PRP Records

Probable Primes Top 10000

(294113 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
22512^587560-113699176874Enzo Doria09/2014
225220596^40995+40995^20596176844Norbert Schneider07/2022
2253(101*10^176815-17)/3176817Robert Price02/2020
2254(25*10^176715-37)/3176716Robert Price10/2019
22555^252763-12862176674Enzo Doria05/2014
225638442^38531+38531^38442176658Norbert Schneider09/2022
22572^586829+23961176654Enzo Doria10/2023
22582^586804+81721176646Enzo Doria08/2016
2259(10^176584+77)/3176584Robert Price01/2018
22602^586570+1874419176576Enzo Doria06/2016
2261(157*10^176482-1)/3176484Robert Price01/2022
22625*2^586202+3176466Jon Grantham07/2023
22632^585994-3311176402Yves Minet12/2014
22648*10^176383-81176384Robert Price02/2021
2265(23*10^176357+61)/3176358Robert Price01/2022
22662^585832-112799176354Enzo Doria07/2014
2267fibonacci(843383)+4176257Jon Grantham08/2023
2268(29*10^176240+49)/3176241Robert Price09/2021
2269(2^585387-11)/3176219Stefano Morozzi08/2022
22702^585336-461039176204Enzo Doria06/2015
2271(25*10^176164+143)/3176165Robert Price08/2020
22722^585095-1848127176132Enzo Doria08/2015
2273(5*10^176101-311)/9176101Robert Price12/2021
22746*10^176092+77176093Robert Price06/2020
22752^584950-115451176088Enzo Doria07/2015
2276(646*10^176044+11)/9176046Robert Price10/2021
2277(7^208283-5^208283)/2176020Jon Grantham08/2023
22782^584671-3697176004Yves Minet03/2017
2279(13*10^175965-37)/3175966Robert Price01/2019
22802*10^175860-87175861Robert Price04/2018
2281(86*10^175774-221)/9175775Robert Price09/2019
22822^583614+216037175686Enzo Doria11/2023
22839*10^175654+47175655Robert Price01/2022
228410^175608+2971175609Mike Oakes05/2010
228510^175608-55829175608Patrick De Geest09/2013
22862^583051+1879793175516Enzo Doria09/2016
2287(76*10^175514+491)/9175515Robert Price10/2021
22882^582860-23829175459Enzo Doria08/2013
2289(8*10^175428-53)/9175428Serge Batalov11/2022
2290(28*10^175417-67)/3175418Robert Price10/2020
22912^582670-23913175402Enzo Doria08/2013
22922^582573-29563175372Enzo Doria08/2015
22932^582435-1862767175331Enzo Doria12/2015
229410^175295-40000001175295Robert Price07/2022
2295(11*10^175250-149)/3175251Robert Price09/2018
2296(29*10^175236+31)/3175237Robert Price04/2021
22972^582072-1848599175222Enzo Doria08/2015
2298(404267#+465)/(3^4*5^2*31)175208Makoto Morimoto06/2019
2299Phi(262767,10)/259613797175168Makoto Kamada12/2022
2300(2^581871-15)/7175160Stefano Morozzi08/2022
2301(5*10^175117-311)/9175117Robert Price12/2021
230210^175093-89175093Riley Fisher10/2023
2303(220221^32768+1)/2175075Serge Batalov03/2018
23042^581560+1874911175068Enzo Doria06/2016
2305(25*10^174987-97)/9174988Robert Price01/2022
2306(75^93307-1)/74174955Paul Bourdelais09/2017
2307(27398^39601-1)/(27398^199-1)174855Ryan Propper11/2023
2308(861^59557-1)/860174798Jinyuan Wang11/2023
2309(47*10^174790+493)/9174791Robert Price03/2019
23102^580528-114035174757Enzo Doria11/2014
2311(19*10^174754+737)/9174755Robert Price07/2018
2312(35*10^174704-377)/9174705Robert Price07/2018
2313(49*10^174681+293)/9174682Robert Price03/2021
23146*10^174681+11174682Robert Price07/2022
23153*10^174665-97174666Robert Price07/2018
23162^580046-459161174612Enzo Doria05/2015
23172^579992-39779174595Enzo Doria09/2015
2318(29*10^174481-149)/3174482Robert Price08/2022
2319(4*10^174423+101)/3174424Robert Price11/2021
2320(2^579371-17)/3174408Stefano Morozzi08/2022
2321(2*10^174301-71)/3174301Robert Price12/2017
232214^152048+3174267Paul Bourdelais12/2020
2323(2^578696+1)/257174203Lelio R Paula09/2015
23242^578656-1851809174193Enzo Doria08/2015
23252^578583-113917174171Enzo Doria10/2014
23262^578434-83174126Yves Minet07/2017
232715^148048-2174118Robert Price06/2015
23285*10^174101+81174102Robert Price03/2019
23292^578346+2794249174100Enzo Doria03/2016
233010^173947+1372429173948Patrick De Geest08/2021
233210^173947-500000001173947Robert Price12/2020
233110^173947-286391173947Patrick De Geest08/2021
23335*10^173904-13173905Robert Price01/2019
