PRP Records

Probable Primes Top 10000

(252932 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 ?
2001(68^71713+1)/69131413Paul Bourdelais09/2017
20022^436451+1884713131385Enzo Doria03/2017
20032^436365+35131359Robert Price11/2015
20042^436300+1866871131340Enzo Doria03/2016
2005(7*10^131339+179)/3131340Robert Price09/2018
2006(37*10^131270+341)/9131271Robert Price08/2018
2007(5*10^131223-29)/3131224Robert Price03/2018
2008(23*2^435891-1)/699131215Lelio R Paula07/2015
2009(11*2^435879+1)/3337131211Lelio R Paula06/2015
2010(2^435808+1)/641/6700417131182Lelio R Paula02/2012
2011(2^435808+1)/4294967297131182Serge Batalov12/2016
20122^435773+1875557131181Enzo Doria06/2016
2013(25*10^131144-7)/9131145Robert Price05/2018
20142^435612-2789939131133Enzo Doria12/2015
201566^72047-65^72047131093Robert Price09/2013
2016(5*10^131090+37)/3131091Robert Price03/2018
20172^435468+75631131089Enzo Doria04/2016
201837^83588-2131083Lelio R Paula08/2015
2019(4^217720+11)/3131081Robert Price02/2017
20202^435202-113193131009Enzo Doria07/2014
2021floor((sqrt(5)-1)/2*10^130911)130911Serge Batalov06/2017
20222^434835-111937130899Enzo Doria05/2014
20232^434685+72257130854Enzo Doria04/2016
2024(7*10^130825+113)/3130826Robert Price02/2018
20252^434539-29317130810Enzo Doria07/2015
20262^434469-114259130789Enzo Doria01/2015
20272^434246+33130722Robert Price11/2015
20282^433911-91130621Lelio R Paula06/2017
20292^433744-114419130570Enzo Doria02/2015
20302^433708+1869451130560Enzo Doria05/2016
20312^433710+93130560Lelio R Paula06/2017
2032(29*2^433547-1)/27130511Lelio R Paula06/2015
20334*10^130480+9130481Robert Price05/2015
2034(23*2^433449-1)/75130481Lelio R Paula06/2015
2035(23*2^433334-1)/3731130445Lelio R Paula06/2015
20362^433023-113497130353Enzo Doria08/2014
20372^433002+1179379130347Enzo Doria06/2016
20382^432974+19130339Robert Price08/2015
2039(2^432457-1)/1672739247834685086279697130159Tony Prest / Never Odd Or Even09/2013
20402^432217+41130111Lelio R Paula06/2017
2041(2^216089*(2^216091-1)-339)/25130098Makoto Morimoto03/2017
2042((2^216091+1066)^2+(2^216091+1066)+41)/47/2069130095Makoto Morimoto05/2016
204397^65480-2130094Lelio R Paula05/2017
20444*10^130088-89130089Robert Price11/2018
20452^432117-113215130081Enzo Doria07/2014
20462^431804+72511129986Enzo Doria04/2016
2047(3^272141-3^136071+1)/7129844Serge Batalov03/2014
2048(47*10^129789-119)/9129790Robert Price05/2019
2049(9*2^431141+1)/17129787Lelio R Paula06/2015
2050(29*2^430881-1)/21129709Lelio R Paula06/2015
20512^430807+1869563129686Enzo Doria05/2016
20522^430721-21429129660Enzo Doria07/2013
20532^430415-276271129568Enzo Doria07/2015
20542^430142-2791721129486Enzo Doria03/2016
2055(7*10^129472-13)/3129473Robert Price07/2018
20562^429568-21017129313Enzo Doria07/2013
2057(11*10^129239-179)/3129240Robert Price09/2018
20582^429194-112685129201Enzo Doria06/2014
20592^429145-2780449129186Enzo Doria04/2016
20602^428892-113453129110Enzo Doria07/2014
