PRP Records

Probable Primes Top 10000

(247113 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 (> 30000) Who ? When ?
2001(234483*27^88884-145)/26127230Curtis Bright05/2015
20022^422515-114997127190Enzo Doria06/2015
20035*10^127179-3127180Robert Price07/2015
2004-516776642557847117490*Bern(37960)/34256837217082767928421792453127042Thomas Ritschel06/2017
2005(78^67141-1)/77127036Paul Bourdelais09/2017
20062^421860-113285126993Enzo Doria07/2014
2007(2^421827-7)/11126982Lelio R Paula05/2015
200811^121910-840126957Enzo Doria12/2012
2009(71^68539+1)/72126882Paul Bourdelais09/2017
2010(5*10^126871-119)/3126872Robert Price03/2018
2011331^50339-10004126846Enzo Doria07/2012
20122^421363-2790757126843Enzo Doria03/2016
2013(106*10^126839-1)/3126841Serge Batalov12/2014
2014(7*2^421243+1)/39126807Lelio R Paula05/2014
20152^421161-286183126783Enzo Doria06/2015
20162^420939-113935126716Enzo Doria10/2014
2017177^56363-2126703Lelio R Paula10/2017
20182^420741-113659126656Enzo Doria08/2014
20192^420694-21126642Lelio R Paula05/2017
2020(13*10^126638+437)/9126639Robert Price04/2018
20214*10^126625+87126626Robert Price08/2018
2022(31*2^420556+1)/7126601Lelio R Paula05/2014
20232^420424-59189126561Enzo Doria10/2015
20242^420126+71893126471Enzo Doria04/2016
2025(43*10^126441+47)/9126442Robert Price12/2018
20262^419866+1877059126393Enzo Doria07/2016
2027F(604711)126377Henri Lifchitz02/2005
20282^419757+72707126360Enzo Doria04/2016
20292^419720-21569126349Enzo Doria07/2013
20302^419637+29126324Henri Lifchitz02/2006
20312^419612+1876741126316Enzo Doria07/2016
20322^419520+2793271126289Enzo Doria03/2016
2033(2^419447-5)/369126264Lelio R Paula05/2014
20342^419328-1859939126231Enzo Doria03/2016
20352^419282-1851507126217Enzo Doria08/2015
20362^419251+1866143126208Enzo Doria03/2016
203711^121185+2126202Robert Price05/2014
2038(23*2^419036-1)/1393126141Lelio R Paula05/2014
20392^418851+23126087Robert Price09/2015
2040(2^418849-9)/2681126083Lelio R Paula05/2014
20412^418829+167126081Lelio R Paula01/2012
2042(31*2^418782-1)/75891126063Lelio R Paula05/2014
2043(19*2^418754-1)/15126058Lelio R Paula05/2014
20442^418319-109501125927Enzo Doria04/2014
20452^418316-112373125926Enzo Doria06/2014
2046(8*10^125894-29)/3125895Robert Price07/2018
2047(26*10^125886-413)/9125887Robert Price05/2018
20482^417968+1869811125821Enzo Doria06/2016
20492^417902+63125802Lelio R Paula09/2015
2050(10^125792-91)/9125792Serge Batalov12/2014
2051(35*10^125754-593)/9125755Robert Price07/2018
2052(32*10^125751-77)/9125752Robert Price06/2018
20532^417704+77011125742Enzo Doria05/2016
2054(10^125706+149)/3125706Serge Batalov12/2014
20552^417419-115309125656Enzo Doria07/2015
20562^417300+77281125620Enzo Doria05/2016
20572^417095-1657125559Yves Minet07/2014
20582^416773-25125462Lelio R Paula09/2015
2059(289511#+292834)/(2^3*146417)125444Makoto Morimoto10/2017
2060(11*2^416691+1)/43125436Lelio R Paula05/2014
