PRP Records

Probable Primes Top 10000

(255312 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 ?
225111^121910-840126957Enzo Doria12/2012
2252(71^68539+1)/72126882Paul Bourdelais09/2017
2253(5*10^126871-119)/3126872Robert Price03/2018
2254331^50339-10004126846Enzo Doria07/2012
22552^421363-2790757126843Enzo Doria03/2016
2256(106*10^126839-1)/3126841Serge Batalov12/2014
2257(7*2^421243+1)/39126807Lelio R Paula05/2014
2258(14*10^126784-83)/3126785Robert Price12/2018
22592^421161-286183126783Enzo Doria06/2015
22602^420939-113935126716Enzo Doria10/2014
2261177^56363-2126703Lelio R Paula10/2017
22622^420741-113659126656Enzo Doria08/2014
22632^420694-21126642Lelio R Paula05/2017
2264(13*10^126638+437)/9126639Robert Price04/2018
22654*10^126625+87126626Robert Price08/2018
2267(31*2^420556+1)/7126601Lelio R Paula05/2014
22667*10^126600-99126601Robert Price06/2019
22682^420424-59189126561Enzo Doria10/2015
22692^420126+71893126471Enzo Doria04/2016
2270(43*10^126441+47)/9126442Robert Price12/2018
22712^419866+1877059126393Enzo Doria07/2016
2272F(604711)126377Henri Lifchitz02/2005
22732^419757+72707126360Enzo Doria04/2016
22742^419720-21569126349Enzo Doria07/2013
22752^419637+29126324Henri Lifchitz02/2006
22762^419612+1876741126316Enzo Doria07/2016
22772^419520+2793271126289Enzo Doria03/2016
2278(2^419447-5)/369126264Lelio R Paula05/2014
22792^419328-1859939126231Enzo Doria03/2016
22802^419282-1851507126217Enzo Doria08/2015
22812^419251+1866143126208Enzo Doria03/2016
228211^121185+2126202Robert Price05/2014
2283(23*2^419036-1)/1393126141Lelio R Paula05/2014
22842^418851+23126087Robert Price09/2015
2285(2^418849-9)/2681126083Lelio R Paula05/2014
22862^418829+167126081Lelio R Paula01/2012
2287(31*2^418782-1)/75891126063Lelio R Paula05/2014
2288(19*2^418754-1)/15126058Lelio R Paula05/2014
22892^418319-109501125927Enzo Doria04/2014
22902^418316-112373125926Enzo Doria06/2014
2291(8*10^125894-29)/3125895Robert Price07/2018
2292(26*10^125886-413)/9125887Robert Price05/2018
22932^417968+1869811125821Enzo Doria06/2016
22942^417902+63125802Lelio R Paula09/2015
2295(10^125792-91)/9125792Serge Batalov12/2014
2296(35*10^125754-593)/9125755Robert Price07/2018
2297(32*10^125751-77)/9125752Robert Price06/2018
22982^417704+77011125742Enzo Doria05/2016
2299(10^125706+149)/3125706Serge Batalov12/2014
23002^417419-115309125656Enzo Doria07/2015
23012^417300+77281125620Enzo Doria05/2016
23022^417095-1657125559Yves Minet07/2014
23032^416773-25125462Lelio R Paula09/2015
2304(289511#+292834)/(2^3*146417)125444Makoto Morimoto10/2017
2305(11*2^416691+1)/43125436Lelio R Paula05/2014
2306(289511#+1896)/(2*3^3*79*780193*9911849)125434Makoto Morimoto06/2019
23072^416641-2*416641+1125422Robert Price05/2018
2308(21*2^416566-1)/17125399Lelio R Paula05/2014
23092^416530+1870429125389Enzo Doria05/2016
2310(56*10^125385+691)/9125386Robert Price05/2019
23112^416490+1875109125376Enzo Doria09/2016
