PRP Records

Probable Primes Top 10000

(253466 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 ?
22512^415259+77243125006Enzo Doria05/2016
22522^415144-3683124971Yves Minet10/2011
22532^414874+79124890Lelio R Paula01/2015
2254(2^414765+7)/1389124854Lelio R Paula05/2014
22552^414618+79459124813Enzo Doria06/2016
22562^414432-1846709124757Enzo Doria07/2015
22572*10^124751-51124752Robert Price04/2018
2258(56*10^124735+367)/9124736Robert Price06/2019
2259(13*2^414274-1)/153124708Lelio R Paula05/2014
2260(7*10^124648+197)/3124649Robert Price07/2018
22622^414032-5124637Henri Lifchitz07/2006
22612^414032+1872331124637Enzo Doria05/2016
226314120^30009-30009^14120124533Norbert Schneider02/2015
226464^68909-63^68909124463Robert Price07/2013
22652^413387+76253124442Enzo Doria04/2016
22662^413352+524287124432Paul Underwood09/2018
2267287117#+391613124424Nicolas PALAU01/2017
2268(4*10^124420+83)/3124421Robert Price02/2018
2269(27*2^413207-1)/108335124385Lelio R Paula05/2014
2270(41*10^124335-383)/9124336Robert Price11/2018
22712^412868-120599124286Paul Bourdelais02/2012
227245^75145-2124231Lelio R Paula08/2015
22732^412645-112213124219Enzo Doria06/2014
22742^412248+74611124100Enzo Doria04/2016
2275(22*10^124096-13)/9124097Robert Price06/2018
22762^412192-3329124083Yves Minet12/2014
2277(25*2^412191-1)/23124082Lelio R Paula05/2014
2278(25*10^124076-67)/3124077Robert Price06/2019
2279F(593689)124074Henri Lifchitz01/2005
2280(11*2^412161+1)/19124073Lelio R Paula05/2014
22812^411884-113279123990Enzo Doria07/2014
2282(2^411832+1)/257123972Lelio R Paula05/2014
2283(26*10^123970-89)/9123971Robert Price06/2018
22842^411790-1853531123962Enzo Doria08/2015
2285(5^177337+1)/6123953Paul Bourdelais11/2008
22862^411711-113257123938Enzo Doria07/2014
2287(23*2^411675-1)/3123928Lelio R Paula05/2014
2288(11*10^123899-179)/3123900Robert Price09/2018
22892^411325-351103123822Enzo Doria06/2015
22902^411052+1872481123739Enzo Doria05/2016
22912^410997+39123723Lelio R Paula05/2014
2292155^56438+154123618Norbert Schneider01/2019
22932^410596-39123602Lelio R Paula05/2014
22942^410540-115079123585Enzo Doria06/2015
2295(7*10^123563+107)/3123564Robert Price02/2018
2296(3*2^410392-1)/9229123537Lelio R Paula05/2014
22972^410206-113081123485Enzo Doria07/2014
2298(25*2^410192+1)/10397123478Lelio R Paula04/2014
22992^409909-189123395Enzo Doria05/2014
23002^409896-109043123391Enzo Doria04/2014
23012^409890+75409123390Enzo Doria04/2016
2302133^58076-2123345Lelio R Paula10/2017
2303F(590041)123311Henri Lifchitz01/2005
23042^409566-113501123292Enzo Doria08/2014
23052^409533+77747123282Enzo Doria05/2016
23062^409436-112799123253Enzo Doria06/2014
23072^409225+1873787123189Enzo Doria06/2016
23082^409174+73009123174Enzo Doria04/2016
23092^409058-112685123139Enzo Doria06/2014
2310(13*10^123137-61)/3123138Robert Price11/2018
23114*10^123113+21123114Robert Price12/2018
23122^408778+77689123055Enzo Doria05/2016
23132^408690-75123028Lelio R Paula11/2013
