PRP Records

Probable Primes Top 10000

(193407 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 ?
7512^648619-24835195254Enzo Doria09/2013
7522^648190-24737195125Enzo Doria09/2013
753(57^111119+1)/58195110Paul Bourdelais10/2017
75411^187185-90194934Enzo Doria09/2012
7552^647068+77281194787Enzo Doria05/2016
75615^165559-14^165559194713Jean-Louis Charton03/2011
757F(931517)194676Henri Lifchitz09/2008
7582^646589+1179407194643Enzo Doria06/2016
7592^646289-114621194553Enzo Doria05/2015
7602^646236-39659194537Enzo Doria09/2015
7612^646161-59833194514Enzo Doria11/2015
7622*10^194413+3194414Robert Price07/2015
7632^645360-1848599194273Enzo Doria08/2015
764(112*10^194150-1)/3194152Serge Batalov12/2014
7652^644382+75169193979Enzo Doria04/2016
7662^644304-1861409193955Enzo Doria11/2015
7675*10^193907-9193908Robert Price05/2015
7682^644043+1876703193877Enzo Doria07/2016
7692^643735+1879733193784Enzo Doria09/2016
770(5^277183+1)/6193742Paul Bourdelais07/2010
7712^643216-286565193628Enzo Doria07/2015
7722^642888-24965193529Enzo Doria09/2013
7732^642448-114825193397Enzo Doria05/2015
7742^642437-1856623193393Enzo Doria10/2015
7752^642039-59797193273Enzo Doria11/2015
7762^641692-286349193169Enzo Doria07/2015
7772^641690-24737193168Enzo Doria09/2013
7782^641514+1876549193115Enzo Doria07/2016
7792^640888-2785619192927Enzo Doria10/2015
7802^640874-2783741192923Enzo Doria09/2015
7812^640181+467192714Lelio R Paula08/2013
7822^639536-1850249192520Enzo Doria08/2015
7832^639110-2792441192392Enzo Doria02/2016
7842^638955-29827192345Enzo Doria08/2015
7852^638713-2784223192272Enzo Doria10/2015
7862^638490-113507192205Enzo Doria08/2014
7872^638189-39943192115Enzo Doria09/2015
7882^638110+1877119192091Enzo Doria07/2016
7892^638066-2785211192078Enzo Doria10/2015
7902^637475-115309191900Enzo Doria07/2015
7912^636661+1876577191655Enzo Doria07/2016
792(34^125101-1)/33191589Paul Bourdelais11/2017
7932^636177-1855123191509Enzo Doria09/2015
7942^636158-113627191503Enzo Doria08/2014
795(37*25^136966+63)/4191472Curtis Bright05/2015
7962^636035+79823191466Enzo Doria06/2016
7972^636011-1860847191459Enzo Doria11/2015
7982^635926-1860611191433Enzo Doria11/2015
7993*10^191152-7191153Robert Price08/2015
8002^634883-1865677191119Enzo Doria02/2016
8012^634801+1871957191095Enzo Doria05/2016
802(35*10^191073+1)/9191074Serge Batalov07/2010
8032^634470-59861190995Enzo Doria11/2015
8042^634368-29519190964Enzo Doria08/2015
8052^634188-350609190910Enzo Doria06/2015
8062^633088-113879190579Enzo Doria10/2014
8072^633064+1874911190572Enzo Doria06/2016
8082^632795-351205190491Enzo Doria06/2015
8092^632156+78391190298Enzo Doria06/2016
8102^632082-1851971190276Enzo Doria08/2015
8112^632020+1880311190257Enzo Doria09/2016
8122^631637-462373190142Enzo Doria08/2015
8132^631122-39251189987Enzo Doria08/2015
8142^630839-97189902Yves Minet07/2017
8152^630359+1788953189757Enzo Doria05/2016
8162^630228+1871971189718Enzo Doria05/2016
8172^630108+781189682Lelio R Paula08/2013
8182^629870-1867811189610Enzo Doria04/2016
819(359^74189-1)/358189558Alexander Zhirkov11/2017
8202^629326+2792929189447Enzo Doria02/2016
821(10^189385-61)/3189385Serge Batalov12/2014
8222^629036+1874011189359Enzo Doria06/2016
8232^628930+80779189327Enzo Doria07/2016
8242^628582+1179439189223Enzo Doria06/2016
8252^627037-2785843188757Enzo Doria10/2015
826L(901657)188436Renaud Lifchitz11/2008
8272^625651+74213188340Enzo Doria04/2016
8282^625584-460919188320Enzo Doria06/2015
829(10^188164+359)/9188164Serge Batalov12/2014
8302^624481-113611187988Enzo Doria08/2014
8312^624077-112723187866Enzo Doria07/2014
8322^624008+1874941187846Enzo Doria06/2016
8332^623870+78679187804Enzo Doria05/2016
8342^623714-114035187757Enzo Doria11/2014
8352^623651-1834251187738Enzo Doria07/2015