23122^416416-114929125354Enzo Doria05/2015
2313(77*10^125330-293)/9125331Robert Price09/2019
2314(172*10^125292-1)/9125294Serge Batalov12/2014
23152^416134+1865899125269Enzo Doria03/2016
2316153^57337-152125264Norbert Schneider12/2018
2317(9*2^415992+1)/13560845125220Lelio R Paula05/2014
2318(23^91943-1)/22125201Robert Price01/2012
231943125^27010-106125185Enzo Doria08/2012
2320(38*10^125166+349)/9125167Robert Price10/2018
23212^415765-112603125158Enzo Doria06/2014
23228*10^125088-13125089Robert Price08/2019
2323(25*10^125076-13)/3125077Robert Price09/2019
2324(29*10^125021-113)/3125022Robert Price10/2019
23252^415290-113591125015Enzo Doria08/2014
23262^415276-460919125011Enzo Doria06/2015
23272^415259+77243125006Enzo Doria05/2016
23282^415144-3683124971Yves Minet10/2011
23292^414874+79124890Lelio R Paula01/2015
2330(2^414765+7)/1389124854Lelio R Paula05/2014
23312^414618+79459124813Enzo Doria06/2016
23322^414432-1846709124757Enzo Doria07/2015
23332*10^124751-51124752Robert Price04/2018
2334(56*10^124735+367)/9124736Robert Price06/2019
2335(13*2^414274-1)/153124708Lelio R Paula05/2014
2336(7*10^124648+197)/3124649Robert Price07/2018
23382^414032-5124637Henri Lifchitz07/2006
23372^414032+1872331124637Enzo Doria05/2016
233914120^30009-30009^14120124533Norbert Schneider02/2015
234064^68909-63^68909124463Robert Price07/2013
23412^413387+76253124442Enzo Doria04/2016
23422^413352+524287124432Paul Underwood09/2018
2343287117#+391613124424Nicolas PALAU01/2017
2344(4*10^124420+83)/3124421Robert Price02/2018
2345(27*2^413207-1)/108335124385Lelio R Paula05/2014
2346(41*10^124335-383)/9124336Robert Price11/2018
23472^412868-120599124286Paul Bourdelais02/2012
234845^75145-2124231Lelio R Paula08/2015
23492^412645-112213124219Enzo Doria06/2014
23502^412248+74611124100Enzo Doria04/2016
2351(22*10^124096-13)/9124097Robert Price06/2018
23522^412192-3329124083Yves Minet12/2014
2353(25*2^412191-1)/23124082Lelio R Paula05/2014
2354(25*10^124076-67)/3124077Robert Price06/2019
2355F(593689)124074Henri Lifchitz01/2005
2356(11*2^412161+1)/19124073Lelio R Paula05/2014
23572^411884-113279123990Enzo Doria07/2014
2358(2^411832+1)/257123972Lelio R Paula05/2014
2359(26*10^123970-89)/9123971Robert Price06/2018
23602^411790-1853531123962Enzo Doria08/2015
2361(5^177337+1)/6123953Paul Bourdelais11/2008
23622^411711-113257123938Enzo Doria07/2014
2363(23*2^411675-1)/3123928Lelio R Paula05/2014
2364(11*10^123899-179)/3123900Robert Price09/2018
23652^411325-351103123822Enzo Doria06/2015
23662^411052+1872481123739Enzo Doria05/2016
23672^410997+39123723Lelio R Paula05/2014
23688*10^123657+87123658Robert Price10/2019
2369155^56438+154123618Norbert Schneider01/2019
23702^410596-39123602Lelio R Paula05/2014
23712^410540-115079123585Enzo Doria06/2015
2372(7*10^123563+107)/3123564Robert Price02/2018
23739*10^123549+89123550Robert Price11/2019
2374(3*2^410392-1)/9229123537Lelio R Paula05/2014
23752^410206-113081123485Enzo Doria07/2014