2334(8*10^173862-59)/3173863Robert Price08/2021
2335(71*10^173854-287)/9173855Robert Price09/2019
2336(43*10^173826+101)/9173827Robert Price11/2018
23372*10^173809-87173810Robert Price04/2018
2338(2^577372-23)/7173806Stefano Morozzi08/2022
2339(L!41532)/2173772Serge Batalov07/2017
23402^577146-49877173739Enzo Doria10/2015
23412^576889+49727173661Enzo Doria09/2016
2342(167*10^173571-17)/3173573Robert Price03/2020
234337803^37916+37916^37803173562Norbert Schneider06/2022
23445*10^173534+29173535Robert Price12/2020
2345(2^576551-1)/4612409/64758208321/242584327930759173528Dario Alpern06/2014
23464*10^173509+99173510Robert Price12/2020
2347(13*10^173467-37)/3173468Robert Price01/2019
23482^576016-113919173399Enzo Doria11/2014
23492^575911-1849387173367Enzo Doria08/2015
23502^575879+215843173357Enzo Doria11/2023
2351515^63898+63898^515173280Norbert Schneider12/2022
23522^575614+9173278Stefano Morozzi04/2021
2353(16*10^173251+107)/3173252Robert Price03/2019
23542^575196-114053173152Enzo Doria11/2014
23557*10^173135-53173136Robert Price06/2020
2356(301*10^173047+23)/9173049Robert Price06/2021
23572^574591-115387172970Enzo Doria07/2015
2358(202*10^172940-13)/9172942Robert Price01/2020
235945^104608+104608^45172940Norbert Schneider06/2021
23602^574328+81121172890Enzo Doria07/2016
2361(115*10^172862-1)/3172864Serge Batalov12/2014
23623*10^172812+13172813Robert Price07/2018
23634*5^247217-9172798Lelio R Paula10/2015
23646*10^172772-31172773Robert Price07/2020
236569061#+(467617#)/(69061#)172766Makoto Morimoto10/2017
2366(34*10^172693-547)/9172694Robert Price03/2021
23675*10^172692+57172693Robert Price12/2018
23682^573668-2782319172692Enzo Doria09/2015
23692^573444-1855109172624Enzo Doria09/2015
2370(14*10^172532-29)/3172533Robert Price09/2021
23713^361608+2172531Robert Price08/2014
2372(54^99563+1)/55172481Paul Bourdelais11/2017
23732^572592-114893172368Enzo Doria05/2015
23744*10^172354-39172355Robert Price09/2020
237537535^37674+37674^37535172338Norbert Schneider05/2022
2376(11*10^172322-119)/9172323Robert Price11/2021
23775^246497-4^246497172295Jean-Louis Charton11/2008
2378(38^109037-1)/37172254Paul Bourdelais10/2017
2379(4*10^172241+89)/3172242Robert Price08/2021
23803*10^172219+73172220Robert Price08/2018
2381A352736(15)172032Kellen Shenton05/2022
23822^571300+25861171979Enzo Doria11/2023
2383(36^110503+1)/37171975Lelio R Paula04/2017
23848*10^171934+71171935Robert Price05/2022
2385(11*10^171933+601)/9171934Robert Price02/2022
2386(22*10^171929-73)/3171930Robert Price04/2019
2387(49*10^171892-319)/9171893Robert Price10/2021
23884*10^171891-63171892Robert Price10/2018
238967*10^171882-9171884Robert Price03/2021
23902^570980-2782289171883Enzo Doria09/2015
2391(25*10^171849-37)/3171850Robert Price10/2019
239210^171832+387909171833Patrick De Geest08/2021
239310^171832-10001171832Robert Price02/2021
2395(2^(12*47563+13)-9)/7171818Kevin Acres11/2013
2394(2^570769-9)/7171818Stefano Morozzi08/2022
2396(74*10^171651-29)/9171652Robert Price06/2022
2397(536*10^171601-23)/9171603Robert Price02/2020
23987*10^171535-99171536Robert Price06/2019
2399(28*10^171534+101)/3171535Robert Price09/2020
24002^569563-1854607171456Enzo Doria09/2015
24013*10^171391+59171392Robert Price08/2018
2402(13*10^171306-37)/3171307Robert Price01/2019
24038*10^171296+87171297Robert Price10/2019
2404(55^98419-1)/54171284Paul Bourdelais12/2017
2405(29*10^171275+67)/3171276Robert Price12/2019
2406(457*10^171248-7)/9171250Robert Price09/2022
2407(194*10^171193+1)/3171195Robert Price01/2022
24082^568642+1876129171179Enzo Doria07/2016
24094*10^171146-47171147Robert Price10/2021
2410(19*10^170970+131)/3170971Robert Price06/2020
2411(46*10^170932+143)/9170933Robert Price01/2019
2412(79*10^170901-1)/3170903Robert Price02/2020
2413(58*10^170842+221)/9170843Robert Price02/2017
2414(29*10^170830+583)/9170831Robert Price06/2021
24153*10^170800+73170801Robert Price08/2018
2416(29*10^170799-119)/9170800Robert Price12/2021
241711^164009-270170798Enzo Doria10/2012