8362^623146+1879609187586Enzo Doria09/2016
8372^622500+81931187392Enzo Doria08/2016
8382^622300-1861739187331Enzo Doria12/2015
8392^622052+76771187257Enzo Doria05/2016
8402^622005-24091187243Enzo Doria08/2013
8412^621879-351787187205Enzo Doria07/2015
8422^621700+79411187151Enzo Doria06/2016
8432^620929-113203186919Enzo Doria07/2014
8442^620347-1777186744Lelio R Paula07/2013
84511^179143-4170186559Enzo Doria12/2012
846(5^266863+1)/6186529Paul Bourdelais07/2010
8472^619297-2792353186427Enzo Doria02/2016
8482^618940-460139186320Enzo Doria06/2015
8492^618046+74179186051Enzo Doria04/2016
8502*10^185930-3185931Robert Price07/2015
851(82^97151+1)/83185928Paul Bourdelais10/2017
8522^617250+9385185811Lelio R Paula07/2013
85339^116749+2185756Robert Price04/2015
8542^616924-39719185713Enzo Doria09/2015
8552^616712+1867621185649Enzo Doria04/2016
856(3^388897+2^388897)/5185551Jean-Louis Charton09/2011
8574*10^185355+9185356Robert Price05/2015
8582^615622+76639185321Enzo Doria05/2016
8592^615591+1879223185312Enzo Doria08/2016
8602^615503+1876643185285Enzo Doria07/2016
8615^265007-4^265007185232Jean-Louis Charton02/2013
8622^614783-2790097185069Enzo Doria12/2015
8632^614745-29323185057Enzo Doria07/2015
864(((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840185052Serge Batalov07/2013
8652^614315+81353184928Enzo Doria08/2016
8662^614294-1849961184921Enzo Doria08/2015
8672^614266+1877809184913Enzo Doria08/2016
8682^613715-1860727184747Enzo Doria11/2015
8692^613487-349987184678Enzo Doria07/2015
870(95^93377+1)/96184672Paul Bourdelais11/2017
87114^161089-161089^14184629Serge Batalov05/2016
8722^613033-114621184542Enzo Doria05/2015
873(9^193247+1)/10184404Paul Bourdelais02/2010
8742^612341-1604809184334Enzo Doria05/2015
875(2^611999-1)/18464214225958267477777390354183184199Dario Alpern06/2017
8763*10^184124-7184125Robert Price08/2015
8772^611628-24537184119Enzo Doria08/2013
8782^611460+71881184068Enzo Doria04/2016
8792^610982-1867301183924Enzo Doria03/2016
8802^610597+1178897183809Enzo Doria05/2016
881(28*10^183760-1)/9183761Serge Batalov10/2014
8822^610401+1277183750Lelio R Paula07/2013
8832^610356-1849019183736Enzo Doria08/2015
884(63^102103+1)/64183717Paul Bourdelais10/2017
8852^609846-1834251183582Enzo Doria07/2015
88611^176176-240183469Enzo Doria11/2012
887(41^113749+1)/42183451Paul Bourdelais11/2017
888(101^91463+1)/102183320Paul Bourdelais11/2017
8892^608965-113989183317Enzo Doria10/2014
890A005165(43592)183312Serge Batalov07/2017
8912^608814-461261183272Enzo Doria06/2015
892(163*10^183227-1)/9183229Serge Batalov12/2014
8932^608293+143807183115Enzo Doria10/2016
8942^608164-462419183076Enzo Doria08/2015
8952^607950-1862303183012Enzo Doria12/2015
8962^607101+1871987182756Enzo Doria05/2016
8972^606869-69175182686Enzo Doria11/2015
8982^606560-357182593Enzo Doria05/2014
8992^605687+1866983182330Enzo Doria03/2016
9002^605655-114445182321Enzo Doria02/2015
901(20^140053+1)/21182212Paul Bourdelais04/2010
9022^605174-112751182176Enzo Doria06/2014
9032^604761+1874507182052Enzo Doria06/2016
9042^604705+1871957182035Enzo Doria05/2016
9052^603915+75233181797Enzo Doria04/2016
90611^174145-360181354Enzo Doria10/2012
9072^602351-396765181326Enzo Doria08/2013
9082^601957-113833181208Enzo Doria09/2014
90966^99581-65^99581181193Robert Price09/2013
91010^181182+383973181183Patrick De Geest04/2016
91110^181182-21181182Serge Batalov12/2014
9122^601521-29143181076Enzo Doria07/2015
9132^601442-2797811181053Enzo Doria04/2016
9145*10^180992-9180993Robert Price05/2015
91510^180979+79477180980Patrick De Geest04/2016
91610^180979+107739180980Patrick De Geest04/2016
91710^180979-11180979Serge Batalov12/2014
9182^601023-113851180926Enzo Doria10/2014
9192^600300-1852559180709Enzo Doria08/2015
