06/2024
3033(10^180689+71)/9180689Serge Batalov07/2015
30342^600209+76487180681Enzo Doria05/2016
30352^599999+378461180618Norman Luhn09/2023
3036(8*10^180536-269)/9180536Robert Price09/2021
30372^599702-369885180529Enzo Doria11/2013
3038Tau(643^11688)180524Nik Lygeros / Olivier Rozier05/2015
3039(2951*29^123418-3)/4180490Curtis Bright05/2015
3040(29*10^180432-17)/3180433Robert Price09/2019
30414*10^180360+93180361Robert Price08/2018
30422^599035+219323180328Enzo Doria03/2024
30432^598942+80779180300Enzo Doria07/2016
3044(38*10^180296+403)/9180297Robert Price10/2018
3045(85*10^180241+77)/9180242Robert Price07/2022
30462^598591-1844797180194Enzo Doria06/2015
3047(100^90089+1)/101180176Paul Bourdelais08/2017
30482^598301+28517180107Enzo Doria01/2024
3049(29*10^180072+691)/9180073Robert Price08/2021
3050(59*10^180038+157)/9180039Robert Price12/2021
305195*10^180019-9180021Robert Price01/2022
30526*10^179970+91179971Robert Price05/2019
3053(4*10^179963-79)/3179964Robert Price02/2018
3054(403*10^179944-43)/9179946Robert Price06/2021
3055Gamma-Prime(179849)179849Eric W. Weisstein06/2011
30562^597424-1859729179843Enzo Doria11/2015
3057Phi(180683,10)179760Maksym Voznyy09/2015
3058(10^180683-1)*9/(10^643-1)/(10^281-1)179760Robert Price07/2016
3059(3^376657-2^376657)/22301107657179701Mike Oakes04/2017
3060(29*10^179697+223)/9179698Robert Price09/2018
3061U(1289697)179687Serge Batalov07/2024
30632^596884+73179680Stefano Morozzi04/2021
3062(11*10^179679+13)/3179680Robert Price03/2022
3064(68*10^179656+7)/3179658Robert Price01/2020
3065(10^179643+173)/3179643Robert Price05/2021
30662^596690-461261179622Enzo Doria07/2015
30672^596684-113939179620Enzo Doria10/2014
30682^596642+39179608Jon Grantham08/2023
30692*10^179602+63179603Robert Price05/2018
307032262^39815-39815^32262179514Frank Doornink02/2024
3071(25*10^179488-403)/9179489Robert Price01/2021
30727*10^179460+99179461Robert Price05/2021
30732^596127+74333179453Enzo Doria07/2023
30743^375887-112696179344Enzo Doria07/2014
30754*10^179265-71179266Robert Price12/2018
30762*10^179193+83179194Robert Price12/2021
30772^595144-1850429179157Enzo Doria08/2015
30782^595122-5179150Stefano Morozzi07/2022
30793*10^179138+89179139Robert Price10/2018
3080(52*10^179062-133)/9179063Robert Price09/2021
30812^594531+82253178972Enzo Doria09/2016
3082(664*10^178939-61)/9178941Robert Price09/2021
30832^594260-2787899178891Enzo Doria11/2015
3084(14*10^178822+67)/9178823Robert Price05/2022
3085(29*10^178732-119)/9178733Robert Price12/2021
30862^593631+101381178701Jorge Menendez04/2018
308710^178695+136719178696Patrick De Geest05/2016
308810^178695-71178695Serge Batalov12/2014
3089(2*10^178649-161)/3178649Robert Price12/2020
3090(691^62903-1)/690178609Michael Stocker05/2020
3091(2^148330+1)^4-2178608Cletus Emmanuel12/2003
30922^593242+28309178584Enzo Doria01/2024
30932^593222-14145178578Jorge Menendez10/2017
30947*10^178566+33178567Robert Price06/2020
30952^593178+1867219178565Enzo Doria03/2016
30962^593152+22441178557Enzo Doria09/2023
3097(38*10^178456+151)/9178457Robert Price03/2022
3098(302*10^178369+13)/9178371Robert Price02/2020
3099(26*10^178296-113)/3178297Robert Price06/2020
3100(18^142031-1)/17178287Paul Bourdelais03/2010
3101(13*10^178233+137)/3178234Robert Price06/2021
3102(5*10^178206+91)/3178207Robert Price04/2018
31032^591872-291929178172Enzo Doria07/2015
31042^591682-286871178115Enzo Doria07/2015
3105(7^210761-5^210761)/2178114Jon Grantham08/2023
31064*10^178091+9178092Robert Price05/2015
31072^591435+335931178040Enzo Doria09/2024