24182*10^170767+41170768Robert Price05/2018
24193^357706-112358170670Enzo Doria07/2014
2420TheodorusPrime(170657)170657Eric W. Weisstein08/2013
24212^566871+1876163170646Enzo Doria07/2016
2422(10657#+(404267#)/(10657#))/(1675379)170624Makoto Morimoto10/2017
24232^566496+7170533Donovan Johnson07/2006
2424(7^201653+1)/8170416Paul Bourdelais02/2010
24257*10^170348+33170349Robert Price06/2020
24262^565183-352021170138Enzo Doria07/2015
24272^565143-114457170125Enzo Doria02/2015
24283*2^565024-5170090Jon Grantham07/2023
24292^564976-49869170075Enzo Doria10/2015
2430(7*10^169944+23)/3169945Robert Price06/2020
2431(37*10^169943+251)/9169944Robert Price09/2021
24322^564526-351401169940Enzo Doria07/2015
24334*10^169759+19169760Robert Price10/2018
2434(2^563903-13)/5169752Stefano Morozzi08/2022
243521^128327-20^128327169677Jean-Louis Charton11/2014
24362^563583+89169656Stefano Morozzi04/2021
24372^563311+215813169574Enzo Doria11/2023
2438(4*10^169559+83)/3169560Robert Price02/2018
2439(194*10^169461-17)/3169463Robert Price09/2020
24402^562749+2793047169405Enzo Doria02/2016
2441(154*10^169337-1)/9169339Serge Batalov12/2014
2442(109*10^169337+11)/3169339Robert Price06/2022
2443(56*10^169311+691)/9169312Robert Price05/2019
24442^562369-29503169290Enzo Doria08/2015
2445(17*10^169283+19)/9169284Robert Price03/2021
244610^169074-5000000001169074Robert Price09/2022
24478*10^169071+59169072Robert Price11/2021
2448(10^169044+173)/3169044Robert Price05/2021
2449(22*10^169019+383)/9169020Robert Price05/2018
2450(64*10^168935+143)/9168936Robert Price05/2021
2451(22*10^168906+47)/3168907Robert Price06/2021
24525*10^168807+87168808Robert Price02/2019
2453(77*10^168803-149)/9168804Robert Price03/2022
24544*10^168788-47168789Robert Price10/2021
2455(154*10^168781+17)/9168783Robert Price06/2022
2456(418*10^168751-31)/9168753Robert Price05/2022
2457(29*10^168711+691)/9168712Robert Price08/2021
24582^560405-39943168699Enzo Doria09/2015
2459(397*10^168634+17)/9168636Robert Price03/2022
246089*10^168614-7168616Robert Price04/2020
2461(23*10^168608-83)/3168609Robert Price08/2019
2462(94*10^168541+11)/3168543Robert Price04/2020
24632^559686-350471168483Enzo Doria06/2015
24642^559672-1855889168479Enzo Doria09/2015
2465(5*10^168379-473)/9168379Robert Price01/2018
24662^559000-59939168276Enzo Doria11/2015
24672^558830+25009168225Enzo Doria11/2023
2468(16*10^168181+41)/3168182Robert Price03/2019
2469(19*10^168173+77)/3168174Robert Price05/2019
2470(74*10^168170+529)/9168171Robert Price02/2022
24712^558640-114149168168Enzo Doria12/2014
24722^558498-1849277168125Enzo Doria08/2015
24732^558476-1850249168119Enzo Doria08/2015
2474(7*10^168067+71)/3168068Robert Price05/2018
24752^558150-1852211168020Enzo Doria08/2015
24762^558125-113661168013Enzo Doria09/2014
2477393^64747-392^64747167980Jean-Louis Charton08/2012
2478(8*10^167965-11)/3167966Robert Price07/2023
2479(13*10^167911+179)/3167912Robert Price11/2018
2480(26*10^167861-167)/3167862Robert Price10/2019
248136^107827-107827167812Kellen Shenton06/2023
248239^105456+2167788Robert Price04/2015
2483(28^115877-1)/27167691Paul Bourdelais12/2017
24846*10^167662-13167663Robert Price07/2022
248510^167639+121911167640Patrick De Geest07/2018
248610^167639-8001167639Robert Price03/2018
24872^556504-462059167525Enzo Doria07/2015
2488(88*10^167522-637)/9167523Robert Price11/2020
24895*10^167510+9167511Robert Price08/2015
24907*10^167437-93167438Robert Price08/2020
249111^160663+6167314Paul Bourdelais02/2021
2492(7*10^167308-493)/9167308Robert Price04/2021
24932^555759+74333167301Enzo Doria07/2023
24942^555343+1874333167175Enzo Doria06/2016
24952^555210-461261167135Enzo Doria07/2015
24969*10^166996+59166997Robert Price01/2020
2497(68*10^166976-329)/9166977Robert Price03/2021
2498(64*10^166901+683)/9166902Robert Price06/2022
24992^554372+1880527166883Enzo Doria11/2016
25002^554299+72173166861Enzo Doria04/2016


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 05 2023 08:12 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!