PRP Records

Probable Primes Top 10000

(297738 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 ?
2501(101^91463+1)/102183320Paul Bourdelais11/2017
25022^608965-113989183317Enzo Doria10/2014
2503A005165(43592)183312Serge Batalov07/2017
2504(61*10^183294+119)/9183295Robert Price05/2019
25052^608814-461261183272Enzo Doria06/2015
2506(163*10^183227-1)/9183229Serge Batalov12/2014
25072^608541-608541^2183190Henri Lifchitz02/2018
25082^608293+143807183115Enzo Doria10/2016
25092^608164-462419183076Enzo Doria08/2015
25102^607950-1862303183012Enzo Doria12/2015
25115*3^383376+2^383376182918Jon Grantham08/2023
2512(46*10^182896+683)/9182897Robert Price03/2019
2513(2*10^182787+73)/3182787Robert Price09/2020
25142^607101+1871987182756Enzo Doria05/2016
25152^606869-69175182686Enzo Doria11/2015
25168*10^182671+71182672Robert Price05/2022
2517(23*10^182666-71)/3182667Robert Price07/2020
25183*10^182614-11182615Robert Price07/2018
25192^606560-357182593Enzo Doria05/2014
252066*10^182420+7182422Robert Price07/2020
25212^605687+1866983182330Enzo Doria03/2016
25222^605655-114445182321Enzo Doria02/2015
252394*10^182291-3182293Robert Price05/2020
2524(20^140053+1)/21182212Paul Bourdelais04/2010
2525(14*10^182177-221)/9182178Robert Price04/2018
25262^605174-112751182176Enzo Doria06/2014
2527(905^61609-1)/904182154Anonymous05/2024
25282^604761+1874507182052Enzo Doria06/2016
25292^604705+1871957182035Enzo Doria05/2016
2530(14*10^182000+229)/9182001Robert Price03/2018
2531(10^181996+41)/3181996Robert Price12/2017
2532(17*10^181979+91)/9181980Robert Price02/2022
2533(5*10^181950-101)/3181951Robert Price04/2018
25342^603915+75233181797Enzo Doria04/2016
253539470^39537+39537^39470181723Norbert Schneider12/2022
2536(10^181710+7)/563747/2019847181698Alfred Reich08/2021
25377*10^181594-57181595Robert Price06/2020
25388*10^181580+29181581Robert Price11/2021
2539(83*10^181544+61)/9181545Serge Batalov01/2023
2540(2*10^181457+7)/9181457Rytis Slatkevicius01/2023
25413*10^181445+23181446Robert Price03/2022
2542(194*10^181369-11)/3181371Robert Price09/2020
254311^174145-360181354Enzo Doria10/2012
25442^602351-396765181326Enzo Doria08/2013
25456*10^181306+17181307Robert Price04/2019
2546(353^71143-1)/352181254Anonymous04/2024
2547(286*10^181220-1)/3181222Robert Price11/2020
25482^601957-113833181208Enzo Doria09/2014
254966^99581-65^99581181193Robert Price09/2013
255010^181182+383973181183Patrick De Geest04/2016
255110^181182-21181182Serge Batalov12/2014
2552(797*10^181171-41)/9181173Robert Price04/2022
25532^601722+74209181137Enzo Doria08/2023
2554(5*10^181127-29)/3181128Robert Price03/2018
25552^601521-29143181076Enzo Doria07/2015
25562^601442-2797811181053Enzo Doria04/2016
255744*10^181029+3181031Robert Price04/2020
25585*10^180992-9180993Robert Price05/2015
255910^180979+79477180980Patrick De Geest04/2016
256010^180979+107739180980Patrick De Geest04/2016
256110^180979-11180979Serge Batalov12/2014
25622^601023-113851180926Enzo Doria10/2014
2563(23*10^180862-143)/3180863Robert Price12/2019
