PRP Records

Probable Primes Top 10000

(252402 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 ?
20013^267267-4127519Henri Lifchitz10/2014
2002(19^99689+5^99689)/24127477Robert Price09/2013
2003(21*2^423372+1)/101127447Lelio R Paula05/2014
20042^423328-21537127435Enzo Doria07/2013
2005(2^423165-7)/25127384Lelio R Paula05/2015
2006(F(5)^182099-F(4)^182099)/F(3)127282Wayne Halsdorf08/2013
2007(234483*27^88884-145)/26127230Curtis Bright05/2015
20082^422515-114997127190Enzo Doria06/2015
20095*10^127179-3127180Robert Price07/2015
2010-516776642557847117490*Bern(37960)/34256837217082767928421792453127042Thomas Ritschel06/2017
2011(78^67141-1)/77127036Paul Bourdelais09/2017
20122^421860-113285126993Enzo Doria07/2014
2013(2^421827-7)/11126982Lelio R Paula05/2015
201411^121910-840126957Enzo Doria12/2012
2015(71^68539+1)/72126882Paul Bourdelais09/2017
2016(5*10^126871-119)/3126872Robert Price03/2018
2017331^50339-10004126846Enzo Doria07/2012
20182^421363-2790757126843Enzo Doria03/2016
2019(106*10^126839-1)/3126841Serge Batalov12/2014
2020(7*2^421243+1)/39126807Lelio R Paula05/2014
20212^421161-286183126783Enzo Doria06/2015
20222^420939-113935126716Enzo Doria10/2014
2023177^56363-2126703Lelio R Paula10/2017
20242^420741-113659126656Enzo Doria08/2014
20252^420694-21126642Lelio R Paula05/2017
2026(13*10^126638+437)/9126639Robert Price04/2018
20274*10^126625+87126626Robert Price08/2018
2028(31*2^420556+1)/7126601Lelio R Paula05/2014
20292^420424-59189126561Enzo Doria10/2015
20302^420126+71893126471Enzo Doria04/2016
2031(43*10^126441+47)/9126442Robert Price12/2018
20322^419866+1877059126393Enzo Doria07/2016
2033F(604711)126377Henri Lifchitz02/2005
20342^419757+72707126360Enzo Doria04/2016
20352^419720-21569126349Enzo Doria07/2013
20362^419637+29126324Henri Lifchitz02/2006
20372^419612+1876741126316Enzo Doria07/2016
20382^419520+2793271126289Enzo Doria03/2016
2039(2^419447-5)/369126264Lelio R Paula05/2014
20402^419328-1859939126231Enzo Doria03/2016
20412^419282-1851507126217Enzo Doria08/2015
20422^419251+1866143126208Enzo Doria03/2016
204311^121185+2126202Robert Price05/2014
2044(23*2^419036-1)/1393126141Lelio R Paula05/2014
20452^418851+23126087Robert Price09/2015
2046(2^418849-9)/2681126083Lelio R Paula05/2014
20472^418829+167126081Lelio R Paula01/2012
2048(31*2^418782-1)/75891126063Lelio R Paula05/2014
2049(19*2^418754-1)/15126058Lelio R Paula05/2014
20502^418319-109501125927Enzo Doria04/2014
20512^418316-112373125926Enzo Doria06/2014
2052(8*10^125894-29)/3125895Robert Price07/2018
2053(26*10^125886-413)/9125887Robert Price05/2018
20542^417968+1869811125821Enzo Doria06/2016
20552^417902+63125802Lelio R Paula09/2015
2056(10^125792-91)/9125792Serge Batalov12/2014
2057(35*10^125754-593)/9125755Robert Price07/2018
2058(32*10^125751-77)/9125752Robert Price06/2018
20592^417704+77011125742Enzo Doria05/2016
2060(10^125706+149)/3125706Serge Batalov12/2014
20612^417419-115309125656Enzo Doria07/2015