2061(11*2^428881-7)/15129106Renaud Lifchitz03/2011
20622^428727-113959129060Enzo Doria10/2014
2063(7*2^428725-1)/13129059Lelio R Paula05/2014
2064(10^129051-31)/3129051Serge Batalov12/2014
20652^428564+71161129011Enzo Doria04/2016
20662^428502-113285128992Enzo Doria07/2014
20672^428421-21373128968Enzo Doria06/2013
2068L(616787)128901Henri Lifchitz09/2008
206991^65772-2128851Lelio R Paula05/2017
20702^428022+43128848Lelio R Paula05/2017
20712^427999-459397128841Enzo Doria05/2015
20722^427993+76847128839Enzo Doria05/2016
20732^427824-1851507128788Enzo Doria08/2015
20742^427807-21469128783Enzo Doria07/2013
207511^123594-240128710Enzo Doria09/2012
20762^427504-21503128692Enzo Doria07/2013
20772^427420+91128667Lelio R Paula05/2017
20782^427269-113635128621Enzo Doria08/2014
20792^427130+1877569128579Enzo Doria08/2016
20802^427016-115349128545Enzo Doria07/2015
2081(4*10^128510+137)/3128511Robert Price03/2018
20822^426889-112879128507Enzo Doria06/2014
20832^426804+1869931128481Enzo Doria05/2016
20842^426750+77635128465Enzo Doria05/2016
20852^426425-91128367Lelio R Paula05/2017
2086(15*2^426398-1)/11128359Lelio R Paula05/2014
20872^426352+74971128345Enzo Doria04/2016
20884*10^128343-21128344Robert Price09/2018
20892^426300-1863689128330Enzo Doria03/2016
20902^426293+1881017128327Enzo Doria11/2016
20912^426043+35128252Robert Price11/2015
2092(4*10^128244-19)/3128245Robert Price03/2018
20932^425808-459959128181Enzo Doria06/2015
20942^425627-113605128127Enzo Doria08/2014
209518565^30002-30002^18565128070Norbert Schneider01/2015
2096(2^425287-9)/2737128021Lelio R Paula05/2015
2097(3*2^425233-1)/25128007Lelio R Paula05/2014
20982^425205+4911128000Marek Hubal02/2017
20992^425118-113663127974Enzo Doria08/2014
21002^425061+1869761127957Enzo Doria05/2016
21012^424918-21141127914Enzo Doria07/2013
21022^424864-29489127897Enzo Doria08/2015
2103(97*10^127858-1)/3127860Serge Batalov12/2014
21042^424632-2786639127827Enzo Doria03/2016
21052^424577-113755127811Enzo Doria09/2014
2106(7*2^424512-1)/3127792Lelio R Paula05/2014
2107(56*10^127752+691)/9127753Robert Price05/2019
210811^122629-720127705Enzo Doria11/2012
21092^423696-21429127546Enzo Doria07/2013
21102^423664-1864559127536Enzo Doria03/2016
21113^267267-4127519Henri Lifchitz10/2014
2112(19^99689+5^99689)/24127477Robert Price09/2013
2113(21*2^423372+1)/101127447Lelio R Paula05/2014
21142^423328-21537127435Enzo Doria07/2013
2115(2^423165-7)/25127384Lelio R Paula05/2015
2116(F(5)^182099-F(4)^182099)/F(3)127282Wayne Halsdorf08/2013
2117(16*10^127259+197)/3127260Robert Price04/2019
2118(234483*27^88884-145)/26127230Curtis Bright05/2015
21192^422515-114997127190Enzo Doria06/2015
21205*10^127179-3127180Robert Price07/2015
2121(44*10^127169-233)/9127170Robert Price01/2019
21225*10^127153+77127154Robert Price12/2018
2123-516776642557847117490*Bern(37960)/34256837217082767928421792453127042Thomas Ritschel06/2017
2124(78^67141-1)/77127036Paul Bourdelais09/2017
