PRP Records

Probable Primes Top 10000

(255169 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 ?
32512^350851+135105617Lelio R Paula10/2011
32522^350841-741105614Lelio R Paula01/2017
32533*10^105582+77105583Robert Price09/2018
32548*10^105571+3105572Robert Price08/2015
32552^350674-78557105564Jorge Menendez03/2018
32562*5^151026-3105563Lelio R Paula11/2014
3257(2^350702+5)/34264674063105562Lelio R Paula12/2013
32586^135647-5^135647105554Jean-Louis Charton02/2009
32593^221211+236105545Lelio R Paula11/2016
3260(32*10^105530-77)/9105531Robert Price06/2018
326110^105515+33105516Lelio R Paula11/2016
326210^105515-41033105515Patrick De Geest12/2016
3263(29*2^350473-1)/267927105499Lelio R Paula03/2014
326417^85732-72105489Lelio R Paula01/2017
32652^350307-110329105453Enzo Doria05/2014
32662^350253-20365105437Enzo Doria06/2013
3267(3*29^72089-1075)/4105423Curtis Bright05/2015
32682^350139-109009105403Enzo Doria04/2014
32693*5^150763+4105380Lelio R Paula11/2014
327012^97643+91105375Lelio R Paula02/2017
32716*5^150744-7105367Lelio R Paula11/2014
32722^349996-112169105360Enzo Doria06/2014
327311^101142-1080105329Enzo Doria12/2012
3274(68*10^105320-41)/9105321Robert Price10/2013
32753^220712-9934105307Enzo Doria05/2014
32767*10^105296+9105297Robert Price09/2015
32772^349739+1873373105282Enzo Doria06/2016
32787^124574+24105278Lelio R Paula11/2016
32792^349708-20957105273Enzo Doria06/2013
32802^349649-20469105255Enzo Doria06/2013
32812^349607-20109105243Enzo Doria06/2013
32822^349594-19085105239Enzo Doria05/2013
32832^349530+1874479105220Enzo Doria06/2016
3284(3^220528+8)/8081105215Lelio R Paula12/2013
32853^220464-112852105189Enzo Doria07/2014
32862^349419-17349105186Enzo Doria05/2013
32872^349400-2579105180Yves Minet07/2014
32888*5^150471+3105176Lelio R Paula11/2014
3289655^37342+37342^655105165Norbert Schneider08/2018
329013^94403+94105160Lelio R Paula12/2016
32912^349301-112309105151Enzo Doria06/2014
32929*2^349220+5105127Lelio R Paula09/2014
32937*3^220317+8105119Lelio R Paula09/2014
32947^124386+88105119Lelio R Paula11/2016
32952^349171-19657105111Enzo Doria06/2013
3296(2^(6*58185+1)-5)/3105093Kevin Acres11/2013
3297(2^349111-5)/3105093Lelio R Paula12/2013
3298675^37142+37142^675105087Norbert Schneider08/2018
32992^348981-2797573105054Enzo Doria04/2016
33002^348869-6555105021Lelio R Paula01/2017
33015^150217+78104998Lelio R Paula11/2016
33022^348703-113005104971Enzo Doria06/2014
33042^348612-809104943Yves Minet05/2013
3303(73*10^104942-1)/9104943Robert Price01/2015
33052^348583-350407104934Enzo Doria06/2015
33062^348531-949104919Yves Minet05/2012
330720^80636-59104910Lelio R Paula12/2016
33088*10^104893-13104894Robert Price08/2019
33092^348437+35104890Lelio R Paula09/2011
33102^348348+135104864Lelio R Paula09/2011
3311(2^348284+9)/25104843Lelio R Paula12/2013
331275^55914-74104843Norbert Schneider01/2015
33132^348268+255255104840Lelio R Paula01/2017
33145^149985-52104836Lelio R Paula11/2016
33152^348224-20249104826Enzo Doria06/2013
33162^348212-20105104823Enzo Doria06/2013
331720^80562+19104814Lelio R Paula12/2016
33182*10^104811-87104812Robert Price04/2018
33192^348149-20053104804Enzo Doria06/2013
33202^348095-171104788Lelio R Paula09/2011
33212^348003-20377104760Enzo Doria06/2013
33222^347994-741104757Lelio R Paula12/2016
3323(13*2^347972-1)/282309104746Lelio R Paula03/2014
33242^347910-109937104732Enzo Doria04/2014
33255^149794+28104702Lelio R Paula11/2016
3326105^51800-2104698Lelio R Paula10/2017
3327(16^86939+3^86939)/19104684Robert Price06/2013
3328(15^89009-1)/14104682Paul Bourdelais03/2010
33292^347731-18609104678Enzo Doria05/2013
33304*6^134519+7104677Lelio R Paula11/2014
33312^347612-18545104642Enzo Doria05/2013
33326^134465+95104635Lelio R Paula11/2016
33332^347517-17301104614Enzo Doria05/2013
33343^219222-310104596Lelio R Paula11/2016
3335(15*2^347399-1)/13104578Lelio R Paula03/2014