20622^417300+77281125620Enzo Doria05/2016
20632^417095-1657125559Yves Minet07/2014
20642^416773-25125462Lelio R Paula09/2015
2065(289511#+292834)/(2^3*146417)125444Makoto Morimoto10/2017
2066(11*2^416691+1)/43125436Lelio R Paula05/2014
20672^416641-2*416641+1125422Robert Price05/2018
2068(21*2^416566-1)/17125399Lelio R Paula05/2014
20692^416530+1870429125389Enzo Doria05/2016
20702^416490+1875109125376Enzo Doria09/2016
20712^416416-114929125354Enzo Doria05/2015
2072(172*10^125292-1)/9125294Serge Batalov12/2014
20732^416134+1865899125269Enzo Doria03/2016
2074(9*2^415992+1)/13560845125220Lelio R Paula05/2014
2075(23^91943-1)/22125201Robert Price01/2012
207643125^27010-106125185Enzo Doria08/2012
2077(38*10^125166+349)/9125167Robert Price10/2018
20782^415765-112603125158Enzo Doria06/2014
20792^415290-113591125015Enzo Doria08/2014
20802^415276-460919125011Enzo Doria06/2015
20812^415259+77243125006Enzo Doria05/2016
20822^415144-3683124971Yves Minet10/2011
20832^414874+79124890Lelio R Paula01/2015
2084(2^414765+7)/1389124854Lelio R Paula05/2014
20852^414618+79459124813Enzo Doria06/2016
20862^414432-1846709124757Enzo Doria07/2015
20872*10^124751-51124752Robert Price04/2018
2088(13*2^414274-1)/153124708Lelio R Paula05/2014
2089(7*10^124648+197)/3124649Robert Price07/2018
20902^414032-5124637Henri Lifchitz07/2006
20912^414032+1872331124637Enzo Doria05/2016
209214120^30009-30009^14120124533Norbert Schneider02/2015
209364^68909-63^68909124463Robert Price07/2013
20942^413387+76253124442Enzo Doria04/2016
20952^413352+524287124432Paul Underwood09/2018
2096287117#+391613124424Nicolas PALAU01/2017
2097(4*10^124420+83)/3124421Robert Price02/2018
2098(27*2^413207-1)/108335124385Lelio R Paula05/2014
2099(41*10^124335-383)/9124336Robert Price11/2018
21002^412868-120599124286Paul Bourdelais02/2012
210145^75145-2124231Lelio R Paula08/2015
21022^412645-112213124219Enzo Doria06/2014
21032^412248+74611124100Enzo Doria04/2016
2104(22*10^124096-13)/9124097Robert Price06/2018
21052^412192-3329124083Yves Minet12/2014
2106(25*2^412191-1)/23124082Lelio R Paula05/2014
2107F(593689)124074Henri Lifchitz01/2005
2108(11*2^412161+1)/19124073Lelio R Paula05/2014
21092^411884-113279123990Enzo Doria07/2014
2110(2^411832+1)/257123972Lelio R Paula05/2014
2111(26*10^123970-89)/9123971Robert Price06/2018
21122^411790-1853531123962Enzo Doria08/2015
2113(5^177337+1)/6123953Paul Bourdelais11/2008
21142^411711-113257123938Enzo Doria07/2014
2115(23*2^411675-1)/3123928Lelio R Paula05/2014
2116(11*10^123899-179)/3123900Robert Price09/2018
21172^411325-351103123822Enzo Doria06/2015
21182^411052+1872481123739Enzo Doria05/2016
21192^410997+39123723Lelio R Paula05/2014
21202^410596-39123602Lelio R Paula05/2014
21212^410540-115079123585Enzo Doria06/2015
2122(7*10^123563+107)/3123564Robert Price02/2018
2123(3*2^410392-1)/9229123537Lelio R Paula05/2014
21242^410206-113081123485Enzo Doria07/2014