2376(25*2^410192+1)/10397123478Lelio R Paula04/2014
23772^409909-189123395Enzo Doria05/2014
23782^409896-109043123391Enzo Doria04/2014
23792^409890+75409123390Enzo Doria04/2016
2380133^58076-2123345Lelio R Paula10/2017
2381F(590041)123311Henri Lifchitz01/2005
23822^409566-113501123292Enzo Doria08/2014
23832^409533+77747123282Enzo Doria05/2016
23842^409436-112799123253Enzo Doria06/2014
23852^409225+1873787123189Enzo Doria06/2016
23862^409174+73009123174Enzo Doria04/2016
23872^409058-112685123139Enzo Doria06/2014
2388(13*10^123137-61)/3123138Robert Price11/2018
23894*10^123113+21123114Robert Price12/2018
23902^408778+77689123055Enzo Doria05/2016
23912^408690-75123028Lelio R Paula11/2013
2392(29*10^122996+673)/9122997Robert Price12/2018
23932^408574-2787341122994Enzo Doria03/2016
23943*10^122977+37122978Robert Price08/2018
2395Phi(157825,10)122961Maksym Voznyy06/2015
2396(68*10^122933-419)/9122934Robert Price07/2019
2397(13*2^408283+1)/1665122904Lelio R Paula05/2014
2398(16*10^122871+77)/3122872Robert Price03/2019
2399(11*2^408100-1)/35122850Lelio R Paula04/2014
2400(19*10^122836-43)/3122837Robert Price05/2019
2401(2^407821-lucasV(1,2,407821)+1)/2122767Mike Oakes11/2016
2402(32*10^122733-77)/9122734Robert Price06/2018
2403(21*2^407604-1)/215122701Lelio R Paula04/2014
2404(22*10^122681+161)/3122682Robert Price05/2019
2405(21*2^407433-1)/13122650Lelio R Paula04/2014
2406(26*10^122625-131)/3122626Robert Price10/2019
2408(73*10^122592-1)/9122593Robert Price01/2015
2407(5*10^122592+91)/3122593Robert Price04/2018
24092^407179-112075122574Enzo Doria06/2014
2410(21*2^407131+1)/207517523122552Lelio R Paula04/2014
2411(66^67349+1)/67122543Paul Bourdelais09/2017
24122^407008-1867919122522Enzo Doria04/2016
241311^117642-300122512Enzo Doria10/2012
2414(F(3*97700+1)^2+L(3*97700+1)^2)/2122509Henri Lifchitz10/2017
24152^406949+72197122504Enzo Doria04/2016
2416(19*10^122501+149)/3122502Robert Price05/2019
24172^406826-65122467Lelio R Paula11/2013
24182^406821-2797363122466Enzo Doria04/2016
24192^406758-17122447Lelio R Paula11/2013
2420(30^82883-1)/29122427Robert Price12/2011
2421(2^406583-1)/813167122388Jens K. Andersen02/2009
24224*10^122377+19122378Robert Price10/2018
2423Phi(246362,10)122365Makoto Kamada09/2019
24243*10^122345-97122346Robert Price07/2018
242597^61575-2122336Lelio R Paula12/2014
24262^406298+2799109122308Enzo Doria04/2016
24277*10^122294+57122295Robert Price06/2019
2428(27*2^406241-1)/10277122289Lelio R Paula04/2014
24292^406229-1849993122288Enzo Doria08/2015
24303*10^122274+7122275Robert Price07/2015
24312^406117+1876577122254Enzo Doria07/2016
24323^256199-2^256199122238Mike Oakes06/2005
24332^405992-78557122216Jorge Menendez03/2018
2434(8*10^122203+43)/3122204Robert Price06/2018
2435(58*10^122170+329)/9122171Robert Price05/2019
24362^405774+179149122151Enzo Doria06/2016
24375*10^122082+41122083Robert Price03/2019
24382^405514-3311122072Yves Minet12/2014
