PRP Records

Probable Primes Top 10000

(255169 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 ?
2251(13*10^126638+437)/9126639Robert Price04/2018
22524*10^126625+87126626Robert Price08/2018
2254(31*2^420556+1)/7126601Lelio R Paula05/2014
22537*10^126600-99126601Robert Price06/2019
22552^420424-59189126561Enzo Doria10/2015
22562^420126+71893126471Enzo Doria04/2016
2257(43*10^126441+47)/9126442Robert Price12/2018
22582^419866+1877059126393Enzo Doria07/2016
2259F(604711)126377Henri Lifchitz02/2005
22602^419757+72707126360Enzo Doria04/2016
22612^419720-21569126349Enzo Doria07/2013
22622^419637+29126324Henri Lifchitz02/2006
22632^419612+1876741126316Enzo Doria07/2016
22642^419520+2793271126289Enzo Doria03/2016
2265(2^419447-5)/369126264Lelio R Paula05/2014
22662^419328-1859939126231Enzo Doria03/2016
22672^419282-1851507126217Enzo Doria08/2015
22682^419251+1866143126208Enzo Doria03/2016
226911^121185+2126202Robert Price05/2014
2270(23*2^419036-1)/1393126141Lelio R Paula05/2014
22712^418851+23126087Robert Price09/2015
2272(2^418849-9)/2681126083Lelio R Paula05/2014
22732^418829+167126081Lelio R Paula01/2012
2274(31*2^418782-1)/75891126063Lelio R Paula05/2014
2275(19*2^418754-1)/15126058Lelio R Paula05/2014
22762^418319-109501125927Enzo Doria04/2014
22772^418316-112373125926Enzo Doria06/2014
2278(8*10^125894-29)/3125895Robert Price07/2018
2279(26*10^125886-413)/9125887Robert Price05/2018
22802^417968+1869811125821Enzo Doria06/2016
22812^417902+63125802Lelio R Paula09/2015
2282(10^125792-91)/9125792Serge Batalov12/2014
2283(35*10^125754-593)/9125755Robert Price07/2018
2284(32*10^125751-77)/9125752Robert Price06/2018
22852^417704+77011125742Enzo Doria05/2016
2286(10^125706+149)/3125706Serge Batalov12/2014
22872^417419-115309125656Enzo Doria07/2015
22882^417300+77281125620Enzo Doria05/2016
22892^417095-1657125559Yves Minet07/2014
22902^416773-25125462Lelio R Paula09/2015
2291(289511#+292834)/(2^3*146417)125444Makoto Morimoto10/2017
2292(11*2^416691+1)/43125436Lelio R Paula05/2014
2293(289511#+1896)/(2*3^3*79*780193*9911849)125434Makoto Morimoto06/2019
22942^416641-2*416641+1125422Robert Price05/2018
2295(21*2^416566-1)/17125399Lelio R Paula05/2014
22962^416530+1870429125389Enzo Doria05/2016
2297(56*10^125385+691)/9125386Robert Price05/2019
22982^416490+1875109125376Enzo Doria09/2016
22992^416416-114929125354Enzo Doria05/2015
2300(77*10^125330-293)/9125331Robert Price09/2019
2301(172*10^125292-1)/9125294Serge Batalov12/2014
23022^416134+1865899125269Enzo Doria03/2016
2303153^57337-152125264Norbert Schneider12/2018
2304(9*2^415992+1)/13560845125220Lelio R Paula05/2014
2305(23^91943-1)/22125201Robert Price01/2012
230643125^27010-106125185Enzo Doria08/2012
2307(38*10^125166+349)/9125167Robert Price10/2018
23082^415765-112603125158Enzo Doria06/2014
23098*10^125088-13125089Robert Price08/2019
2310(25*10^125076-13)/3125077Robert Price09/2019
2311(29*10^125021-113)/3125022Robert Price10/2019
