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 ?
32512^351460-17289105801Enzo Doria05/2013
325219^82735+22105798Lelio R Paula01/2017
32532^351435-109077105793Enzo Doria04/2014
32542^351393+1089105780Lelio R Paula01/2017
32552^351364+72631105772Enzo Doria04/2016
32562^351305+1872467105754Enzo Doria05/2016
32573^221649+16105754Lelio R Paula11/2016
32588*3^221637-5105749Lelio R Paula09/2014
32592^351279-2780449105746Enzo Doria03/2016
326015^89903-26105735Lelio R Paula02/2017
32612^351213-73105726Lelio R Paula10/2011
32622^351192-4589105720Yves Minet07/2011
326320^81250-33105709Lelio R Paula12/2016
32642^351076-113159105685Enzo Doria07/2014
326593^53688-2105684Lelio R Paula09/2013
32662^351060-4559105680Yves Minet07/2011
3267((10^52836-1)*10000/9+5927)*10^52836+(10^52836-1)/9105676Hans Havermann08/2019
326811^101473-750105674Enzo Doria11/2012
32693*5^151181-8105672Lelio R Paula11/2014
327015^89831-34105650Lelio R Paula02/2017
327211^101448-360105648Enzo Doria08/2012
32713*7^125011+4105648Lelio R Paula11/2014
32732^350943-113269105645Enzo Doria07/2014
32742^350868-19725105622Enzo Doria06/2013
32752^350858-59291105619Enzo Doria10/2015
32762^350851+135105617Lelio R Paula10/2011
32772^350841-741105614Lelio R Paula01/2017
32783*10^105582+77105583Robert Price09/2018
32798*10^105571+3105572Robert Price08/2015
32802^350674-78557105564Jorge Menendez03/2018
32812*5^151026-3105563Lelio R Paula11/2014
3282(2^350702+5)/34264674063105562Lelio R Paula12/2013
32836^135647-5^135647105554Jean-Louis Charton02/2009
32843^221211+236105545Lelio R Paula11/2016
3285(32*10^105530-77)/9105531Robert Price06/2018
328610^105515+33105516Lelio R Paula11/2016
328710^105515-41033105515Patrick De Geest12/2016
3288(29*2^350473-1)/267927105499Lelio R Paula03/2014
328917^85732-72105489Lelio R Paula01/2017
32902^350307-110329105453Enzo Doria05/2014
32912^350253-20365105437Enzo Doria06/2013
3292(3*29^72089-1075)/4105423Curtis Bright05/2015
32932^350139-109009105403Enzo Doria04/2014
32943*5^150763+4105380Lelio R Paula11/2014
329512^97643+91105375Lelio R Paula02/2017
32966*5^150744-7105367Lelio R Paula11/2014
32972^349996-112169105360Enzo Doria06/2014
329811^101142-1080105329Enzo Doria12/2012
3299(68*10^105320-41)/9105321Robert Price10/2013
33003^220712-9934105307Enzo Doria05/2014
33017*10^105296+9105297Robert Price09/2015
33022^349739+1873373105282Enzo Doria06/2016
33037^124574+24105278Lelio R Paula11/2016
33042^349708-20957105273Enzo Doria06/2013
33052^349649-20469105255Enzo Doria06/2013
33062^349607-20109105243Enzo Doria06/2013
33072^349594-19085105239Enzo Doria05/2013
33082^349530+1874479105220Enzo Doria06/2016
3309(3^220528+8)/8081105215Lelio R Paula12/2013
33103^220464-112852105189Enzo Doria07/2014
33112^349419-17349105186Enzo Doria05/2013
33122^349400-2579105180Yves Minet07/2014
33138*5^150471+3105176Lelio R Paula11/2014
3314655^37342+37342^655105165Norbert Schneider08/2018
331513^94403+94105160Lelio R Paula12/2016
33162^349301-112309105151Enzo Doria06/2014
33179*2^349220+5105127Lelio R Paula09/2014
33187*3^220317+8105119Lelio R Paula09/2014
33197^124386+88105119Lelio R Paula11/2016
33202^349171-19657105111Enzo Doria06/2013
3321(2^(6*58185+1)-5)/3105093Kevin Acres11/2013
3322(2^349111-5)/3105093Lelio R Paula12/2013
3323675^37142+37142^675105087Norbert Schneider08/2018
33242^348981-2797573105054Enzo Doria04/2016
33252^348869-6555105021Lelio R Paula01/2017
33265^150217+78104998Lelio R Paula11/2016
3327(28*10^104972+149)/3104973Robert Price12/2019
33282^348703-113005104971Enzo Doria06/2014
33302^348612-809104943Yves Minet05/2013
3329(73*10^104942-1)/9104943Robert Price01/2015
33312^348583-350407104934Enzo Doria06/2015
33322^348531-949104919Yves Minet05/2012
333320^80636-59104910Lelio R Paula12/2016
33348*10^104893-13104894Robert Price08/2019
33352^348437+35104890Lelio R Paula09/2011