24392^405514-115511122072Enzo Doria07/2015
24402^405422-113261122045Enzo Doria07/2014
24412^405173+71237121970Enzo Doria04/2016
2442(2^405016+1)/257121920Lelio R Paula04/2014
24432^404858+71329121875Enzo Doria04/2016
24442^404813-114703121861Enzo Doria04/2015
24452^404764+77791121847Enzo Doria05/2016
2446317^48694+48694^317121787Norbert Schneider08/2015
24472^404536-115259121778Enzo Doria06/2015
24482^404501-631121767Yves Minet07/2012
244963^67620+2121672Lelio R Paula08/2015
2450(16*10^121633+167)/3121634Robert Price06/2019
2451(17*10^121621+1)/9121622Serge Batalov05/2010
2452(15*2^403912+1)/271121589Lelio R Paula05/2014
2453(10^121543-79)/3121543Robert Price01/2018
24542^403676+76831121519Enzo Doria05/2016
2455(7*10^121487+143)/3121488Robert Price03/2018
24562^403363-113635121425Enzo Doria08/2014
24572^403336-1861469121417Enzo Doria03/2016
2458p(24442)#/2-64121381Robert Price04/2017
245911^116555-720121380Enzo Doria11/2012
24602^403100-461267121346Enzo Doria07/2015
24612^403093-112213121344Enzo Doria06/2014
2462(316^48539+1)/317121330Eric Chen10/2017
24632^403004+1866361121317Enzo Doria03/2016
24642^402953+89121301Lelio R Paula10/2013
24652^402944-2788319121299Enzo Doria03/2016
2466(44*10^121297-719)/9121298Robert Price12/2018
2467(27*2^402865+1)/5121276Lelio R Paula04/2014
24682^402828-113183121264Enzo Doria07/2014
2469(17*10^121242+1)/9121243Serge Batalov05/2010
2470(15*2^402757+1)/101121242Lelio R Paula05/2014
24722^402715+1874223121230Enzo Doria06/2016
2471(35*10^121229-593)/9121230Robert Price07/2018
2473(91^61879+1)/92121222Paul Bourdelais09/2017
24747*10^121144+9121145Robert Price09/2015
24752^401725-113251120932Enzo Doria07/2014
2476(15*2^401677-1)/19120917Lelio R Paula05/2014
24772^401652+73711120910Enzo Doria04/2016
2478(2^401632+3)/79120902Lelio R Paula04/2014
24792^401406-2791331120836Enzo Doria03/2016
2480(28^83497+1)/29120832Robert Price07/2013
2481(22*10^120828+161)/3120829Robert Price05/2019
24822^401369+1867367120825Enzo Doria03/2016
2483(10^120782+29)/3120782Serge Batalov12/2014
24842^401215-1657120778Yves Minet07/2014
24852^401159+53120761Lelio R Paula10/2013
24862^401031-113047120723Enzo Doria07/2014
2487(71*10^120703-287)/9120704Robert Price09/2019
2488(29*2^400909-1)/303120685Lelio R Paula04/2014
24892^400571-15120584Lelio R Paula10/2013
2490(10^120574+359)/9120574Serge Batalov12/2014
24912^400424-216413120540Enzo Doria04/2013
2492(17*2^400200-1)/587120471Lelio R Paula05/2014
24932^400166+1874899120462Enzo Doria06/2016
2494(3*2^400045-1)/865120424Lelio R Paula04/2014
24952^399966+73759120402Enzo Doria04/2016
2496(112*10^120395-1)/3120397Serge Batalov12/2014
24972^399918-95120388Lelio R Paula04/2013
2498(49*10^120380-139)/9120381Robert Price03/2019
24992^399792-1849259120350Enzo Doria08/2015
25009*10^120342-7120343Robert Price09/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 14 2019 11:13 (Time in France)

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