2125(25*2^410192+1)/10397123478Lelio R Paula04/2014
21262^409909-189123395Enzo Doria05/2014
21272^409896-109043123391Enzo Doria04/2014
21282^409890+75409123390Enzo Doria04/2016
2129133^58076-2123345Lelio R Paula10/2017
2130F(590041)123311Henri Lifchitz01/2005
21312^409566-113501123292Enzo Doria08/2014
21322^409533+77747123282Enzo Doria05/2016
21332^409436-112799123253Enzo Doria06/2014
21342^409225+1873787123189Enzo Doria06/2016
21352^409174+73009123174Enzo Doria04/2016
21362^409058-112685123139Enzo Doria06/2014
2137(13*10^123137-61)/3123138Robert Price11/2018
21384*10^123113+21123114Robert Price12/2018
21392^408778+77689123055Enzo Doria05/2016
21402^408690-75123028Lelio R Paula11/2013
2141(29*10^122996+673)/9122997Robert Price12/2018
21422^408574-2787341122994Enzo Doria03/2016
21433*10^122977+37122978Robert Price08/2018
2144Phi(157825,10)122961Maksym Voznyy06/2015
2145(13*2^408283+1)/1665122904Lelio R Paula05/2014
2146(11*2^408100-1)/35122850Lelio R Paula04/2014
2147(2^407821-lucasV(1,2,407821)+1)/2122767Mike Oakes11/2016
2148(32*10^122733-77)/9122734Robert Price06/2018
2149(21*2^407604-1)/215122701Lelio R Paula04/2014
2150(21*2^407433-1)/13122650Lelio R Paula04/2014
2151(73*10^122592-1)/9122593Robert Price01/2015
2152(5*10^122592+91)/3122593Robert Price04/2018
21532^407179-112075122574Enzo Doria06/2014
2154(21*2^407131+1)/207517523122552Lelio R Paula04/2014
2155(66^67349+1)/67122543Paul Bourdelais09/2017
21562^407008-1867919122522Enzo Doria04/2016
215711^117642-300122512Enzo Doria10/2012
2158(F(3*97700+1)^2+L(3*97700+1)^2)/2122509Henri Lifchitz10/2017
21592^406949+72197122504Enzo Doria04/2016
21602^406826-65122467Lelio R Paula11/2013
21612^406821-2797363122466Enzo Doria04/2016
21622^406758-17122447Lelio R Paula11/2013
2163(30^82883-1)/29122427Robert Price12/2011
2164(2^406583-1)/813167122388Jens K. Andersen02/2009
21654*10^122377+19122378Robert Price10/2018
21663*10^122345-97122346Robert Price07/2018
216797^61575-2122336Lelio R Paula12/2014
21682^406298+2799109122308Enzo Doria04/2016
2169(27*2^406241-1)/10277122289Lelio R Paula04/2014
21702^406229-1849993122288Enzo Doria08/2015
21713*10^122274+7122275Robert Price07/2015
21722^406117+1876577122254Enzo Doria07/2016
21733^256199-2^256199122238Mike Oakes06/2005
21742^405992-78557122216Jorge Menendez03/2018
2175(8*10^122203+43)/3122204Robert Price06/2018
21762^405774+179149122151Enzo Doria06/2016
21772^405514-3311122072Yves Minet12/2014
21782^405514-115511122072Enzo Doria07/2015
21792^405422-113261122045Enzo Doria07/2014
21802^405173+71237121970Enzo Doria04/2016
2181(2^405016+1)/257121920Lelio R Paula04/2014
21822^404858+71329121875Enzo Doria04/2016
21832^404813-114703121861Enzo Doria04/2015
21842^404764+77791121847Enzo Doria05/2016
2185317^48694+48694^317121787Norbert Schneider08/2015
21862^404536-115259121778Enzo Doria06/2015
21872^404501-631121767Yves Minet07/2012
218863^67620+2121672Lelio R Paula08/2015
