PRP Records

Probable Primes Top 10000

(253476 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 ?
52512^294492-6588651Lelio R Paula10/2012
525220^68120-5388627Lelio R Paula01/2016
5253122^42477-12188623Norbert Schneider10/2018
52542^294391-11325788621Enzo Doria07/2014
52555^126784-1547688619Enzo Doria02/2013
52562^294327+988602Lelio R Paula10/2012
52572^294320+1891588600Lelio R Paula10/2013
5258(98*10^88595-89)/9988595Ray Chandler07/2011
5259(17*2^294262-1)/1388582Lelio R Paula02/2014
5260(2*10^88545+7)/988545Erik Branger03/2011
52612^294137-13388545Lelio R Paula10/2012
5262(2^294092-1017)/117188528Lelio R Paula01/2013
52634^147036+147036^4+188525Robert Price04/2014
5264(14^77213-5^77213)/988496Robert Price04/2013
52652^293965+279337788493Enzo Doria03/2016
526611^84971-15088489Enzo Doria08/2012
526748^52626-4788478Norbert Schneider08/2018
5268(2^293956-1017)/3985137669667788476Lelio R Paula01/2013
526911^84958-219088475Enzo Doria12/2012
52702^293880-11134788467Enzo Doria05/2014
5271(106*10^88459-1)/388461Serge Batalov12/2014
527210^88457+27873388458Patrick De Geest07/2017
527310^88457-40188457Robert Price06/2017
527411^84908-168088423Enzo Doria12/2012
52752^293679-11207588407Enzo Doria06/2014
52766^113608-6588405Lelio R Paula12/2015
52772^293624+8287588390Lelio R Paula10/2013
52782^293612-11233788387Enzo Doria06/2014
5279758^30693+30693^75888386Norbert Schneider05/2017
5280gcd(V(1062695),5*F(212539)*(F(212539)-1)+1)88383Serge Batalov04/2015
52815*10^88377+7788378Robert Price06/2016
5282(5*2^293526+1)/30388359Lelio R Paula01/2013
52832^293461-278584388341Enzo Doria03/2016
52842^293416-103788328Yves Minet11/2012
5285(2^293384-7)/388317Lelio R Paula01/2013
5286(3^185092-5)/488311Lelio R Paula01/2013
5287(5*10^88303-173)/388304Robert Price11/2017
528814^77039-5788297Lelio R Paula11/2015
52893*10^88293-5988294Robert Price10/2017
52905^126303+4288283Lelio R Paula10/2015
529219^69025-1888266Theodore Burton01/2006
5291140^41128+13988266Norbert Schneider04/2019
52935*10^88261-388262Dmitry Domanov11/2010
52948^97731-7^(97731-1)88260Robert Price04/2016
52955*10^88254+5988255Robert Price09/2016
52964*3^184968-788253Lelio R Paula08/2014
52977^104426+8888251Lelio R Paula10/2015
52982^293142+9988245Lelio R Paula10/2012
529911^84736-213088244Enzo Doria12/2012
5300(10^110315+1)/(10^22063+1)/582481268216764857846028164188225Makoto Kamada04/2019
53012^293068-8988223Lelio R Paula10/2012
53022^293014-10965588207Enzo Doria04/2014
53038*7^104371-388205Lelio R Paula10/2014
53042^292995-214588201Lelio R Paula10/2013
53055*10^88182+7788183Robert Price06/2016
53072^292929+4387788181Donovan Johnson04/2005
53066^113321+13188181Lelio R Paula12/2015
53082^292904-58394988173Paul Bourdelais04/2013
53092^292894-11185188170Enzo Doria05/2014
53102^292872-279734988164Enzo Doria03/2016
53112^292860-10968588160Enzo Doria04/2014
53129*6^113288-588157Lelio R Paula10/2014
5313(2*10^88112-23)/388112Robert Price09/2017
5314(73*10^88105+17)/988106Robert Price10/2015
531511^84588+7888090Lelio R Paula11/2015
5316(265*10^88077+11)/388079Robert Price03/2017
531791^44959-90^4495988077Robert Price07/2015
53186^113177-5^11317788069Jean-Louis Charton01/2009
5319(10^88020+101)/388020Robert Price04/2016
532052^51285-5188006Norbert Schneider09/2018
5321(10^(2*43982+1)-6*10^43982-1)/387965Robert Price02/2016
5322(424*10^87930-1)/987932Robert Price11/2017
5323p(18225)#/2+12887929Robert Price04/2017
53244*6^112977+787914Lelio R Paula10/2014
532514^76677+6987882Lelio R Paula11/2015
5326(22*10^87863-1)/387864Robert Price12/2014
53272^291822-279781187848Enzo Doria04/2016
53282^291716-11138987816Enzo Doria05/2014
5329(782*10^87809-71)/987811Robert Price06/2017
53303^184039+182087809Lelio R Paula12/2015
533112^81356+4187798Lelio R Paula11/2015
53326^112792-1898387770Enzo Doria03/2013
53333*6^112787-587766Lelio R Paula10/2014