25643*10^180852+29180853Robert Price05/2018
2565(277*10^180782-7)/9180784Robert Price02/2022
25662^600412+29851180743Enzo Doria03/2024
2567(8*10^180725-629)/9180725Robert Price01/2022
2568(79*10^180710-1)/3180712Robert Price02/2020
25692^600300-1852559180709Enzo Doria08/2015
2570(2*10^180706-77)/3180706Robert Price02/2021
2571(156^82393-1)/155180696Anonymous06/2024
2572(10^180689+71)/9180689Serge Batalov07/2015
25732^600209+76487180681Enzo Doria05/2016
25742^599999+378461180618Norman Luhn09/2023
2575(8*10^180536-269)/9180536Robert Price09/2021
25762^599702-369885180529Enzo Doria11/2013
2577Tau(643^11688)180524Nik Lygeros / Olivier Rozier05/2015
2578(2951*29^123418-3)/4180490Curtis Bright05/2015
2579(29*10^180432-17)/3180433Robert Price09/2019
25804*10^180360+93180361Robert Price08/2018
25812^599035+219323180328Enzo Doria03/2024
25822^598942+80779180300Enzo Doria07/2016
2583(38*10^180296+403)/9180297Robert Price10/2018
2584(85*10^180241+77)/9180242Robert Price07/2022
25852^598591-1844797180194Enzo Doria06/2015
2586(100^90089+1)/101180176Paul Bourdelais08/2017
25872^598301+28517180107Enzo Doria01/2024
2588(29*10^180072+691)/9180073Robert Price08/2021
2589(59*10^180038+157)/9180039Robert Price12/2021
259095*10^180019-9180021Robert Price01/2022
25916*10^179970+91179971Robert Price05/2019
2592(4*10^179963-79)/3179964Robert Price02/2018
2593(403*10^179944-43)/9179946Robert Price06/2021
2594Gamma-Prime(179849)179849Eric W. Weisstein06/2011
25952^597424-1859729179843Enzo Doria11/2015
2596Phi(180683,10)179760Maksym Voznyy09/2015
2597(10^180683-1)*9/(10^643-1)/(10^281-1)179760Robert Price07/2016
2598(3^376657-2^376657)/22301107657179701Mike Oakes04/2017
2599(29*10^179697+223)/9179698Robert Price09/2018
2600U(1289697)179687Serge Batalov07/2024
26022^596884+73179680Stefano Morozzi04/2021
2601(11*10^179679+13)/3179680Robert Price03/2022
2603(68*10^179656+7)/3179658Robert Price01/2020
2604(10^179643+173)/3179643Robert Price05/2021
26052^596690-461261179622Enzo Doria07/2015
26062^596684-113939179620Enzo Doria10/2014
26072^596642+39179608Jon Grantham08/2023
26082*10^179602+63179603Robert Price05/2018
260932262^39815-39815^32262179514Frank Doornink02/2024
2610(25*10^179488-403)/9179489Robert Price01/2021
26117*10^179460+99179461Robert Price05/2021
26122^596127+74333179453Enzo Doria07/2023
26133^375887-112696179344Enzo Doria07/2014
26144*10^179265-71179266Robert Price12/2018
26152*10^179193+83179194Robert Price12/2021
26162^595144-1850429179157Enzo Doria08/2015
26172^595122-5179150Stefano Morozzi07/2022
26183*10^179138+89179139Robert Price10/2018
2619(52*10^179062-133)/9179063Robert Price09/2021
26202^594531+82253178972Enzo Doria09/2016
2621(664*10^178939-61)/9178941Robert Price09/2021
26222^594260-2787899178891Enzo Doria11/2015
2623(14*10^178822+67)/9178823Robert Price05/2022
2624(29*10^178732-119)/9178733Robert Price12/2021
26252^593631+101381178701Jorge Menendez04/2018
262610^178695+136719178696Patrick De Geest05/2016
262710^178695-71178695Serge Batalov12/2014