20612^416641-2*416641+1125422Robert Price05/2018
2062(21*2^416566-1)/17125399Lelio R Paula05/2014
20632^416530+1870429125389Enzo Doria05/2016
20642^416490+1875109125376Enzo Doria09/2016
20652^416416-114929125354Enzo Doria05/2015
2066(172*10^125292-1)/9125294Serge Batalov12/2014
20672^416134+1865899125269Enzo Doria03/2016
2068(9*2^415992+1)/13560845125220Lelio R Paula05/2014
2069(23^91943-1)/22125201Robert Price01/2012
207043125^27010-106125185Enzo Doria08/2012
2071(38*10^125166+349)/9125167Robert Price10/2018
20722^415765-112603125158Enzo Doria06/2014
20732^415290-113591125015Enzo Doria08/2014
20742^415276-460919125011Enzo Doria06/2015
20752^415259+77243125006Enzo Doria05/2016
20762^415144-3683124971Yves Minet10/2011
20772^414874+79124890Lelio R Paula01/2015
2078(2^414765+7)/1389124854Lelio R Paula05/2014
20792^414618+79459124813Enzo Doria06/2016
20802^414432-1846709124757Enzo Doria07/2015
20812*10^124751-51124752Robert Price04/2018
2082(13*2^414274-1)/153124708Lelio R Paula05/2014
2083(7*10^124648+197)/3124649Robert Price07/2018
20852^414032-5124637Henri Lifchitz07/2006
20842^414032+1872331124637Enzo Doria05/2016
208614120^30009-30009^14120124533Norbert Schneider02/2015
208764^68909-63^68909124463Robert Price07/2013
20882^413387+76253124442Enzo Doria04/2016
20892^413352+524287124432Paul Underwood09/2018
2090287117#+391613124424Nicolas PALAU01/2017
2091(4*10^124420+83)/3124421Robert Price02/2018
2092(27*2^413207-1)/108335124385Lelio R Paula05/2014
2093(41*10^124335-383)/9124336Robert Price11/2018
20942^412868-120599124286Paul Bourdelais02/2012
209545^75145-2124231Lelio R Paula08/2015
20962^412645-112213124219Enzo Doria06/2014
20972^412248+74611124100Enzo Doria04/2016
2098(22*10^124096-13)/9124097Robert Price06/2018
20992^412192-3329124083Yves Minet12/2014
2100(25*2^412191-1)/23124082Lelio R Paula05/2014
2101F(593689)124074Henri Lifchitz01/2005
2102(11*2^412161+1)/19124073Lelio R Paula05/2014
21032^411884-113279123990Enzo Doria07/2014
2104(2^411832+1)/257123972Lelio R Paula05/2014
2105(26*10^123970-89)/9123971Robert Price06/2018
21062^411790-1853531123962Enzo Doria08/2015
2107(5^177337+1)/6123953Paul Bourdelais11/2008
21082^411711-113257123938Enzo Doria07/2014
2109(23*2^411675-1)/3123928Lelio R Paula05/2014
2110(11*10^123899-179)/3123900Robert Price09/2018
21112^411325-351103123822Enzo Doria06/2015
21122^411052+1872481123739Enzo Doria05/2016
21132^410997+39123723Lelio R Paula05/2014
21142^410596-39123602Lelio R Paula05/2014
21152^410540-115079123585Enzo Doria06/2015
2116(7*10^123563+107)/3123564Robert Price02/2018
2117(3*2^410392-1)/9229123537Lelio R Paula05/2014
21182^410206-113081123485Enzo Doria07/2014
2119(25*2^410192+1)/10397123478Lelio R Paula04/2014
21202^409909-189123395Enzo Doria05/2014
21212^409896-109043123391Enzo Doria04/2014
21222^409890+75409123390Enzo Doria04/2016
2123133^58076-2123345Lelio R Paula10/2017
2124F(590041)123311Henri Lifchitz01/2005
21252^409566-113501123292Enzo Doria08/2014