53347^103848+8287762Lelio R Paula10/2015
5335(19*2^291534-1)/17869639587754Lelio R Paula02/2014
5336(3^183915+5)/12887748Lelio R Paula01/2013
533719^68619+2487747Lelio R Paula12/2015
53392^291480+118587745Lelio R Paula10/2013
53382^291482+186736987745Enzo Doria03/2016
53402^291467-93787741Yves Minet05/2013
5341(25*10^87726+161)/387727Robert Price01/2017
534211^84239-285087726Enzo Doria12/2012
534310^87720+21554187721Patrick De Geest01/2011
534410^87720-387720Markus Tervooren07/2010
5345(5*10^87712-473)/987712Robert Price12/2017
5346(2^291357+5)/684787704Lelio R Paula01/2013
534793^44541-287679Lelio R Paula09/2013
53482^291261-10956187679Enzo Doria04/2014
5349(4*10^87669+149)/987669Robert Price03/2017
53502^291217+425787666Lelio R Paula10/2013
53512*12^81214-5^8121487645Mike Oakes12/2010
5352(5*10^87622-473)/987622Robert Price12/2017
535312^81188+8587617Lelio R Paula11/2015
5354(21*2^290980-1)/587595Lelio R Paula02/2014
53552^290958+12787588Lelio R Paula09/2012
53562^290923-6787577Lelio R Paula09/2012
53573*10^87573-9787574Robert Price08/2017
5358(13*10^87565+11)/387566Robert Price05/2015
5359(2^290857-7)/5587555Lelio R Paula01/2013
53602^290802+8287587541Lelio R Paula10/2013
5361(509203*2^290792-1)/756098787536Lelio R Paula04/2015
53623^183441+23687524Lelio R Paula12/2015
53632^290618-3387485Lelio R Paula09/2012
5364(184*10^87473-1)/387475Robert Price02/2017
53652^290534-11515187460Enzo Doria06/2015
53662^290512-10975787453Enzo Doria04/2014
5367(32*10^87448-41)/987449Robert Price05/2015
5368(2^290491+9)/317987444Lelio R Paula01/2013
5369(25*2^290489-1)/5180987443Lelio R Paula02/2014
53702^290426+8287587427Lelio R Paula11/2013
53713*2^290415-787425Lelio R Paula08/2014
537310^87408+5787409Robert Price03/2011
53722^290366+7477987409Enzo Doria04/2016
537410^87408-12356987408Patrick De Geest07/2013
53752^290265+5890587379Lelio R Paula10/2013
53767^103391+1687376Lelio R Paula10/2015
5377(115*10^87368-7)/987370Robert Price11/2017
5378(92^44491-1)/9187369Paul Bourdelais08/2017
53798*7^103379+387367Lelio R Paula10/2014
5380(2^290226+7)/7187365Lelio R Paula01/2013
538113^78407-3087341Lelio R Paula11/2015
53824*10^87337-9987338Robert Price12/2016
53837*10^87319+3987320Robert Price07/2016
53843*5^124921+287317Lelio R Paula10/2014
53853^182984+8887306Lelio R Paula12/2015
5386(10^87323-1)/(9*33909262597306826117)87303Alfred Reich02/2019
53874*10^87287-9987288Robert Price12/2016
538811^83813-186087283Enzo Doria12/2012
5389734^30453+30453^73487270Norbert Schneider04/2017
539012^80855+2987258Lelio R Paula11/2015
53913*6^112119-587247Lelio R Paula10/2014
539212^80806+7987205Lelio R Paula11/2015
539391382^9+9^9138287201Andrey Kulsha11/2004
5394(21181*2^289657+1)/8187198Lelio R Paula06/2014
53956^112054-4787195Lelio R Paula12/2015
5396(55459*2^289632+1)/5587191Lelio R Paula06/2014
539715^74131-6887185Lelio R Paula11/2015
53982^289583-74187174Lelio R Paula10/2013
53997^103146+1287169Lelio R Paula10/2015
54005*2^289556-387166Lelio R Paula08/2014
54012^289543-11273587162Enzo Doria06/2014
54028*3^182655-787150Lelio R Paula08/2014
54032*10^87144+8187145Robert Price01/2017
54047^103106+2*3^10310687135Mike Oakes08/2010
54058*3^182614+787130Lelio R Paula08/2014
5406(2^289368-509203)/987108Lelio R Paula01/2013
54073^182566+1487107Robert Price09/2013
5408(3^182385-5)/287020Lelio R Paula01/2013
540911^83534-886992Lelio R Paula11/2015
54104^144479-1426786986Mike Oakes03/2011
5411(145*10^86982-1)/986984Serge Batalov12/2014
5412(151*10^86963-1)/386965Robert Price04/2017
541315^73940-5886961Lelio R Paula11/2015
54142^288761-11314386926Enzo Doria07/2014
54152^288747+308386922Yves Minet03/2011
541630^58842+2986917Norbert Schneider03/2017
5417(10^86906-13)/386906Robert Price02/2017
54182^288692-11002786905Enzo Doria04/2014
5419(2^288682+7)/25989544986894Lelio R Paula01/2013
5420(2^288636+47)/129386885Lelio R Paula01/2013