33362^347372-17853104570Enzo Doria05/2013
33372^347314+99104552Lelio R Paula09/2011
33382^347300-22233104548Enzo Doria06/2013
33392^347287-19845104544Enzo Doria06/2013
3340(31*2^347254-1)/891104533Lelio R Paula03/2014
33415*F(250091)*(F(250091)-1)+1104532Serge Batalov04/2015
33427*2^347239-3104531Lelio R Paula09/2014
3343(3^219098-8)/514147439969104525Lelio R Paula12/2013
33445*3^219047+8104513Lelio R Paula09/2014
33452^347148-109073104502Enzo Doria04/2014
33462^347129-20145104497Enzo Doria06/2013
33474*10^104461-57104462Robert Price10/2018
33482^346923-19585104435Enzo Doria05/2013
3349(11*2^346864-1)/175104416Lelio R Paula03/2014
33502^346854+346854^2+1104414Robert Price06/2014
33512^346834+11715104408Lelio R Paula04/2015
335279^55009+78104387Norbert Schneider02/2015
33533^218744+58104368Lelio R Paula11/2016
33542^346649+65104352Lelio R Paula09/2011
33552^346638-17265104349Enzo Doria05/2013
33565*10^104326+77104327Robert Price12/2018
33582^346527-111817104316Enzo Doria05/2014
33576^134055+101104316Lelio R Paula11/2016
335992105!4+8104312Robert Price09/2019
33606^134013+163104283Lelio R Paula11/2016
336118^83049-89104250Lelio R Paula01/2017
33622^346213+484049104221Enzo Doria04/2017
336318^83021-91104214Lelio R Paula01/2017
336410^104212+128779104213Patrick De Geest05/2016
336510^104212+237447104213Patrick De Geest05/2016
336610^104212+242139104213Patrick De Geest05/2016
336710^104212+269199104213Patrick De Geest05/2016
3368(10^104212-71)/1104212Serge Batalov12/2014
33692^346078+7695104180Lelio R Paula12/2016
33702^346055-19537104173Enzo Doria05/2013
3371(3*2^346057+1)/77104173Lelio R Paula12/2013
33722^346037-20125104168Enzo Doria06/2013
3373(34*10^104168-7)/9/13/551179104162Makoto Morimoto05/2016
33746^133854-17993104159Enzo Doria03/2013
33752^345990+1874239104154Enzo Doria06/2016
33762^345988-20373104153Enzo Doria06/2013
3377(26*10^104132-503)/9104133Robert Price07/2018
33783*5^148968+8104125Lelio R Paula11/2014
3379(7*10^104113+53)/3104114Robert Price05/2018
3380p(21253)#/2+8104113Robert Price01/2017
3381322^41507+41507^322104094Norbert Schneider12/2014
33826^133768-17423104092Enzo Doria03/2013
33832^345786-19557104092Enzo Doria05/2013
3384171^46606-2104072Lelio R Paula10/2017
33852^345704-149104068Lelio R Paula09/2011
33866^133704-17273104042Enzo Doria02/2013
3387(3*2^345590-1)/23104033Lelio R Paula03/2014
3388(19*2^345590+1)/33859104030Lelio R Paula12/2013
33892^345547+11104021Lelio R Paula09/2011
3390(19*10^104014-49)/3104015Robert Price05/2019
33912^345504+723104008Lelio R Paula09/2011
33922^345498-20037104006Enzo Doria06/2013
339318^82854-37104005Lelio R Paula01/2017
33942^345486-109065104002Enzo Doria04/2014
33952^345487-1851507104002Enzo Doria08/2015
33962^345476+777103999Lelio R Paula09/2011
33974*10^103981-83103982Robert Price10/2018
3398(5*2^345321-1)/3103953Lelio R Paula03/2014
3399(2^345267-9)/539049127103927Lelio R Paula12/2013
3400(19*10^103907+77)/3103908Robert Price05/2019
3401(78557*2^345163+1)/78589103905Lelio R Paula07/2014
34022^345106-112181103888Enzo Doria06/2014
34032^345079+99103880Lelio R Paula09/2011
340411^99736-1500103865Enzo Doria12/2012
34052^344842-20157103808Enzo Doria06/2013
3406(47*2^344822+1)/1071103801Lelio R Paula05/2015
34072^344802-20765103796Enzo Doria06/2013
34082^344794-3821103794Yves Minet05/2011
34092^344782-109103103790Enzo Doria04/2014
34103^217521-112292103784Enzo Doria06/2014
34112^344759-3505103783Lelio R Paula11/2016
34122^344735-147103776Lelio R Paula09/2011
3413L(496533)-p(496533)103770Robert Price02/2018
34142*10^103749-69103750Robert Price03/2018
3415(55459*2^344617+1)/3103745Lelio R Paula07/2014
34162^344607-108891103738Enzo Doria03/2014
34172^344541-19561103718Enzo Doria05/2013
3418(1017*2^344529-1)/569103714Lelio R Paula05/2015
3419(4*10^103703-1)/3103704Serge Batalov08/2009
34202^344444-455103688Yves Minet03/2012