2314(29*10^122996+673)/9122997Robert Price12/2018
23152^408574-2787341122994Enzo Doria03/2016
23163*10^122977+37122978Robert Price08/2018
2317Phi(157825,10)122961Maksym Voznyy06/2015
2318(68*10^122933-419)/9122934Robert Price07/2019
2319(13*2^408283+1)/1665122904Lelio R Paula05/2014
2320(16*10^122871+77)/3122872Robert Price03/2019
2321(11*2^408100-1)/35122850Lelio R Paula04/2014
2322(19*10^122836-43)/3122837Robert Price05/2019
2323(2^407821-lucasV(1,2,407821)+1)/2122767Mike Oakes11/2016
2324(32*10^122733-77)/9122734Robert Price06/2018
2325(21*2^407604-1)/215122701Lelio R Paula04/2014
2326(22*10^122681+161)/3122682Robert Price05/2019
2327(21*2^407433-1)/13122650Lelio R Paula04/2014
2328(73*10^122592-1)/9122593Robert Price01/2015
2329(5*10^122592+91)/3122593Robert Price04/2018
23302^407179-112075122574Enzo Doria06/2014
2331(21*2^407131+1)/207517523122552Lelio R Paula04/2014
2332(66^67349+1)/67122543Paul Bourdelais09/2017
23332^407008-1867919122522Enzo Doria04/2016
233411^117642-300122512Enzo Doria10/2012
2335(F(3*97700+1)^2+L(3*97700+1)^2)/2122509Henri Lifchitz10/2017
23362^406949+72197122504Enzo Doria04/2016
2337(19*10^122501+149)/3122502Robert Price05/2019
23382^406826-65122467Lelio R Paula11/2013
23392^406821-2797363122466Enzo Doria04/2016
23402^406758-17122447Lelio R Paula11/2013
2341(30^82883-1)/29122427Robert Price12/2011
2342(2^406583-1)/813167122388Jens K. Andersen02/2009
23434*10^122377+19122378Robert Price10/2018
23443*10^122345-97122346Robert Price07/2018
234597^61575-2122336Lelio R Paula12/2014
23462^406298+2799109122308Enzo Doria04/2016
23477*10^122294+57122295Robert Price06/2019
2348(27*2^406241-1)/10277122289Lelio R Paula04/2014
23492^406229-1849993122288Enzo Doria08/2015
23503*10^122274+7122275Robert Price07/2015
23512^406117+1876577122254Enzo Doria07/2016
23523^256199-2^256199122238Mike Oakes06/2005
23532^405992-78557122216Jorge Menendez03/2018
2354(8*10^122203+43)/3122204Robert Price06/2018
2355(58*10^122170+329)/9122171Robert Price05/2019
23562^405774+179149122151Enzo Doria06/2016
23575*10^122082+41122083Robert Price03/2019
23582^405514-3311122072Yves Minet12/2014
23592^405514-115511122072Enzo Doria07/2015
23602^405422-113261122045Enzo Doria07/2014
23612^405173+71237121970Enzo Doria04/2016
2362(2^405016+1)/257121920Lelio R Paula04/2014
23632^404858+71329121875Enzo Doria04/2016
23642^404813-114703121861Enzo Doria04/2015
23652^404764+77791121847Enzo Doria05/2016
2366317^48694+48694^317121787Norbert Schneider08/2015
23672^404536-115259121778Enzo Doria06/2015
23682^404501-631121767Yves Minet07/2012
236963^67620+2121672Lelio R Paula08/2015
2370(16*10^121633+167)/3121634Robert Price06/2019
2371(17*10^121621+1)/9121622Serge Batalov05/2010
2372(15*2^403912+1)/271121589Lelio R Paula05/2014
2373(10^121543-79)/3121543Robert Price01/2018
23742^403676+76831121519Enzo Doria05/2016
2375(7*10^121487+143)/3121488Robert Price03/2018
23762^403363-113635121425Enzo Doria08/2014
23772^403336-1861469121417Enzo Doria03/2016
2378p(24442)#/2-64121381Robert Price04/2017