2189(17*10^121621+1)/9121622Serge Batalov05/2010
2190(15*2^403912+1)/271121589Lelio R Paula05/2014
2191(10^121543-79)/3121543Robert Price01/2018
21922^403676+76831121519Enzo Doria05/2016
2193(7*10^121487+143)/3121488Robert Price03/2018
21942^403363-113635121425Enzo Doria08/2014
21952^403336-1861469121417Enzo Doria03/2016
2196p(24442)#/2-64121381Robert Price04/2017
219711^116555-720121380Enzo Doria11/2012
21982^403100-461267121346Enzo Doria07/2015
21992^403093-112213121344Enzo Doria06/2014
2200(316^48539+1)/317121330Eric Chen10/2017
22012^403004+1866361121317Enzo Doria03/2016
22022^402953+89121301Lelio R Paula10/2013
22032^402944-2788319121299Enzo Doria03/2016
2204(27*2^402865+1)/5121276Lelio R Paula04/2014
22052^402828-113183121264Enzo Doria07/2014
2206(17*10^121242+1)/9121243Serge Batalov05/2010
2207(15*2^402757+1)/101121242Lelio R Paula05/2014
22092^402715+1874223121230Enzo Doria06/2016
2208(35*10^121229-593)/9121230Robert Price07/2018
2210(91^61879+1)/92121222Paul Bourdelais09/2017
22117*10^121144+9121145Robert Price09/2015
22122^401725-113251120932Enzo Doria07/2014
2213(15*2^401677-1)/19120917Lelio R Paula05/2014
22142^401652+73711120910Enzo Doria04/2016
2215(2^401632+3)/79120902Lelio R Paula04/2014
22162^401406-2791331120836Enzo Doria03/2016
2217(28^83497+1)/29120832Robert Price07/2013
22182^401369+1867367120825Enzo Doria03/2016
2219(10^120782+29)/3120782Serge Batalov12/2014
22202^401215-1657120778Yves Minet07/2014
22212^401159+53120761Lelio R Paula10/2013
22222^401031-113047120723Enzo Doria07/2014
2223(29*2^400909-1)/303120685Lelio R Paula04/2014
22242^400571-15120584Lelio R Paula10/2013
2225(10^120574+359)/9120574Serge Batalov12/2014
22262^400424-216413120540Enzo Doria04/2013
2227(17*2^400200-1)/587120471Lelio R Paula05/2014
22282^400166+1874899120462Enzo Doria06/2016
2229(3*2^400045-1)/865120424Lelio R Paula04/2014
22302^399966+73759120402Enzo Doria04/2016
2231(112*10^120395-1)/3120397Serge Batalov12/2014
22322^399918-95120388Lelio R Paula04/2013
22332^399792-1849259120350Enzo Doria08/2015
22349*10^120342-7120343Robert Price09/2015
22352^399526-1861721120270Enzo Doria11/2015
2236(10^(2*60126+1)+36*10^60126-1)/9120253Robert Price10/2015
22372^399322-2798111120208Enzo Doria04/2016
223872^64693-71^64693120157Robert Price03/2014
22392^399111-28489120145Enzo Doria08/2015
22412^398877+105120074Donovan Johnson01/2006
2240(101*10^120072-87)/7120074Hans Havermann02/2015
2242(88^61751+1)/89120072Paul Bourdelais09/2017
22432^398710+57120024Lelio R Paula04/2013
22442^398691-115057120018Enzo Doria06/2015
2245L(574219)120005Renaud Lifchitz03/2004
22462^398571+60413119982Yves Minet03/2011
2247p(24179)#/2-64119949Robert Price04/2017
22482^398448+1872001119945Enzo Doria05/2016
22498*10^119930-3119931Ray Chandler04/2011
2250(10^119880+179)/9119880Serge Batalov12/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 17 2018 20:37 (Time in France)

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