3108410747#+478483178007Makoto Morimoto02/2016
31093*10^177872+73177873Robert Price08/2018
31102^590762-396765177838Enzo Doria08/2013
3111(136*10^177754-1)/9177756Serge Batalov12/2014
3112ReverseConsecutiveIntegerPrime(37765)177719Eric W. Weisstein04/2010
3113Smr(37765)177719Eric W. Weisstein12/2021
3114598^128^209+209^128^598177594Henri Lifchitz03/2025
3115(266*10^177577-11)/3177579Robert Price04/2020
3116(11*10^177466-113)/3177467Robert Price10/2018
31173*10^177373-97177374Robert Price07/2018
31182^589204+1881151177369Enzo Doria11/2016
31192^589132-69479177347Enzo Doria01/2016
3120(3^371666)/(371666^3)177314Henri Lifchitz05/2025
3121(101*10^177302-17)/3177304Robert Price02/2020
31222^588912-113519177281Enzo Doria08/2014
3123(682*10^177266-7)/9177268Robert Price08/2021
312415^150706+2177245Robert Price06/2015
31252^588403+335931177127Enzo Doria09/2024
3126(31208^39601-1)/(31208^199-1)177084Ryan Propper11/2023
31272^588194-1861001177065Enzo Doria11/2015
31285*10^177016-37177017Robert Price11/2021
3129fibonacci(846926)-4176997Jon Grantham08/2023
3130(23*10^176964-47)/3176965Robert Price09/2019
313120530^41031+41031^20530176942Norbert Schneider07/2022
3132(19*10^176932+521)/9176933Robert Price05/2018
3133(8*10^176908+43)/3176909Robert Price06/2018
3134(85*10^176900+203)/9176901Robert Price09/2020
31352^587560-113699176874Enzo Doria09/2014
313620596^40995+40995^20596176844Norbert Schneider07/2022
3137(101*10^176815-17)/3176817Robert Price02/2020
3138(25*10^176715-37)/3176716Robert Price10/2019
31395^252763-12862176674Enzo Doria05/2014
314038442^38531+38531^38442176658Norbert Schneider09/2022
31412^586829+23961176654Enzo Doria10/2023
31422^586804+81721176646Enzo Doria08/2016
3143(10^176584+77)/3176584Robert Price01/2018
31442^586570+1874419176576Enzo Doria06/2016
3145(157*10^176482-1)/3176484Robert Price01/2022
31465*2^586202+3176466Jon Grantham07/2023
314727122^39799-39799^27122176442Frank Doornink01/2024
31482^585994-3311176402Yves Minet12/2014
31498*10^176383-81176384Robert Price02/2021
3150(23*10^176357+61)/3176358Robert Price01/2022
31512^585832-112799176354Enzo Doria07/2014
3152fibonacci(843383)+4176257Jon Grantham08/2023
3153(29*10^176240+49)/3176241Robert Price09/2021
3154(2^585387-11)/3176219Stefano Morozzi08/2022
31552^585336-461039176204Enzo Doria06/2015
3156(25*10^176164+143)/3176165Robert Price08/2020
31572^585095-1848127176132Enzo Doria08/2015
3158(5*10^176101-311)/9176101Robert Price12/2021
31596*10^176092+77176093Robert Price06/2020
31602^584950-115451176088Enzo Doria07/2015
3161(646*10^176044+11)/9176046Robert Price10/2021
3162(7^208283-5^208283)/2176020Jon Grantham08/2023
31632^584671-3697176004Yves Minet03/2017
3164(13*10^175965-37)/3175966Robert Price01/2019
316531728^39089-39089^31728175957Frank Doornink01/2024
31662*10^175860-87175861Robert Price04/2018
316727009^39670-39670^27009175798Frank Doornink01/2024
3168(86*10^175774-221)/9175775Robert Price09/2019
31692^583614+216037175686Enzo Doria11/2023
31709*10^175654+47175655Robert Price01/2022
317125430^39869-39869^25430175637Frank Doornink01/2024
317210^175608+2971175609Mike Oakes05/2010
317310^175608-55829175608Patrick De Geest09/2013
31742^583051+1879793175516Enzo Doria09/2016
3175(76*10^175514+491)/9175515Robert Price10/2021
31772^582860-23829175459Enzo Doria08/2013
3176(200^76253-1)/199175459Anonymous06/2024
3178(8*10^175428-53)/9175428Serge Batalov11/2022
3179(28*10^175417-67)/3175418Robert Price10/2020
31802^582670-23913175402Enzo Doria08/2013
31812^582573-29563175372Enzo Doria08/2015