21252^421860-113285126993Enzo Doria07/2014
2126(2^421827-7)/11126982Lelio R Paula05/2015
212711^121910-840126957Enzo Doria12/2012
2128(71^68539+1)/72126882Paul Bourdelais09/2017
2129(5*10^126871-119)/3126872Robert Price03/2018
2130331^50339-10004126846Enzo Doria07/2012
21312^421363-2790757126843Enzo Doria03/2016
2132(106*10^126839-1)/3126841Serge Batalov12/2014
2133(7*2^421243+1)/39126807Lelio R Paula05/2014
2134(14*10^126784-83)/3126785Robert Price12/2018
21352^421161-286183126783Enzo Doria06/2015
21362^420939-113935126716Enzo Doria10/2014
2137177^56363-2126703Lelio R Paula10/2017
21382^420741-113659126656Enzo Doria08/2014
21392^420694-21126642Lelio R Paula05/2017
2140(13*10^126638+437)/9126639Robert Price04/2018
21414*10^126625+87126626Robert Price08/2018
2142(31*2^420556+1)/7126601Lelio R Paula05/2014
21432^420424-59189126561Enzo Doria10/2015
21442^420126+71893126471Enzo Doria04/2016
2145(43*10^126441+47)/9126442Robert Price12/2018
21462^419866+1877059126393Enzo Doria07/2016
2147F(604711)126377Henri Lifchitz02/2005
21482^419757+72707126360Enzo Doria04/2016
21492^419720-21569126349Enzo Doria07/2013
21502^419637+29126324Henri Lifchitz02/2006
21512^419612+1876741126316Enzo Doria07/2016
21522^419520+2793271126289Enzo Doria03/2016
2153(2^419447-5)/369126264Lelio R Paula05/2014
21542^419328-1859939126231Enzo Doria03/2016
21552^419282-1851507126217Enzo Doria08/2015
21562^419251+1866143126208Enzo Doria03/2016
215711^121185+2126202Robert Price05/2014
2158(23*2^419036-1)/1393126141Lelio R Paula05/2014
21592^418851+23126087Robert Price09/2015
2160(2^418849-9)/2681126083Lelio R Paula05/2014
21612^418829+167126081Lelio R Paula01/2012
2162(31*2^418782-1)/75891126063Lelio R Paula05/2014
2163(19*2^418754-1)/15126058Lelio R Paula05/2014
21642^418319-109501125927Enzo Doria04/2014
21652^418316-112373125926Enzo Doria06/2014
2166(8*10^125894-29)/3125895Robert Price07/2018
2167(26*10^125886-413)/9125887Robert Price05/2018
21682^417968+1869811125821Enzo Doria06/2016
21692^417902+63125802Lelio R Paula09/2015
2170(10^125792-91)/9125792Serge Batalov12/2014
2171(35*10^125754-593)/9125755Robert Price07/2018
2172(32*10^125751-77)/9125752Robert Price06/2018
21732^417704+77011125742Enzo Doria05/2016
2174(10^125706+149)/3125706Serge Batalov12/2014
21752^417419-115309125656Enzo Doria07/2015
21762^417300+77281125620Enzo Doria05/2016
21772^417095-1657125559Yves Minet07/2014
21782^416773-25125462Lelio R Paula09/2015
2179(289511#+292834)/(2^3*146417)125444Makoto Morimoto10/2017
2180(11*2^416691+1)/43125436Lelio R Paula05/2014
2181(289511#+1896)/(2*3^3*79*780193*9911849)125434Makoto Morimoto06/2019
21822^416641-2*416641+1125422Robert Price05/2018
2183(21*2^416566-1)/17125399Lelio R Paula05/2014
21842^416530+1870429125389Enzo Doria05/2016
2185(56*10^125385+691)/9125386Robert Price05/2019
21862^416490+1875109125376Enzo Doria09/2016
21872^416416-114929125354Enzo Doria05/2015
2188(172*10^125292-1)/9125294Serge Batalov12/2014