33362^348348+135104864Lelio R Paula09/2011
3337(2^348284+9)/25104843Lelio R Paula12/2013
333875^55914-74104843Norbert Schneider01/2015
33392^348268+255255104840Lelio R Paula01/2017
33405^149985-52104836Lelio R Paula11/2016
33412^348224-20249104826Enzo Doria06/2013
33422^348212-20105104823Enzo Doria06/2013
334320^80562+19104814Lelio R Paula12/2016
33442*10^104811-87104812Robert Price04/2018
33452^348149-20053104804Enzo Doria06/2013
33462^348095-171104788Lelio R Paula09/2011
33472^348003-20377104760Enzo Doria06/2013
33482^347994-741104757Lelio R Paula12/2016
3349(13*2^347972-1)/282309104746Lelio R Paula03/2014
33502^347910-109937104732Enzo Doria04/2014
33515^149794+28104702Lelio R Paula11/2016
3352105^51800-2104698Lelio R Paula10/2017
3353(16^86939+3^86939)/19104684Robert Price06/2013
3354(15^89009-1)/14104682Paul Bourdelais03/2010
33552^347731-18609104678Enzo Doria05/2013
33564*6^134519+7104677Lelio R Paula11/2014
33572^347612-18545104642Enzo Doria05/2013
33586^134465+95104635Lelio R Paula11/2016
33592^347517-17301104614Enzo Doria05/2013
33603^219222-310104596Lelio R Paula11/2016
3361(15*2^347399-1)/13104578Lelio R Paula03/2014
33622^347372-17853104570Enzo Doria05/2013
33632^347314+99104552Lelio R Paula09/2011
33642^347300-22233104548Enzo Doria06/2013
33652^347287-19845104544Enzo Doria06/2013
3366(31*2^347254-1)/891104533Lelio R Paula03/2014
33675*F(250091)*(F(250091)-1)+1104532Serge Batalov04/2015
33687*2^347239-3104531Lelio R Paula09/2014
3369(3^219098-8)/514147439969104525Lelio R Paula12/2013
33705*3^219047+8104513Lelio R Paula09/2014
33712^347148-109073104502Enzo Doria04/2014
33722^347129-20145104497Enzo Doria06/2013
33734*10^104461-57104462Robert Price10/2018
33742^346923-19585104435Enzo Doria05/2013
3375(11*2^346864-1)/175104416Lelio R Paula03/2014
33762^346854+346854^2+1104414Robert Price06/2014
33772^346834+11715104408Lelio R Paula04/2015
337879^55009+78104387Norbert Schneider02/2015
33793^218744+58104368Lelio R Paula11/2016
33809*10^104361+89104362Robert Price11/2019
33812^346649+65104352Lelio R Paula09/2011
33822^346638-17265104349Enzo Doria05/2013
33835*10^104326+77104327Robert Price12/2018
33852^346527-111817104316Enzo Doria05/2014
33846^134055+101104316Lelio R Paula11/2016
338692105!4+8104312Robert Price09/2019
33876^134013+163104283Lelio R Paula11/2016
338818^83049-89104250Lelio R Paula01/2017
33892^346213+484049104221Enzo Doria04/2017
339018^83021-91104214Lelio R Paula01/2017
339110^104212+128779104213Patrick De Geest05/2016
339210^104212+237447104213Patrick De Geest05/2016
339310^104212+242139104213Patrick De Geest05/2016
339410^104212+269199104213Patrick De Geest05/2016
3395(10^104212-71)/1104212Serge Batalov12/2014
33962^346078+7695104180Lelio R Paula12/2016
33972^346055-19537104173Enzo Doria05/2013
3398(3*2^346057+1)/77104173Lelio R Paula12/2013
33992^346037-20125104168Enzo Doria06/2013
3400(34*10^104168-7)/9/13/551179104162Makoto Morimoto05/2016
34016^133854-17993104159Enzo Doria03/2013
34022^345990+1874239104154Enzo Doria06/2016
34032^345988-20373104153Enzo Doria06/2013
3404(26*10^104132-503)/9104133Robert Price07/2018
34053*5^148968+8104125Lelio R Paula11/2014
3406(7*10^104113+53)/3104114Robert Price05/2018
3407p(21253)#/2+8104113Robert Price01/2017
3408322^41507+41507^322104094Norbert Schneider12/2014
34096^133768-17423104092Enzo Doria03/2013
34102^345786-19557104092Enzo Doria05/2013
3411171^46606-2104072Lelio R Paula10/2017
34122^345704-149104068Lelio R Paula09/2011
34136^133704-17273104042Enzo Doria02/2013
3414(3*2^345590-1)/23104033Lelio R Paula03/2014
3415(19*2^345590+1)/33859104030Lelio R Paula12/2013
34162^345547+11104021Lelio R Paula09/2011
3417(19*10^104014-49)/3104015Robert Price05/2019
34182^345504+723104008Lelio R Paula09/2011
34192^345498-20037104006Enzo Doria06/2013
342018^82854-37104005Lelio R Paula01/2017
34212^345486-109065104002Enzo Doria04/2014