23122^415290-113591125015Enzo Doria08/2014
23132^415276-460919125011Enzo Doria06/2015
23142^415259+77243125006Enzo Doria05/2016
23152^415144-3683124971Yves Minet10/2011
23162^414874+79124890Lelio R Paula01/2015
2317(2^414765+7)/1389124854Lelio R Paula05/2014
23182^414618+79459124813Enzo Doria06/2016
23192^414432-1846709124757Enzo Doria07/2015
23202*10^124751-51124752Robert Price04/2018
2321(56*10^124735+367)/9124736Robert Price06/2019
2322(13*2^414274-1)/153124708Lelio R Paula05/2014
2323(7*10^124648+197)/3124649Robert Price07/2018
23252^414032-5124637Henri Lifchitz07/2006
23242^414032+1872331124637Enzo Doria05/2016
232614120^30009-30009^14120124533Norbert Schneider02/2015
232764^68909-63^68909124463Robert Price07/2013
23282^413387+76253124442Enzo Doria04/2016
23292^413352+524287124432Paul Underwood09/2018
2330287117#+391613124424Nicolas PALAU01/2017
2331(4*10^124420+83)/3124421Robert Price02/2018
2332(27*2^413207-1)/108335124385Lelio R Paula05/2014
2333(41*10^124335-383)/9124336Robert Price11/2018
23342^412868-120599124286Paul Bourdelais02/2012
233545^75145-2124231Lelio R Paula08/2015
23362^412645-112213124219Enzo Doria06/2014
23372^412248+74611124100Enzo Doria04/2016
2338(22*10^124096-13)/9124097Robert Price06/2018
23392^412192-3329124083Yves Minet12/2014
2340(25*2^412191-1)/23124082Lelio R Paula05/2014
2341(25*10^124076-67)/3124077Robert Price06/2019
2342F(593689)124074Henri Lifchitz01/2005
2343(11*2^412161+1)/19124073Lelio R Paula05/2014
23442^411884-113279123990Enzo Doria07/2014
2345(2^411832+1)/257123972Lelio R Paula05/2014
2346(26*10^123970-89)/9123971Robert Price06/2018
23472^411790-1853531123962Enzo Doria08/2015
2348(5^177337+1)/6123953Paul Bourdelais11/2008
23492^411711-113257123938Enzo Doria07/2014
2350(23*2^411675-1)/3123928Lelio R Paula05/2014
2351(11*10^123899-179)/3123900Robert Price09/2018
23522^411325-351103123822Enzo Doria06/2015
23532^411052+1872481123739Enzo Doria05/2016
23542^410997+39123723Lelio R Paula05/2014
2355155^56438+154123618Norbert Schneider01/2019
23562^410596-39123602Lelio R Paula05/2014
23572^410540-115079123585Enzo Doria06/2015
2358(7*10^123563+107)/3123564Robert Price02/2018
2359(3*2^410392-1)/9229123537Lelio R Paula05/2014
23602^410206-113081123485Enzo Doria07/2014
2361(25*2^410192+1)/10397123478Lelio R Paula04/2014
23622^409909-189123395Enzo Doria05/2014
23632^409896-109043123391Enzo Doria04/2014
23642^409890+75409123390Enzo Doria04/2016
2365133^58076-2123345Lelio R Paula10/2017
2366F(590041)123311Henri Lifchitz01/2005
23672^409566-113501123292Enzo Doria08/2014
23682^409533+77747123282Enzo Doria05/2016
23692^409436-112799123253Enzo Doria06/2014
23702^409225+1873787123189Enzo Doria06/2016
23712^409174+73009123174Enzo Doria04/2016
23722^409058-112685123139Enzo Doria06/2014
2373(13*10^123137-61)/3123138Robert Price11/2018
23744*10^123113+21123114Robert Price12/2018
23752^408778+77689123055Enzo Doria05/2016
23762^408690-75123028Lelio R Paula11/2013
