PRP Records

Probable Primes Top 10000

(174961 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 ?
40012^294391-11325788621Enzo Doria07/2014
40025^126784-1547688619Enzo Doria02/2013
40032^294327+988602Lelio R Paula10/2012
40042^294320+1891588600Lelio R Paula10/2013
4005(98*10^88595-89)/9988595Ray Chandler07/2011
4006(17*2^294262-1)/1388582Lelio R Paula02/2014
4008(2*10^88545+7)/988545Erik Branger03/2011
40072^294137-13388545Lelio R Paula10/2012
4009(2^294092-1017)/117188528Lelio R Paula01/2013
40104^147036+147036^4+188525Robert Price04/2014
4011(14^77213-5^77213)/988496Robert Price04/2013
40122^293965+279337788493Enzo Doria03/2016
401311^84971-15088489Enzo Doria08/2012
4014(2^293956-1017)/3985137669667788476Lelio R Paula01/2013
401511^84958-219088475Enzo Doria12/2012
40162^293880-11134788467Enzo Doria05/2014
4017(106*10^88459-1)/388461Serge Batalov12/2014
401810^88457-40188457Robert Price06/2017
401911^84908-168088423Enzo Doria12/2012
40202^293679-11207588407Enzo Doria06/2014
40216^113608-6588405Lelio R Paula12/2015
40222^293624+8287588390Lelio R Paula10/2013
40232^293612-11233788387Enzo Doria06/2014
4024758^30693+30693^75888386Norbert Schneider05/2017
4025gcd(V(1062695),5*F(212539)*(F(212539)-1)+1)88383Serge Batalov04/2015
40265*10^88377+7788378Robert Price06/2016
4027(5*2^293526+1)/30388359Lelio R Paula01/2013
40282^293461-278584388341Enzo Doria03/2016
40292^293416-103788328Yves Minet11/2012
4030(2^293384-7)/388317Lelio R Paula01/2013
4031(3^185092-5)/488311Lelio R Paula01/2013
403214^77039-5788297Lelio R Paula11/2015
40335^126303+4288283Lelio R Paula10/2015
403419^69025-1888266Theodore Burton01/2006
40355*10^88261-388262Dmitry Domanov11/2010
40368^97731-7^(97731-1)88260Robert Price04/2016
40375*10^88254+5988255Robert Price09/2016
40384*3^184968-788253Lelio R Paula08/2014
40397^104426+8888251Lelio R Paula10/2015
40402^293142+9988245Lelio R Paula10/2012
404111^84736-213088244Enzo Doria12/2012
40422^293068-8988223Lelio R Paula10/2012
40432^293014-10965588207Enzo Doria04/2014
40448*7^104371-388205Lelio R Paula10/2014
40452^292995-214588201Lelio R Paula10/2013
40465*10^88182+7788183Robert Price06/2016
40482^292929+4387788181Donovan Johnson04/2005
40476^113321+13188181Lelio R Paula12/2015
40492^292904-58394988173Paul Bourdelais04/2013
40502^292894-11185188170Enzo Doria05/2014
40512^292872-279734988164Enzo Doria03/2016
40522^292860-10968588160Enzo Doria04/2014
40539*6^113288-588157Lelio R Paula10/2014
4054(73*10^88105+17)/988106Robert Price10/2015
405511^84588+7888090Lelio R Paula11/2015
4056(265*10^88077+11)/388079Robert Price03/2017
405791^44959-90^4495988077Robert Price07/2015
40586^113177-5^11317788069Jean-Louis Charton01/2009
4059(10^88020+101)/388020Robert Price04/2016
4060(10^(2*43982+1)-6*10^43982-1)/387965Robert Price02/2016
4061p(18225)#/2+12887929Robert Price04/2017
40624*6^112977+787914Lelio R Paula10/2014
406314^76677+6987882Lelio R Paula11/2015
4064(22*10^87863-1)/387864Robert Price12/2014
40652^291822-279781187848Enzo Doria04/2016
40662^291716-11138987816Enzo Doria05/2014
4067(782*10^87809-71)/987811Robert Price06/2017
40683^184039+182087809Lelio R Paula12/2015
406912^81356+4187798Lelio R Paula11/2015
40706^112792-1898387770Enzo Doria03/2013
40713*6^112787-587766Lelio R Paula10/2014
40727^103848+8287762Lelio R Paula10/2015
4073(19*2^291534-1)/17869639587754Lelio R Paula02/2014
4074(3^183915+5)/12887748Lelio R Paula01/2013
407519^68619+2487747Lelio R Paula12/2015
40772^291480+118587745Lelio R Paula10/2013
40762^291482+186736987745Enzo Doria03/2016
40782^291467-93787741Yves Minet05/2013
4079(25*10^87726+161)/387727Robert Price01/2017
408011^84239-285087726Enzo Doria12/2012
408110^87720+21554187721Patrick De Geest01/2011
408210^87720-387720Markus Tervooren07/2010
4083(2^291357+5)/684787704Lelio R Paula01/2013
408593^44541-287679Lelio R Paula09/2013