920(10^180689+71)/9180689Serge Batalov07/2015
9212^600209+76487180681Enzo Doria05/2016
9222^599702-369885180529Enzo Doria11/2013
923Tau(643^11688)180524Nik Lygeros / Olivier Rozier05/2015
924(2951*29^123418-3)/4180490Curtis Bright05/2015
9252^598942+80779180300Enzo Doria07/2016
9262^598591-1844797180194Enzo Doria06/2015
927(100^90089+1)/101180176Paul Bourdelais08/2017
928Gamma-Prime(179849)179849Eric W. Weisstein06/2011
9292^597424-1859729179843Enzo Doria11/2015
930Phi(180683,10)179760Maksym Voznyy09/2015
931(10^180683-1)*9/(10^643-1)/(10^281-1)179760Robert Price07/2016
932(3^376657-2^376657)/22301107657179701Mike Oakes04/2017
9332^596690-461261179622Enzo Doria07/2015
9342^596684-113939179620Enzo Doria10/2014
9353^375887-112696179344Enzo Doria07/2014
9362^595144-1850429179157Enzo Doria08/2015
9372^594531+82253178972Enzo Doria09/2016
9382^594260-2787899178891Enzo Doria11/2015
93910^178695+136719178696Patrick De Geest05/2016
94010^178695-71178695Serge Batalov12/2014
941(2^148330+1)^4-2178608Cletus Emmanuel12/2003
9422^593222-14145178578Jorge Menendez10/2017
9432^593178+1867219178565Enzo Doria03/2016
944(18^142031-1)/17178287Paul Bourdelais03/2010
9452^591872-291929178172Enzo Doria07/2015
9462^591682-286871178115Enzo Doria07/2015
9474*10^178091+9178092Robert Price05/2015
948410747#+478483178007Makoto Morimoto02/2016
9492^590762-396765177838Enzo Doria08/2013
950(136*10^177754-1)/9177756Serge Batalov12/2014
951ReverseConsecutiveIntegerPrime(37765)177719Eric W. Weisstein04/2010
9522^589204+1881151177369Enzo Doria11/2016
9532^589132-69479177347Enzo Doria01/2016
9542^588912-113519177281Enzo Doria08/2014
95515^150706+2177245Robert Price06/2015
9562^588194-1861001177065Enzo Doria11/2015
9572^587560-113699176874Enzo Doria09/2014
9585^252763-12862176674Enzo Doria05/2014
9592^586804+81721176646Enzo Doria08/2016
9602^586570+1874419176576Enzo Doria06/2016
9612^585994-3311176402Yves Minet12/2014
9622^585832-112799176354Enzo Doria07/2014
9632^585336-461039176204Enzo Doria06/2015
9642^585095-1848127176132Enzo Doria08/2015
9652^584950-115451176088Enzo Doria07/2015
9662^584671-3697176004Yves Minet03/2017
96710^175608+2971175609Mike Oakes05/2010
96810^175608-55829175608Patrick De Geest09/2013
9692^583051+1879793175516Enzo Doria09/2016
9702^582860-23829175459Enzo Doria08/2013
9712^582670-23913175402Enzo Doria08/2013
9722^582573-29563175372Enzo Doria08/2015
9732^582435-1862767175331Enzo Doria12/2015
9742^582072-1848599175222Enzo Doria08/2015
9752^581560+1874911175068Enzo Doria06/2016
976(75^93307-1)/74174955Paul Bourdelais09/2017
9772^580528-114035174757Enzo Doria11/2014
9782^580046-459161174612Enzo Doria05/2015
9792^579992-39779174595Enzo Doria09/2015
980(2^578696+1)/257174203Lelio R Paula09/2015
9812^578656-1851809174193Enzo Doria08/2015
9822^578583-113917174171Enzo Doria10/2014
9832^578434-83174126Yves Minet07/2017
98415^148048-2174118Robert Price06/2015
9852^578346+2794249174100Enzo Doria03/2016
986(L!41532)/2173772Serge Batalov07/2017
9872^577146-49877173739Enzo Doria10/2015
9882^576889+49727173661Enzo Doria09/2016
989(2^576551-1)/4612409/64758208321/242584327930759173528Dario Alpern06/2014
9902^576016-113919173399Enzo Doria11/2014
9912^575911-1849387173367Enzo Doria08/2015
9922^575196-114053173152Enzo Doria11/2014
9932^574591-115387172970Enzo Doria07/2015
9942^574328+81121172890Enzo Doria07/2016
995(115*10^172862-1)/3172864Serge Batalov12/2014
9964*5^247217-9172798Lelio R Paula10/2015
99769061#+(467617#)/(69061#)172766Makoto Morimoto10/2017
9982^573668-2782319172692Enzo Doria09/2015
9992^573444-1855109172624Enzo Doria09/2015
10003^361608+2172531Robert Price08/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 12 2017 10:35 (Time in France)

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