2377(29*10^122996+673)/9122997Robert Price12/2018
23782^408574-2787341122994Enzo Doria03/2016
23793*10^122977+37122978Robert Price08/2018
2380Phi(157825,10)122961Maksym Voznyy06/2015
2381(68*10^122933-419)/9122934Robert Price07/2019
2382(13*2^408283+1)/1665122904Lelio R Paula05/2014
2383(16*10^122871+77)/3122872Robert Price03/2019
2384(11*2^408100-1)/35122850Lelio R Paula04/2014
2385(19*10^122836-43)/3122837Robert Price05/2019
2386(2^407821-lucasV(1,2,407821)+1)/2122767Mike Oakes11/2016
2387(32*10^122733-77)/9122734Robert Price06/2018
2388(21*2^407604-1)/215122701Lelio R Paula04/2014
2389(22*10^122681+161)/3122682Robert Price05/2019
2390(21*2^407433-1)/13122650Lelio R Paula04/2014
2391(73*10^122592-1)/9122593Robert Price01/2015
2392(5*10^122592+91)/3122593Robert Price04/2018
23932^407179-112075122574Enzo Doria06/2014
2394(21*2^407131+1)/207517523122552Lelio R Paula04/2014
2395(66^67349+1)/67122543Paul Bourdelais09/2017
23962^407008-1867919122522Enzo Doria04/2016
239711^117642-300122512Enzo Doria10/2012
2398(F(3*97700+1)^2+L(3*97700+1)^2)/2122509Henri Lifchitz10/2017
23992^406949+72197122504Enzo Doria04/2016
2400(19*10^122501+149)/3122502Robert Price05/2019
24012^406826-65122467Lelio R Paula11/2013
24022^406821-2797363122466Enzo Doria04/2016
24032^406758-17122447Lelio R Paula11/2013
2404(30^82883-1)/29122427Robert Price12/2011
2405(2^406583-1)/813167122388Jens K. Andersen02/2009
24064*10^122377+19122378Robert Price10/2018
2407Phi(246362,10)122365Makoto Kamada09/2019
24083*10^122345-97122346Robert Price07/2018
240997^61575-2122336Lelio R Paula12/2014
24102^406298+2799109122308Enzo Doria04/2016
24117*10^122294+57122295Robert Price06/2019
2412(27*2^406241-1)/10277122289Lelio R Paula04/2014
24132^406229-1849993122288Enzo Doria08/2015
24143*10^122274+7122275Robert Price07/2015
24152^406117+1876577122254Enzo Doria07/2016
24163^256199-2^256199122238Mike Oakes06/2005
24172^405992-78557122216Jorge Menendez03/2018
2418(8*10^122203+43)/3122204Robert Price06/2018
2419(58*10^122170+329)/9122171Robert Price05/2019
24202^405774+179149122151Enzo Doria06/2016
24215*10^122082+41122083Robert Price03/2019
24222^405514-3311122072Yves Minet12/2014
24232^405514-115511122072Enzo Doria07/2015
24242^405422-113261122045Enzo Doria07/2014
24252^405173+71237121970Enzo Doria04/2016
2426(2^405016+1)/257121920Lelio R Paula04/2014
24272^404858+71329121875Enzo Doria04/2016
24282^404813-114703121861Enzo Doria04/2015
24292^404764+77791121847Enzo Doria05/2016
2430317^48694+48694^317121787Norbert Schneider08/2015
24312^404536-115259121778Enzo Doria06/2015
24322^404501-631121767Yves Minet07/2012
243363^67620+2121672Lelio R Paula08/2015
2434(16*10^121633+167)/3121634Robert Price06/2019
2435(17*10^121621+1)/9121622Serge Batalov05/2010
2436(15*2^403912+1)/271121589Lelio R Paula05/2014
2437(10^121543-79)/3121543Robert Price01/2018
24382^403676+76831121519Enzo Doria05/2016
2439(7*10^121487+143)/3121488Robert Price03/2018