21892^416134+1865899125269Enzo Doria03/2016
2190153^57337-152125264Norbert Schneider12/2018
2191(9*2^415992+1)/13560845125220Lelio R Paula05/2014
2192(23^91943-1)/22125201Robert Price01/2012
219343125^27010-106125185Enzo Doria08/2012
2194(38*10^125166+349)/9125167Robert Price10/2018
21952^415765-112603125158Enzo Doria06/2014
21962^415290-113591125015Enzo Doria08/2014
21972^415276-460919125011Enzo Doria06/2015
21982^415259+77243125006Enzo Doria05/2016
21992^415144-3683124971Yves Minet10/2011
22002^414874+79124890Lelio R Paula01/2015
2201(2^414765+7)/1389124854Lelio R Paula05/2014
22022^414618+79459124813Enzo Doria06/2016
22032^414432-1846709124757Enzo Doria07/2015
22042*10^124751-51124752Robert Price04/2018
2205(56*10^124735+367)/9124736Robert Price06/2019
2206(13*2^414274-1)/153124708Lelio R Paula05/2014
2207(7*10^124648+197)/3124649Robert Price07/2018
22092^414032-5124637Henri Lifchitz07/2006
22082^414032+1872331124637Enzo Doria05/2016
221014120^30009-30009^14120124533Norbert Schneider02/2015
221164^68909-63^68909124463Robert Price07/2013
22122^413387+76253124442Enzo Doria04/2016
22132^413352+524287124432Paul Underwood09/2018
2214287117#+391613124424Nicolas PALAU01/2017
2215(4*10^124420+83)/3124421Robert Price02/2018
2216(27*2^413207-1)/108335124385Lelio R Paula05/2014
2217(41*10^124335-383)/9124336Robert Price11/2018
22182^412868-120599124286Paul Bourdelais02/2012
221945^75145-2124231Lelio R Paula08/2015
22202^412645-112213124219Enzo Doria06/2014
22212^412248+74611124100Enzo Doria04/2016
2222(22*10^124096-13)/9124097Robert Price06/2018
22232^412192-3329124083Yves Minet12/2014
2224(25*2^412191-1)/23124082Lelio R Paula05/2014
2225F(593689)124074Henri Lifchitz01/2005
2226(11*2^412161+1)/19124073Lelio R Paula05/2014
22272^411884-113279123990Enzo Doria07/2014
2228(2^411832+1)/257123972Lelio R Paula05/2014
2229(26*10^123970-89)/9123971Robert Price06/2018
22302^411790-1853531123962Enzo Doria08/2015
2231(5^177337+1)/6123953Paul Bourdelais11/2008
22322^411711-113257123938Enzo Doria07/2014
2233(23*2^411675-1)/3123928Lelio R Paula05/2014
2234(11*10^123899-179)/3123900Robert Price09/2018
22352^411325-351103123822Enzo Doria06/2015
22362^411052+1872481123739Enzo Doria05/2016
22372^410997+39123723Lelio R Paula05/2014
2238155^56438+154123618Norbert Schneider01/2019
22392^410596-39123602Lelio R Paula05/2014
22402^410540-115079123585Enzo Doria06/2015
2241(7*10^123563+107)/3123564Robert Price02/2018
2242(3*2^410392-1)/9229123537Lelio R Paula05/2014
22432^410206-113081123485Enzo Doria07/2014
2244(25*2^410192+1)/10397123478Lelio R Paula04/2014
22452^409909-189123395Enzo Doria05/2014
22462^409896-109043123391Enzo Doria04/2014
22472^409890+75409123390Enzo Doria04/2016
2248133^58076-2123345Lelio R Paula10/2017
2249F(590041)123311Henri Lifchitz01/2005
22502^409566-113501123292Enzo Doria08/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2019 07:14 (Time in France)

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