40842^291261-10956187679Enzo Doria04/2014
4086(4*10^87669+149)/987669Robert Price03/2017
40872^291217+425787666Lelio R Paula10/2013
40882*12^81214-5^8121487645Mike Oakes12/2010
408912^81188+8587617Lelio R Paula11/2015
4090(21*2^290980-1)/587595Lelio R Paula02/2014
40912^290958+12787588Lelio R Paula09/2012
40922^290923-6787577Lelio R Paula09/2012
4093(13*10^87565+11)/387566Robert Price05/2015
4094(2^290857-7)/5587555Lelio R Paula01/2013
40952^290802+8287587541Lelio R Paula10/2013
4096(509203*2^290792-1)/756098787536Lelio R Paula04/2015
40973^183441+23687524Lelio R Paula12/2015
40982^290618-3387485Lelio R Paula09/2012
4099(184*10^87473-1)/387475Robert Price02/2017
41002^290534-11515187460Enzo Doria06/2015
41012^290512-10975787453Enzo Doria04/2014
4102(32*10^87448-41)/987449Robert Price05/2015
4103(2^290491+9)/317987444Lelio R Paula01/2013
4104(25*2^290489-1)/5180987443Lelio R Paula02/2014
41052^290426+8287587427Lelio R Paula11/2013
41063*2^290415-787425Lelio R Paula08/2014
410810^87408+5787409Robert Price03/2011
41072^290366+7477987409Enzo Doria04/2016
410910^87408-12356987408Patrick De Geest07/2013
41102^290265+5890587379Lelio R Paula10/2013
41117^103391+1687376Lelio R Paula10/2015
41128*7^103379+387367Lelio R Paula10/2014
4113(2^290226+7)/7187365Lelio R Paula01/2013
411413^78407-3087341Lelio R Paula11/2015
41154*10^87337-9987338Robert Price12/2016
41167*10^87319+3987320Robert Price07/2016
41173*5^124921+287317Lelio R Paula10/2014
41183^182984+8887306Lelio R Paula12/2015
41194*10^87287-9987288Robert Price12/2016
412011^83813-186087283Enzo Doria12/2012
4121734^30453+30453^73487270Norbert Schneider04/2017
412212^80855+2987258Lelio R Paula11/2015
41233*6^112119-587247Lelio R Paula10/2014
412412^80806+7987205Lelio R Paula11/2015
412591382^9+9^9138287201Andrey Kulsha11/2004
4126(21181*2^289657+1)/8187198Lelio R Paula06/2014
41276^112054-4787195Lelio R Paula12/2015
4128(55459*2^289632+1)/5587191Lelio R Paula06/2014
412915^74131-6887185Lelio R Paula11/2015
41302^289583-74187174Lelio R Paula10/2013
41317^103146+1287169Lelio R Paula10/2015
41325*2^289556-387166Lelio R Paula08/2014
41332^289543-11273587162Enzo Doria06/2014
41348*3^182655-787150Lelio R Paula08/2014
41352*10^87144+8187145Robert Price01/2017
41367^103106+2*3^10310687135Mike Oakes08/2010
41378*3^182614+787130Lelio R Paula08/2014
4138(2^289368-509203)/987108Lelio R Paula01/2013
41393^182566+1487107Robert Price09/2013
4140(3^182385-5)/287020Lelio R Paula01/2013
414111^83534-886992Lelio R Paula11/2015
41424^144479-1426786986Mike Oakes03/2011
4143(145*10^86982-1)/986984Serge Batalov12/2014
4144(151*10^86963-1)/386965Robert Price04/2017
414515^73940-5886961Lelio R Paula11/2015
41462^288761-11314386926Enzo Doria07/2014
41472^288747+308386922Yves Minet03/2011
414830^58842+2986917Norbert Schneider03/2017
4149(10^86906-13)/386906Robert Price02/2017
41502^288692-11002786905Enzo Doria04/2014
4151(2^288682+7)/25989544986894Lelio R Paula01/2013
4152(2^288636+47)/129386885Lelio R Paula01/2013
41533^182089-3486879Robert Price11/2013
41542^288543-10980186861Enzo Doria04/2014
415560^48847-5986858Norbert Schneider10/2014
41562^288470-6487586839Lelio R Paula10/2013
415710^86816+3299786817Patrick De Geest07/2013
415810^86816-9986816Robert Price05/2011
415941487!2+25686786Robert Price01/2015
4160(5*2^288301-1)/99986785Lelio R Paula02/2014
41612^288243+7604386770Enzo Doria04/2016
4162(29*2^288232+1)/1586767Lelio R Paula01/2013
41639*6^111495+586761Lelio R Paula10/2014
4164(5*2^288202+1)/8186757Lelio R Paula01/2013
41659*7^102654-286754Lelio R Paula10/2014
41662^288122-11284186734Enzo Doria06/2014
41675^124062-6886716Lelio R Paula10/2015
4168(2^288007-3)/12586697Lelio R Paula01/2013
4169379*10^86691+986694Arkadiusz Wesolowski10/2011
41707^102555+4886670Lelio R Paula10/2015
41712^287809-11135586640Enzo Doria05/2014