24402^403363-113635121425Enzo Doria08/2014
24412^403336-1861469121417Enzo Doria03/2016
2442p(24442)#/2-64121381Robert Price04/2017
244311^116555-720121380Enzo Doria11/2012
24442^403100-461267121346Enzo Doria07/2015
24452^403093-112213121344Enzo Doria06/2014
2446(316^48539+1)/317121330Eric Chen10/2017
24472^403004+1866361121317Enzo Doria03/2016
24482^402953+89121301Lelio R Paula10/2013
24492^402944-2788319121299Enzo Doria03/2016
2450(44*10^121297-719)/9121298Robert Price12/2018
2451(27*2^402865+1)/5121276Lelio R Paula04/2014
24522^402828-113183121264Enzo Doria07/2014
2453(17*10^121242+1)/9121243Serge Batalov05/2010
2454(15*2^402757+1)/101121242Lelio R Paula05/2014
24552^402715+1874223121230Enzo Doria06/2016
2456(35*10^121229-593)/9121230Robert Price07/2018
2457(91^61879+1)/92121222Paul Bourdelais09/2017
24587*10^121144+9121145Robert Price09/2015
24592^401725-113251120932Enzo Doria07/2014
2460(15*2^401677-1)/19120917Lelio R Paula05/2014
24612^401652+73711120910Enzo Doria04/2016
2462(2^401632+3)/79120902Lelio R Paula04/2014
24632^401406-2791331120836Enzo Doria03/2016
2464(28^83497+1)/29120832Robert Price07/2013
2465(22*10^120828+161)/3120829Robert Price05/2019
24662^401369+1867367120825Enzo Doria03/2016
2467(10^120782+29)/3120782Serge Batalov12/2014
24682^401215-1657120778Yves Minet07/2014
24692^401159+53120761Lelio R Paula10/2013
24702^401031-113047120723Enzo Doria07/2014
2471(71*10^120703-287)/9120704Robert Price09/2019
2472(29*2^400909-1)/303120685Lelio R Paula04/2014
24732^400571-15120584Lelio R Paula10/2013
2474(10^120574+359)/9120574Serge Batalov12/2014
24752^400424-216413120540Enzo Doria04/2013
2476(17*2^400200-1)/587120471Lelio R Paula05/2014
24772^400166+1874899120462Enzo Doria06/2016
2478(3*2^400045-1)/865120424Lelio R Paula04/2014
24792^399966+73759120402Enzo Doria04/2016
2480(112*10^120395-1)/3120397Serge Batalov12/2014
24812^399918-95120388Lelio R Paula04/2013
2482(49*10^120380-139)/9120381Robert Price03/2019
24832^399792-1849259120350Enzo Doria08/2015
24849*10^120342-7120343Robert Price09/2015
2485(13*10^120306-37)/3120307Robert Price01/2019
24862^399526-1861721120270Enzo Doria11/2015
2487(10^(2*60126+1)+36*10^60126-1)/9120253Robert Price10/2015
24882^399322-2798111120208Enzo Doria04/2016
248972^64693-71^64693120157Robert Price03/2014
24902^399111-28489120145Enzo Doria08/2015
24922^398877+105120074Donovan Johnson01/2006
2491(101*10^120072-87)/7120074Hans Havermann02/2015
2493(88^61751+1)/89120072Paul Bourdelais09/2017
24942^398710+57120024Lelio R Paula04/2013
24952^398691-115057120018Enzo Doria06/2015
2496L(574219)120005Renaud Lifchitz03/2004
24972^398571+60413119982Yves Minet03/2011
2498p(24179)#/2-64119949Robert Price04/2017
24992^398448+1872001119945Enzo Doria05/2016
2500634^42803+42803^634119938Norbert Schneider07/2019


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 13 2019 10:51 (Time in France)

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