54213^182089-3486879Robert Price11/2013
54222^288543-10980186861Enzo Doria04/2014
542360^48847-5986858Norbert Schneider10/2014
54242^288470-6487586839Lelio R Paula10/2013
542510^86816+3299786817Patrick De Geest07/2013
542610^86816-9986816Robert Price05/2011
5427(89*10^86802-539)/986803Robert Price11/2017
542841487!2+25686786Robert Price01/2015
5429(5*2^288301-1)/99986785Lelio R Paula02/2014
54302^288243+7604386770Enzo Doria04/2016
5431(29*2^288232+1)/1586767Lelio R Paula01/2013
54329*6^111495+586761Lelio R Paula10/2014
5433(5*2^288202+1)/8186757Lelio R Paula01/2013
54349*7^102654-286754Lelio R Paula10/2014
54352^288122-11284186734Enzo Doria06/2014
54365^124062-6886716Lelio R Paula10/2015
5437(2^288007-3)/12586697Lelio R Paula01/2013
5438379*10^86691+986694Arkadiusz Wesolowski10/2011
54397^102555+4886670Lelio R Paula10/2015
54402^287902-496186668Yves Minet05/2019
544177779!4+286660Robert Price08/2017
54422^287809-11135586640Enzo Doria05/2014
5443(47*2^287795+1)/786636Lelio R Paula04/2015
54449*7^102504+886627Lelio R Paula10/2014
54453^181551+3286622Robert Price11/2013
54462^287735-52134786617Paul Bourdelais05/2013
5447(1017*2^287600-1)/9186578Lelio R Paula04/2015
54482^287540-11296786559Enzo Doria06/2014
54493^181407+2086554Robert Price10/2013
5450(13*10^86546+83)/386547Robert Price09/2016
54512^287482-471586541Yves Minet05/2019
54523^181378-2^(181378-1)86540Robert Price01/2016
545383^45080-286513Lelio R Paula08/2013
5454(78557*2^287351+1)/61186504Lelio R Paula06/2014
545525*29^59147+2093686498Curtis Bright05/2015
54562^287298+187135986486Enzo Doria05/2016
5457118^41740-11786481Norbert Schneider08/2018
54583*10^86478+8986479Robert Price03/2017
54592^287272-7904986478Paul Bourdelais02/2012
5460906705*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5461811824*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5462779064*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5463768385*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5464700891*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5465652320*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5466377920*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
5467255060*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
5468187111*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
5469(10^86453-1)/986453Lew Baxter10/2000
547087^44563-86^4456386431Robert Price05/2015
54716^111057+6186420Lelio R Paula12/2015
54722^287057-10990986413Enzo Doria04/2014
54735^123608+2286399Lelio R Paula10/2015
5474(31*10^86364-121)/986365Robert Price06/2016
54752^286859+7166386354Enzo Doria04/2016
54762^286740+2983586318Lelio R Paula10/2013
54772*10^86310+9^8631086311Mike Oakes05/2011
547811^82878-186086309Enzo Doria12/2012
54792^286547+1609586260Lelio R Paula10/2013
5480(58*10^86242+329)/986243Robert Price11/2017
54812^286455-11042786232Enzo Doria05/2014
5482(37*10^86230+53)/986231Robert Price05/2015
54838*3^180700+586217Lelio R Paula08/2014
54843^180697-4086215Lelio R Paula12/2015
5485(13*2^286318-1)/1325786188Lelio R Paula02/2014
54862^286165+7786145Lelio R Paula08/2012
54879*2^286140+786138Lelio R Paula08/2014
5488(29*2^286108-1)/200236786123Lelio R Paula02/2014
548910^86110+16111386111Patrick De Geest07/2013
549010^86110-6986110Robert Price05/2011
54912^286036-86968810586106Lelio R Paula07/2016
5492(77*10^86072+31)/986073Robert Price10/2015
54932^285923+34586072Lelio R Paula09/2013
549413^77266-9086070Lelio R Paula11/2015
54952^285910-45890386068Enzo Doria04/2015
54962^285904-12586066Lelio R Paula08/2012
54972^285836+6583586046Lelio R Paula09/2013
5498(2^285766+78557)/386024Lelio R Paula01/2013
5499(5*10^86011-107)/386012Robert Price01/2017
55006^110522+16386003Lelio R Paula12/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 25 2019 15:53 (Time in France)

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