237911^116555-720121380Enzo Doria11/2012
23802^403100-461267121346Enzo Doria07/2015
23812^403093-112213121344Enzo Doria06/2014
2382(316^48539+1)/317121330Eric Chen10/2017
23832^403004+1866361121317Enzo Doria03/2016
23842^402953+89121301Lelio R Paula10/2013
23852^402944-2788319121299Enzo Doria03/2016
2386(44*10^121297-719)/9121298Robert Price12/2018
2387(27*2^402865+1)/5121276Lelio R Paula04/2014
23882^402828-113183121264Enzo Doria07/2014
2389(17*10^121242+1)/9121243Serge Batalov05/2010
2390(15*2^402757+1)/101121242Lelio R Paula05/2014
23922^402715+1874223121230Enzo Doria06/2016
2391(35*10^121229-593)/9121230Robert Price07/2018
2393(91^61879+1)/92121222Paul Bourdelais09/2017
23947*10^121144+9121145Robert Price09/2015
23952^401725-113251120932Enzo Doria07/2014
2396(15*2^401677-1)/19120917Lelio R Paula05/2014
23972^401652+73711120910Enzo Doria04/2016
2398(2^401632+3)/79120902Lelio R Paula04/2014
23992^401406-2791331120836Enzo Doria03/2016
2400(28^83497+1)/29120832Robert Price07/2013
2401(22*10^120828+161)/3120829Robert Price05/2019
24022^401369+1867367120825Enzo Doria03/2016
2403(10^120782+29)/3120782Serge Batalov12/2014
24042^401215-1657120778Yves Minet07/2014
24052^401159+53120761Lelio R Paula10/2013
24062^401031-113047120723Enzo Doria07/2014
2407(29*2^400909-1)/303120685Lelio R Paula04/2014
24082^400571-15120584Lelio R Paula10/2013
2409(10^120574+359)/9120574Serge Batalov12/2014
24102^400424-216413120540Enzo Doria04/2013
2411(17*2^400200-1)/587120471Lelio R Paula05/2014
24122^400166+1874899120462Enzo Doria06/2016
2413(3*2^400045-1)/865120424Lelio R Paula04/2014
24142^399966+73759120402Enzo Doria04/2016
2415(112*10^120395-1)/3120397Serge Batalov12/2014
24162^399918-95120388Lelio R Paula04/2013
2417(49*10^120380-139)/9120381Robert Price03/2019
24182^399792-1849259120350Enzo Doria08/2015
24199*10^120342-7120343Robert Price09/2015
2420(13*10^120306-37)/3120307Robert Price01/2019
24212^399526-1861721120270Enzo Doria11/2015
2422(10^(2*60126+1)+36*10^60126-1)/9120253Robert Price10/2015
24232^399322-2798111120208Enzo Doria04/2016
242472^64693-71^64693120157Robert Price03/2014
24252^399111-28489120145Enzo Doria08/2015
24272^398877+105120074Donovan Johnson01/2006
2426(101*10^120072-87)/7120074Hans Havermann02/2015
2428(88^61751+1)/89120072Paul Bourdelais09/2017
24292^398710+57120024Lelio R Paula04/2013
24302^398691-115057120018Enzo Doria06/2015
2431L(574219)120005Renaud Lifchitz03/2004
24322^398571+60413119982Yves Minet03/2011
2433p(24179)#/2-64119949Robert Price04/2017
24342^398448+1872001119945Enzo Doria05/2016
2435634^42803+42803^634119938Norbert Schneider07/2019
24368*10^119930-3119931Ray Chandler04/2011
2437(10^119880+179)/9119880Serge Batalov12/2014
2438(9*2^398145+1)/73119853Lelio R Paula04/2014
2439(10^119836+77)/3119836Robert Price01/2018
24402^398029+1872527119819Enzo Doria05/2016
24412^397897-113541119779Enzo Doria08/2014
2442(21*2^397661-1)/27593119705Lelio R Paula04/2014
2443(58^67853-1)/57119653Paul Bourdelais09/2017