3421(13*53^238539*617^9)/10^307661103673Hans Havermann06/2017
34222^344317-109933103650Enzo Doria04/2014
34232^344309-1852033103648Enzo Doria08/2015
34242^344213-21253103619Enzo Doria06/2013
34252^344196-465103614Lelio R Paula11/2016
34262^344187-20001103611Enzo Doria06/2013
3427(117191#+(355573#)/(117191#))/(200233679)103602Makoto Morimoto10/2017
342820^79621-19^79621103590Jean-Louis Charton03/2011
3429Phi(155391,10)/1243129103586Maksym Voznyy09/2015
34302^344085-20365103580Enzo Doria06/2013
34315^148169+54103566Lelio R Paula11/2016
34322^344017-108795103560Enzo Doria03/2014
34332^343971-5077103546Lelio R Paula09/2011
3434(7*10^103531+71)/3103532Robert Price05/2018
34352^343899+141103524Lelio R Paula08/2011
3436(2^343933+1)/(3*98294339989393)103520Gord Palameta08/2018
34376^133029-67103517Lelio R Paula11/2016
3438(17*2^343877+1)/13625103515Lelio R Paula12/2013
3439(136*10^103474-1)/9103476Serge Batalov12/2014
34405^148014-24103458Lelio R Paula11/2016
3441(22*10^103450+53)/3103451Robert Price07/2019
34422^343604+9931103436Yves Minet01/2011
34432^343601-21189103435Enzo Doria06/2013
34442^343508-115229103407Enzo Doria06/2015
3445(509203*2^343491-1)/16147103403Lelio R Paula05/2015
34463^216685-113056103386Enzo Doria07/2014
344791355!4+1024103381Robert Price09/2019
344844^62903-43^62903103379Jean-Louis Charton08/2012
344911^99262-20103371Lelio R Paula12/2016
3450(509203*2^343357-1)/5103366Lelio R Paula05/2015
34522^343356-2791889103361Enzo Doria03/2016
3451(25*10^103360-241)/9103361Robert Price05/2018
3453Phi(104989,10)/2939693103350Maksym Voznyy09/2015
34542^343182-171103309Lelio R Paula08/2011
3455(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
34562^343079-1835611103278Enzo Doria05/2015
34572^343063-1147103273Yves Minet06/2013
34589*6^132689+7103254Lelio R Paula11/2014
34592^342979-18085103247Enzo Doria05/2013
3460(16*10^103244-31)/3103245Robert Price03/2019
34612^342966-16995103244Lelio R Paula11/2016
3462(16*10^103214-31)/3103215Robert Price03/2019
3463(37*10^103211+611)/9103212Robert Price11/2018
34645^147650+16103203Lelio R Paula11/2016
3465gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
34662^342817+2707067103199Enzo Doria03/2016
346743^63177-42103198Theodore Burton02/2007
34682^342805-21025103195Enzo Doria06/2013
34692^342714+12285103168Lelio R Paula11/2016
347018^82178-4481103156Enzo Doria03/2013
34712^342665-17349103153Enzo Doria05/2013
34722^342612+175103137Lelio R Paula08/2011
34735*2^342585-3103130Lelio R Paula09/2014
3474(16*10^103127+77)/3103128Robert Price03/2019
34752^342503-19209103104Enzo Doria05/2013
34762^342476+51103096Lelio R Paula08/2011
34772^342460-18885103091Enzo Doria05/2013
34787^121968+82103075Lelio R Paula10/2016
34792^342392-108863103071Enzo Doria03/2014
34803^216014+28103065Lelio R Paula11/2016
34812^342353-108879103059Enzo Doria03/2014
348210^103055+276081103056Patrick De Geest12/2016
348310^103055-53103055Lelio R Paula11/2016
3484(58*10^103046+419)/9103047Robert Price05/2019
34857^121933+4103046Lelio R Paula11/2014
348619^80560-68103017Lelio R Paula10/2016
34872^342209+76607103016Enzo Doria05/2016
3489328^40945+40945^328103013Norbert Schneider12/2014
348812^95454-91103013Lelio R Paula10/2016
349025833^9716+9716^25833103009Hans Havermann01/2019
349165^56809-64^56809102990Robert Price08/2013
34925^147338-6102985Lelio R Paula11/2014
34932^342084-112739102978Enzo Doria06/2014
34949*6^132330+7102974Lelio R Paula11/2014
34952^342034-16737102963Enzo Doria05/2013
3496(9787*2^342011-1)/25102959Lelio R Paula05/2015
3497(3^215802-5)/124343756102956Lelio R Paula12/2013
34982^341991-17421102950Enzo Doria05/2013
34992^341969-112225102943Enzo Doria06/2014
3500(9787*2^341864-1)/3102915Lelio R Paula05/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 13 2019 10:51 (Time in France)

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