21262^409533+77747123282Enzo Doria05/2016
21272^409436-112799123253Enzo Doria06/2014
21282^409225+1873787123189Enzo Doria06/2016
21292^409174+73009123174Enzo Doria04/2016
21302^409058-112685123139Enzo Doria06/2014
2131(13*10^123137-61)/3123138Robert Price11/2018
21324*10^123113+21123114Robert Price12/2018
21332^408778+77689123055Enzo Doria05/2016
21342^408690-75123028Lelio R Paula11/2013
2135(29*10^122996+673)/9122997Robert Price12/2018
21362^408574-2787341122994Enzo Doria03/2016
21373*10^122977+37122978Robert Price08/2018
2138Phi(157825,10)122961Maksym Voznyy06/2015
2139(13*2^408283+1)/1665122904Lelio R Paula05/2014
2140(11*2^408100-1)/35122850Lelio R Paula04/2014
2141(2^407821-lucasV(1,2,407821)+1)/2122767Mike Oakes11/2016
2142(32*10^122733-77)/9122734Robert Price06/2018
2143(21*2^407604-1)/215122701Lelio R Paula04/2014
2144(21*2^407433-1)/13122650Lelio R Paula04/2014
2145(73*10^122592-1)/9122593Robert Price01/2015
2146(5*10^122592+91)/3122593Robert Price04/2018
21472^407179-112075122574Enzo Doria06/2014
2148(21*2^407131+1)/207517523122552Lelio R Paula04/2014
2149(66^67349+1)/67122543Paul Bourdelais09/2017
21502^407008-1867919122522Enzo Doria04/2016
215111^117642-300122512Enzo Doria10/2012
2152(F(3*97700+1)^2+L(3*97700+1)^2)/2122509Henri Lifchitz10/2017
21532^406949+72197122504Enzo Doria04/2016
21542^406826-65122467Lelio R Paula11/2013
21552^406821-2797363122466Enzo Doria04/2016
21562^406758-17122447Lelio R Paula11/2013
2157(30^82883-1)/29122427Robert Price12/2011
2158(2^406583-1)/813167122388Jens K. Andersen02/2009
21594*10^122377+19122378Robert Price10/2018
21603*10^122345-97122346Robert Price07/2018
216197^61575-2122336Lelio R Paula12/2014
21622^406298+2799109122308Enzo Doria04/2016
2163(27*2^406241-1)/10277122289Lelio R Paula04/2014
21642^406229-1849993122288Enzo Doria08/2015
21653*10^122274+7122275Robert Price07/2015
21662^406117+1876577122254Enzo Doria07/2016
21673^256199-2^256199122238Mike Oakes06/2005
21682^405992-78557122216Jorge Menendez03/2018
2169(8*10^122203+43)/3122204Robert Price06/2018
21702^405774+179149122151Enzo Doria06/2016
21712^405514-3311122072Yves Minet12/2014
21722^405514-115511122072Enzo Doria07/2015
21732^405422-113261122045Enzo Doria07/2014
21742^405173+71237121970Enzo Doria04/2016
2175(2^405016+1)/257121920Lelio R Paula04/2014
21762^404858+71329121875Enzo Doria04/2016
21772^404813-114703121861Enzo Doria04/2015
21782^404764+77791121847Enzo Doria05/2016
2179317^48694+48694^317121787Norbert Schneider08/2015
21802^404536-115259121778Enzo Doria06/2015
21812^404501-631121767Yves Minet07/2012
218263^67620+2121672Lelio R Paula08/2015
2183(17*10^121621+1)/9121622Serge Batalov05/2010
2184(15*2^403912+1)/271121589Lelio R Paula05/2014
2185(10^121543-79)/3121543Robert Price01/2018
21862^403676+76831121519Enzo Doria05/2016
2187(7*10^121487+143)/3121488Robert Price03/2018
21882^403363-113635121425Enzo Doria08/2014
21892^403336-1861469121417Enzo Doria03/2016