4172(47*2^287795+1)/786636Lelio R Paula04/2015
41739*7^102504+886627Lelio R Paula10/2014
41743^181551+3286622Robert Price11/2013
41752^287735-52134786617Paul Bourdelais05/2013
4176(1017*2^287600-1)/9186578Lelio R Paula04/2015
41772^287540-11296786559Enzo Doria06/2014
41783^181407+2086554Robert Price10/2013
4179(13*10^86546+83)/386547Robert Price09/2016
41803^181378-2^(181378-1)86540Robert Price01/2016
418183^45080-286513Lelio R Paula08/2013
4182(78557*2^287351+1)/61186504Lelio R Paula06/2014
418325*29^59147+2093686498Curtis Bright05/2015
41842^287298+187135986486Enzo Doria05/2016
41853*10^86478+8986479Robert Price03/2017
41862^287272-7904986478Paul Bourdelais02/2012
4187906705*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4188811824*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4189779064*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4190768385*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4191700891*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4192652320*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4193377920*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4194255060*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4195187111*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4196(10^86453-1)/986453Lew Baxter10/2000
419787^44563-86^4456386431Robert Price05/2015
41986^111057+6186420Lelio R Paula12/2015
41992^287057-10990986413Enzo Doria04/2014
42005^123608+2286399Lelio R Paula10/2015
4201(31*10^86364-121)/986365Robert Price06/2016
42022^286859+7166386354Enzo Doria04/2016
42032^286740+2983586318Lelio R Paula10/2013
42042*10^86310+9^8631086311Mike Oakes05/2011
420511^82878-186086309Enzo Doria12/2012
42062^286547+1609586260Lelio R Paula10/2013
42072^286455-11042786232Enzo Doria05/2014
4208(37*10^86230+53)/986231Robert Price05/2015
42098*3^180700+586217Lelio R Paula08/2014
42103^180697-4086215Lelio R Paula12/2015
4211(13*2^286318-1)/1325786188Lelio R Paula02/2014
42122^286165+7786145Lelio R Paula08/2012
42139*2^286140+786138Lelio R Paula08/2014
4214(29*2^286108-1)/200236786123Lelio R Paula02/2014
421510^86110+16111386111Patrick De Geest07/2013
421610^86110-6986110Robert Price05/2011
42172^286036-86968810586106Lelio R Paula07/2016
4218(77*10^86072+31)/986073Robert Price10/2015
42192^285923+34586072Lelio R Paula09/2013
422013^77266-9086070Lelio R Paula11/2015
42212^285910-45890386068Enzo Doria04/2015
42222^285904-12586066Lelio R Paula08/2012
42232^285836+6583586046Lelio R Paula09/2013
4224(2^285766+78557)/386024Lelio R Paula01/2013
4225(5*10^86011-107)/386012Robert Price01/2017
42266^110522+16386003Lelio R Paula12/2015
422741^53323-40^5332385999Robert Price07/2012
42282^285678-10961785998Enzo Doria04/2014
42296^110506-1667385991Enzo Doria02/2013
42312^285569-74185965Lelio R Paula09/2013
4230(32*10^85964+31)/985965Robert Price05/2015
42326*10^85910-785911Dmitry Domanov11/2010
42334*10^85881+6385882Robert Price06/2016
4234(10^85864+53)/985864Robert Price01/2015
42352^285230+34585863Lelio R Paula09/2013
42362^285199+7568385854Enzo Doria04/2016
4237p(17832)#/2+51285845Robert Price05/2017
423811^82426-123085838Enzo Doria11/2012
42392^285113-10988185828Enzo Doria04/2014
42405^122746-9285796Lelio R Paula10/2015
42412^285001-11346185794Enzo Doria08/2014
4242(11*10^85782-131)/385783Robert Price02/2017
42432^284913-11049185768Enzo Doria05/2014
42446^110220+4785768Lelio R Paula12/2015
42453*6^110202-585755Lelio R Paula10/2014
4246(157^39047-1)/15685742Alexander Zhirkov06/2016
4247(3^179705+7)/25085739Lelio R Paula12/2012
42482^284734-655585714Lelio R Paula09/2013
4249(10^85712+53)/985712Robert Price01/2015
4250(6883*2^284668-1)/385697Lelio R Paula04/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 22 2017 08:34 (Time in France)

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