31822^582435-1862767175331Enzo Doria12/2015
318310^175295-40000001175295Robert Price07/2022
318431093^39018-39018^31093175295Frank Doornink01/2024
3185(11*10^175250-149)/3175251Robert Price09/2018
3186(29*10^175236+31)/3175237Robert Price04/2021
31872^582072-1848599175222Enzo Doria08/2015
3188(404267#+465)/(3^4*5^2*31)175208Makoto Morimoto06/2019
3189Phi(262767,10)/259613797175168Makoto Kamada12/2022
3190(2^581871-15)/7175160Stefano Morozzi08/2022
3191(5*10^175117-311)/9175117Robert Price12/2021
319231193^38966-38966^31193175116Frank Doornink01/2024
31932^581695+225893175108Enzo Doria08/2024
319410^175093-89175093Riley Fisher10/2023
3195(220221^32768+1)/2175075Serge Batalov03/2018
31962^581560+1874911175068Enzo Doria06/2016
3197(25*10^174987-97)/9174988Robert Price01/2022
3198(75^93307-1)/74174955Paul Bourdelais09/2017
319926446^39555-39555^26446174927Frank Doornink03/2024
320031522^38883-38883^31522174920Frank Doornink01/2024
3201(27398^39601-1)/(27398^199-1)174855Ryan Propper11/2023
3202(861^59557-1)/860174798Jinyuan Wang11/2023
320331492^38859-38859^31492174796Frank Doornink01/2024
3204(47*10^174790+493)/9174791Robert Price03/2019
32052^580528-114035174757Enzo Doria11/2014
3206(19*10^174754+737)/9174755Robert Price07/2018
3207V(1045270)/4181081/12543241/81333115129561174730Serge Batalov07/2024
3208(35*10^174704-377)/9174705Robert Price07/2018
3210(49*10^174681+293)/9174682Robert Price03/2021
32096*10^174681+11174682Robert Price07/2022
32113*10^174665-97174666Robert Price07/2018
32122^580046-459161174612Enzo Doria05/2015
32132^579992-39779174595Enzo Doria09/2015
321425613^39582-39582^25613174496Frank Doornink02/2024
3215(29*10^174481-149)/3174482Robert Price08/2022
3216(4*10^174423+101)/3174424Robert Price11/2021
3217(2^579371-17)/3174408Stefano Morozzi08/2022
3218(2*10^174301-71)/3174301Robert Price12/2017
321914^152048+3174267Paul Bourdelais12/2020
3220(2^578696+1)/257174203Lelio R Paula09/2015
32212^578656-1851809174193Enzo Doria08/2015
32222^578583-113917174171Enzo Doria10/2014
32232^578434-83174126Yves Minet07/2017
322415^148048-2174118Robert Price06/2015
32255*10^174101+81174102Robert Price03/2019
32262^578346+2794249174100Enzo Doria03/2016
322710^173947+1372429173948Patrick De Geest08/2021
322910^173947-500000001173947Robert Price12/2020
322810^173947-286391173947Patrick De Geest08/2021
32305*10^173904-13173905Robert Price01/2019
3231(8*10^173862-59)/3173863Robert Price08/2021
3232(71*10^173854-287)/9173855Robert Price09/2019
3233(43*10^173826+101)/9173827Robert Price11/2018
32352*10^173809-87173810Robert Price04/2018
3234(17^141263-1)/27122512173810Paul Vanderveen05/2025
3236(2^577372-23)/7173806Stefano Morozzi08/2022
3237(L!41532)/2173772Serge Batalov07/2017
32382^577146-49877173739Enzo Doria10/2015
32392^576889+49727173661Enzo Doria09/2016
3240(19^173604)%(10^173604)173604Henri Lifchitz05/2025
3241(167*10^173571-17)/3173573Robert Price03/2020
324237803^37916+37916^37803173562Norbert Schneider06/2022
32435*10^173534+29173535Robert Price12/2020
3244(2^576551-1)/4612409/64758208321/242584327930759173528Dario Alpern06/2014
32454*10^173509+99173510Robert Price12/2020
3246(13*10^173467-37)/3173468Robert Price01/2019
32472^576016-113919173399Enzo Doria11/2014
32482^575911-1849387173367Enzo Doria08/2015
324921554^40005-40005^21554173363Norbert Schneider04/2025
32502^575879+215843173357Enzo Doria11/2023


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 05 2025 13:49 (Time in France)

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