24442^397426+73849119638Enzo Doria04/2016
24452^396933-112723119489Enzo Doria06/2014
244611^114738-150119488Enzo Doria10/2012
2447(4*10^119474+149)/9119474Robert Price04/2018
24482^396790-21119446Lelio R Paula04/2013
2449(2^396633-7)/5119398Lelio R Paula04/2014
2450105^59050+104119352Norbert Schneider11/2016
2451126^56824-125119352Norbert Schneider12/2018
2452139^55690-138119345Norbert Schneider04/2019
2453790^41179+41179^790119322Norbert Schneider04/2019
24542^396374+73729119321Enzo Doria04/2016
24552^396258-459491119286Enzo Doria05/2015
24562^396128-396128-1119247Karsten Bonath06/2018
2457(2^395986+5)/76881119199Lelio R Paula04/2014
2458(23*2^395942-1)/91119190Lelio R Paula04/2014
2459(11*2^395548+1)/3119073Lelio R Paula04/2014
2460(30^80599+1)/31119054Robert Price07/2013
2461(43*10^119024-403)/9119025Robert Price01/2019
24622^395062-109121118926Enzo Doria04/2014
24632^395055-4627118924Yves Minet05/2019
2464(2^394918+78557)/3118882Lelio R Paula01/2015
2465(16*10^118852+77)/3118853Robert Price03/2019
2466(2^394739+3)/1883118826Lelio R Paula04/2014
24672^394266+71389118686Enzo Doria04/2016
24682^394215-51261118671Tony Prest / Never Odd Or Even04/2018
2469(2^394215-48793)/5/5118670Tony Prest / Never Odd Or Even04/2018
2470(2^394215-17063)/3/3/5118669Tony Prest / Never Odd Or Even04/2018
2471(2^394215-24393)/5/5/5/5/5118668Tony Prest / Never Odd Or Even04/2018
2472(2^394215-35885)/3/71/173118666Tony Prest / Never Odd Or Even04/2018
2473(2^394215-47925)/353/2269118665Tony Prest / Never Odd Or Even04/2018
2474(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673118650Tony Prest / Never Odd Or Even04/2018
2475(17*10^118635+13)/3118636Robert Price01/2019
24765^169727+2118635Lelio R Paula08/2013
24772^394034-3118617M. Frind & P. Underwood09/2002
2478(7*10^118607+179)/3118608Robert Price09/2018
24793^248572-6242118599Enzo Doria05/2014
2480(3*2^393964-1)/181118594Lelio R Paula04/2014
24817^140303-6118570Robert Price11/2014
24822^393427+75683118434Enzo Doria04/2016
24832^393376-114749118418Enzo Doria04/2015
24842^393180+73118359Lelio R Paula04/2013
2485p(23881)#/2+256118328Robert Price05/2017
2486(10^118324+359)/9118324Serge Batalov12/2014
2487p(23879)#/2+64118317Robert Price03/2017
2488(53*10^118216+1)/9118217Serge Batalov11/2010
2489(7*2^392697+1)/15118214Renaud Lifchitz03/2011
2490(157^53819-1)/156118179Alexander Zhirkov06/2016
2491(19*2^392551+1)/3118171Lelio R Paula04/2014
24922^392516-29219118160Enzo Doria07/2015
2493Phi(177231,10)118152Maksym Voznyy09/2015
24942^392413-112123118129Enzo Doria06/2014
2495(2^392342+5)/27118106Lelio R Paula04/2014
24962^392300-1841429118095Enzo Doria06/2015
24972^392220+75241118070Enzo Doria04/2016
249810^118009+664447118010Patrick De Geest07/2018
249910^118009-20001118009Robert Price01/2018
2500(14*10^117991+61)/3117992Robert Price12/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 20 2019 14:10 (Time in France)

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