2628(2*10^178649-161)/3178649Robert Price12/2020
2629(691^62903-1)/690178609Michael Stocker05/2020
2630(2^148330+1)^4-2178608Cletus Emmanuel12/2003
26312^593242+28309178584Enzo Doria01/2024
26322^593222-14145178578Jorge Menendez10/2017
26337*10^178566+33178567Robert Price06/2020
26342^593178+1867219178565Enzo Doria03/2016
26352^593152+22441178557Enzo Doria09/2023
2636(38*10^178456+151)/9178457Robert Price03/2022
2637(302*10^178369+13)/9178371Robert Price02/2020
2638(26*10^178296-113)/3178297Robert Price06/2020
2639(18^142031-1)/17178287Paul Bourdelais03/2010
2640(13*10^178233+137)/3178234Robert Price06/2021
2641(5*10^178206+91)/3178207Robert Price04/2018
26422^591872-291929178172Enzo Doria07/2015
26432^591682-286871178115Enzo Doria07/2015
2644(7^210761-5^210761)/2178114Jon Grantham08/2023
26454*10^178091+9178092Robert Price05/2015
26462^591435+335931178040Enzo Doria09/2024
2647410747#+478483178007Makoto Morimoto02/2016
26483*10^177872+73177873Robert Price08/2018
26492^590762-396765177838Enzo Doria08/2013
2650(136*10^177754-1)/9177756Serge Batalov12/2014
2651ReverseConsecutiveIntegerPrime(37765)177719Eric W. Weisstein04/2010
2652Smr(37765)177719Eric W. Weisstein12/2021
2653(266*10^177577-11)/3177579Robert Price04/2020
2654(11*10^177466-113)/3177467Robert Price10/2018
26553*10^177373-97177374Robert Price07/2018
26562^589204+1881151177369Enzo Doria11/2016
26572^589132-69479177347Enzo Doria01/2016
2658(101*10^177302-17)/3177304Robert Price02/2020
26592^588912-113519177281Enzo Doria08/2014
2660(682*10^177266-7)/9177268Robert Price08/2021
266115^150706+2177245Robert Price06/2015
26622^588403+335931177127Enzo Doria09/2024
2663(31208^39601-1)/(31208^199-1)177084Ryan Propper11/2023
26642^588194-1861001177065Enzo Doria11/2015
26655*10^177016-37177017Robert Price11/2021
2666fibonacci(846926)-4176997Jon Grantham08/2023
2667(23*10^176964-47)/3176965Robert Price09/2019
266820530^41031+41031^20530176942Norbert Schneider07/2022
2669(19*10^176932+521)/9176933Robert Price05/2018
2670(8*10^176908+43)/3176909Robert Price06/2018
2671(85*10^176900+203)/9176901Robert Price09/2020
26722^587560-113699176874Enzo Doria09/2014
267320596^40995+40995^20596176844Norbert Schneider07/2022
2674(101*10^176815-17)/3176817Robert Price02/2020
2675(25*10^176715-37)/3176716Robert Price10/2019
26765^252763-12862176674Enzo Doria05/2014
267738442^38531+38531^38442176658Norbert Schneider09/2022
26782^586829+23961176654Enzo Doria10/2023
26792^586804+81721176646Enzo Doria08/2016
2680(10^176584+77)/3176584Robert Price01/2018
26812^586570+1874419176576Enzo Doria06/2016
2682(157*10^176482-1)/3176484Robert Price01/2022
26835*2^586202+3176466Jon Grantham07/2023
268427122^39799-39799^27122176442Frank Doornink01/2024
26852^585994-3311176402Yves Minet12/2014
26868*10^176383-81176384Robert Price02/2021
2687(23*10^176357+61)/3176358Robert Price01/2022
26882^585832-112799176354Enzo Doria07/2014
2689fibonacci(843383)+4176257Jon Grantham08/2023
2690(29*10^176240+49)/3176241Robert Price09/2021
2691(2^585387-11)/3176219Stefano Morozzi08/2022