34222^345487-1851507104002Enzo Doria08/2015
34232^345476+777103999Lelio R Paula09/2011
34244*10^103981-83103982Robert Price10/2018
3425(5*2^345321-1)/3103953Lelio R Paula03/2014
3426(2^345267-9)/539049127103927Lelio R Paula12/2013
3427(19*10^103907+77)/3103908Robert Price05/2019
3428(78557*2^345163+1)/78589103905Lelio R Paula07/2014
34292^345106-112181103888Enzo Doria06/2014
34302^345079+99103880Lelio R Paula09/2011
343111^99736-1500103865Enzo Doria12/2012
34322^344842-20157103808Enzo Doria06/2013
3433(47*2^344822+1)/1071103801Lelio R Paula05/2015
34342^344802-20765103796Enzo Doria06/2013
34352^344794-3821103794Yves Minet05/2011
34362^344782-109103103790Enzo Doria04/2014
34373^217521-112292103784Enzo Doria06/2014
34382^344759-3505103783Lelio R Paula11/2016
34392^344735-147103776Lelio R Paula09/2011
3440L(496533)-p(496533)103770Robert Price02/2018
34412*10^103749-69103750Robert Price03/2018
3442(55459*2^344617+1)/3103745Lelio R Paula07/2014
34432^344607-108891103738Enzo Doria03/2014
34442^344541-19561103718Enzo Doria05/2013
3445(1017*2^344529-1)/569103714Lelio R Paula05/2015
3446(4*10^103703-1)/3103704Serge Batalov08/2009
34472^344444-455103688Yves Minet03/2012
3448(13*53^238539*617^9)/10^307661103673Hans Havermann06/2017
34492^344317-109933103650Enzo Doria04/2014
34502^344309-1852033103648Enzo Doria08/2015
34512^344213-21253103619Enzo Doria06/2013
34522^344196-465103614Lelio R Paula11/2016
34532^344187-20001103611Enzo Doria06/2013
3454(117191#+(355573#)/(117191#))/(200233679)103602Makoto Morimoto10/2017
345520^79621-19^79621103590Jean-Louis Charton03/2011
3456Phi(155391,10)/1243129103586Maksym Voznyy09/2015
34572^344085-20365103580Enzo Doria06/2013
34585^148169+54103566Lelio R Paula11/2016
34592^344017-108795103560Enzo Doria03/2014
34602^343971-5077103546Lelio R Paula09/2011
3461(7*10^103531+71)/3103532Robert Price05/2018
34622^343899+141103524Lelio R Paula08/2011
3463(2^343933+1)/(3*98294339989393)103520Gord Palameta08/2018
34646^133029-67103517Lelio R Paula11/2016
3465(17*2^343877+1)/13625103515Lelio R Paula12/2013
3466(136*10^103474-1)/9103476Serge Batalov12/2014
34675^148014-24103458Lelio R Paula11/2016
3468(22*10^103450+53)/3103451Robert Price07/2019
34692^343604+9931103436Yves Minet01/2011
34702^343601-21189103435Enzo Doria06/2013
34712^343508-115229103407Enzo Doria06/2015
3472(509203*2^343491-1)/16147103403Lelio R Paula05/2015
34733^216685-113056103386Enzo Doria07/2014
347491355!4+1024103381Robert Price09/2019
347544^62903-43^62903103379Jean-Louis Charton08/2012
347611^99262-20103371Lelio R Paula12/2016
3477(509203*2^343357-1)/5103366Lelio R Paula05/2015
34782^343356-2791889103361Enzo Doria03/2016
3479(25*10^103360-241)/9103361Robert Price05/2018
3480Phi(104989,10)/2939693103350Maksym Voznyy09/2015
34812^343182-171103309Lelio R Paula08/2011
3482(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
34832^343079-1835611103278Enzo Doria05/2015
34842^343063-1147103273Yves Minet06/2013
34859*6^132689+7103254Lelio R Paula11/2014
34862^342979-18085103247Enzo Doria05/2013
3487(16*10^103244-31)/3103245Robert Price03/2019
34882^342966-16995103244Lelio R Paula11/2016
3489(16*10^103214-31)/3103215Robert Price03/2019
3490(37*10^103211+611)/9103212Robert Price11/2018
34915^147650+16103203Lelio R Paula11/2016
3492gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
34932^342817+2707067103199Enzo Doria03/2016
349443^63177-42103198Theodore Burton02/2007
34952^342805-21025103195Enzo Doria06/2013
34962^342714+12285103168Lelio R Paula11/2016
349718^82178-4481103156Enzo Doria03/2013
34982^342665-17349103153Enzo Doria05/2013
34992^342612+175103137Lelio R Paula08/2011
35005*2^342585-3103130Lelio R Paula09/2014


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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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