2190p(24442)#/2-64121381Robert Price04/2017
219111^116555-720121380Enzo Doria11/2012
21922^403100-461267121346Enzo Doria07/2015
21932^403093-112213121344Enzo Doria06/2014
2194(316^48539+1)/317121330Eric Chen10/2017
21952^403004+1866361121317Enzo Doria03/2016
21962^402953+89121301Lelio R Paula10/2013
21972^402944-2788319121299Enzo Doria03/2016
2198(27*2^402865+1)/5121276Lelio R Paula04/2014
21992^402828-113183121264Enzo Doria07/2014
2200(17*10^121242+1)/9121243Serge Batalov05/2010
2201(15*2^402757+1)/101121242Lelio R Paula05/2014
22022^402715+1874223121230Enzo Doria06/2016
2203(35*10^121229-593)/9121230Robert Price07/2018
2204(91^61879+1)/92121222Paul Bourdelais09/2017
22057*10^121144+9121145Robert Price09/2015
22062^401725-113251120932Enzo Doria07/2014
2207(15*2^401677-1)/19120917Lelio R Paula05/2014
22082^401652+73711120910Enzo Doria04/2016
2209(2^401632+3)/79120902Lelio R Paula04/2014
22102^401406-2791331120836Enzo Doria03/2016
2211(28^83497+1)/29120832Robert Price07/2013
22122^401369+1867367120825Enzo Doria03/2016
2213(10^120782+29)/3120782Serge Batalov12/2014
22142^401215-1657120778Yves Minet07/2014
22152^401159+53120761Lelio R Paula10/2013
22162^401031-113047120723Enzo Doria07/2014
2217(29*2^400909-1)/303120685Lelio R Paula04/2014
22182^400571-15120584Lelio R Paula10/2013
2219(10^120574+359)/9120574Serge Batalov12/2014
22202^400424-216413120540Enzo Doria04/2013
2221(17*2^400200-1)/587120471Lelio R Paula05/2014
22222^400166+1874899120462Enzo Doria06/2016
2223(3*2^400045-1)/865120424Lelio R Paula04/2014
22242^399966+73759120402Enzo Doria04/2016
2225(112*10^120395-1)/3120397Serge Batalov12/2014
22262^399918-95120388Lelio R Paula04/2013
22272^399792-1849259120350Enzo Doria08/2015
22289*10^120342-7120343Robert Price09/2015
22292^399526-1861721120270Enzo Doria11/2015
2230(10^(2*60126+1)+36*10^60126-1)/9120253Robert Price10/2015
22312^399322-2798111120208Enzo Doria04/2016
223272^64693-71^64693120157Robert Price03/2014
22332^399111-28489120145Enzo Doria08/2015
22352^398877+105120074Donovan Johnson01/2006
2234(101*10^120072-87)/7120074Hans Havermann02/2015
2236(88^61751+1)/89120072Paul Bourdelais09/2017
22372^398710+57120024Lelio R Paula04/2013
22382^398691-115057120018Enzo Doria06/2015
2239L(574219)120005Renaud Lifchitz03/2004
22402^398571+60413119982Yves Minet03/2011
2241p(24179)#/2-64119949Robert Price04/2017
22422^398448+1872001119945Enzo Doria05/2016
22438*10^119930-3119931Ray Chandler04/2011
2244(10^119880+179)/9119880Serge Batalov12/2014
2245(9*2^398145+1)/73119853Lelio R Paula04/2014
2246(10^119836+77)/3119836Robert Price01/2018
22472^398029+1872527119819Enzo Doria05/2016
22482^397897-113541119779Enzo Doria08/2014
2249(21*2^397661-1)/27593119705Lelio R Paula04/2014
2250(58^67853-1)/57119653Paul Bourdelais09/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 11 2018 05:54 (Time in France)

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