26922^585336-461039176204Enzo Doria06/2015
2693(25*10^176164+143)/3176165Robert Price08/2020
26942^585095-1848127176132Enzo Doria08/2015
2695(5*10^176101-311)/9176101Robert Price12/2021
26966*10^176092+77176093Robert Price06/2020
26972^584950-115451176088Enzo Doria07/2015
2698(646*10^176044+11)/9176046Robert Price10/2021
2699(7^208283-5^208283)/2176020Jon Grantham08/2023
27002^584671-3697176004Yves Minet03/2017
2701(13*10^175965-37)/3175966Robert Price01/2019
270231728^39089-39089^31728175957Frank Doornink01/2024
27032*10^175860-87175861Robert Price04/2018
270427009^39670-39670^27009175798Frank Doornink01/2024
2705(86*10^175774-221)/9175775Robert Price09/2019
27062^583614+216037175686Enzo Doria11/2023
27079*10^175654+47175655Robert Price01/2022
270825430^39869-39869^25430175637Frank Doornink01/2024
270910^175608+2971175609Mike Oakes05/2010
271010^175608-55829175608Patrick De Geest09/2013
27112^583051+1879793175516Enzo Doria09/2016
2712(76*10^175514+491)/9175515Robert Price10/2021
27142^582860-23829175459Enzo Doria08/2013
2713(200^76253-1)/199175459Anonymous06/2024
2715(8*10^175428-53)/9175428Serge Batalov11/2022
2716(28*10^175417-67)/3175418Robert Price10/2020
27172^582670-23913175402Enzo Doria08/2013
27182^582573-29563175372Enzo Doria08/2015
27192^582435-1862767175331Enzo Doria12/2015
272010^175295-40000001175295Robert Price07/2022
272131093^39018-39018^31093175295Frank Doornink01/2024
2722(11*10^175250-149)/3175251Robert Price09/2018
2723(29*10^175236+31)/3175237Robert Price04/2021
27242^582072-1848599175222Enzo Doria08/2015
2725(404267#+465)/(3^4*5^2*31)175208Makoto Morimoto06/2019
2726Phi(262767,10)/259613797175168Makoto Kamada12/2022
2727(2^581871-15)/7175160Stefano Morozzi08/2022
2728(5*10^175117-311)/9175117Robert Price12/2021
272931193^38966-38966^31193175116Frank Doornink01/2024
27302^581695+225893175108Enzo Doria08/2024
273110^175093-89175093Riley Fisher10/2023
2732(220221^32768+1)/2175075Serge Batalov03/2018
27332^581560+1874911175068Enzo Doria06/2016
2734(25*10^174987-97)/9174988Robert Price01/2022
2735(75^93307-1)/74174955Paul Bourdelais09/2017
273626446^39555-39555^26446174927Frank Doornink03/2024
273731522^38883-38883^31522174920Frank Doornink01/2024
2738(27398^39601-1)/(27398^199-1)174855Ryan Propper11/2023
2739(861^59557-1)/860174798Jinyuan Wang11/2023
274031492^38859-38859^31492174796Frank Doornink01/2024
2741(47*10^174790+493)/9174791Robert Price03/2019
27422^580528-114035174757Enzo Doria11/2014
2743(19*10^174754+737)/9174755Robert Price07/2018
2744V(1045270)/4181081/12543241/81333115129561174730Serge Batalov07/2024
2745(35*10^174704-377)/9174705Robert Price07/2018
2747(49*10^174681+293)/9174682Robert Price03/2021
27466*10^174681+11174682Robert Price07/2022
27483*10^174665-97174666Robert Price07/2018
27492^580046-459161174612Enzo Doria05/2015
27502^579992-39779174595Enzo Doria09/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 12 2024 22:37 (Time in France)

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