PRP Records

Probable Primes Top 10000

(252402 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 ?
4751(14^77213-5^77213)/988496Robert Price04/2013
47522^293965+279337788493Enzo Doria03/2016
475311^84971-15088489Enzo Doria08/2012
475448^52626-4788478Norbert Schneider08/2018
4755(2^293956-1017)/3985137669667788476Lelio R Paula01/2013
475611^84958-219088475Enzo Doria12/2012
47572^293880-11134788467Enzo Doria05/2014
4758(106*10^88459-1)/388461Serge Batalov12/2014
475910^88457+27873388458Patrick De Geest07/2017
476010^88457-40188457Robert Price06/2017
476111^84908-168088423Enzo Doria12/2012
47622^293679-11207588407Enzo Doria06/2014
47636^113608-6588405Lelio R Paula12/2015
47642^293624+8287588390Lelio R Paula10/2013
47652^293612-11233788387Enzo Doria06/2014
4766758^30693+30693^75888386Norbert Schneider05/2017
4767gcd(V(1062695),5*F(212539)*(F(212539)-1)+1)88383Serge Batalov04/2015
47685*10^88377+7788378Robert Price06/2016
4769(5*2^293526+1)/30388359Lelio R Paula01/2013
47702^293461-278584388341Enzo Doria03/2016
47712^293416-103788328Yves Minet11/2012
4772(2^293384-7)/388317Lelio R Paula01/2013
4773(3^185092-5)/488311Lelio R Paula01/2013
4774(5*10^88303-173)/388304Robert Price11/2017
477514^77039-5788297Lelio R Paula11/2015
47763*10^88293-5988294Robert Price10/2017
47775^126303+4288283Lelio R Paula10/2015
477819^69025-1888266Theodore Burton01/2006
47795*10^88261-388262Dmitry Domanov11/2010
47808^97731-7^(97731-1)88260Robert Price04/2016
47815*10^88254+5988255Robert Price09/2016
47824*3^184968-788253Lelio R Paula08/2014
47837^104426+8888251Lelio R Paula10/2015
47842^293142+9988245Lelio R Paula10/2012
478511^84736-213088244Enzo Doria12/2012
47862^293068-8988223Lelio R Paula10/2012
47872^293014-10965588207Enzo Doria04/2014
47888*7^104371-388205Lelio R Paula10/2014
47892^292995-214588201Lelio R Paula10/2013
47905*10^88182+7788183Robert Price06/2016
47912^292929+4387788181Donovan Johnson04/2005
47926^113321+13188181Lelio R Paula12/2015
47932^292904-58394988173Paul Bourdelais04/2013
47942^292894-11185188170Enzo Doria05/2014
47952^292872-279734988164Enzo Doria03/2016
47962^292860-10968588160Enzo Doria04/2014
47979*6^113288-588157Lelio R Paula10/2014
4798(2*10^88112-23)/388112Robert Price09/2017
4799(73*10^88105+17)/988106Robert Price10/2015
480011^84588+7888090Lelio R Paula11/2015
4801(265*10^88077+11)/388079Robert Price03/2017
480291^44959-90^4495988077Robert Price07/2015
48036^113177-5^11317788069Jean-Louis Charton01/2009
4804(10^88020+101)/388020Robert Price04/2016
480552^51285-5188006Norbert Schneider09/2018
4806(10^(2*43982+1)-6*10^43982-1)/387965Robert Price02/2016
4807(424*10^87930-1)/987932Robert Price11/2017
4808p(18225)#/2+12887929Robert Price04/2017
48094*6^112977+787914Lelio R Paula10/2014
481014^76677+6987882Lelio R Paula11/2015
4811(22*10^87863-1)/387864Robert Price12/2014
48122^291822-279781187848Enzo Doria04/2016
48132^291716-11138987816Enzo Doria05/2014
4814(782*10^87809-71)/987811Robert Price06/2017
48153^184039+182087809Lelio R Paula12/2015
481612^81356+4187798Lelio R Paula11/2015
48176^112792-1898387770Enzo Doria03/2013
48183*6^112787-587766Lelio R Paula10/2014
48197^103848+8287762Lelio R Paula10/2015
4820(19*2^291534-1)/17869639587754Lelio R Paula02/2014
4821(3^183915+5)/12887748Lelio R Paula01/2013
482219^68619+2487747Lelio R Paula12/2015
48242^291480+118587745Lelio R Paula10/2013
48232^291482+186736987745Enzo Doria03/2016
48252^291467-93787741Yves Minet05/2013
4826(25*10^87726+161)/387727Robert Price01/2017
482711^84239-285087726Enzo Doria12/2012
482810^87720+21554187721Patrick De Geest01/2011
482910^87720-387720Markus Tervooren07/2010
4830(5*10^87712-473)/987712Robert Price12/2017
4831(2^291357+5)/684787704Lelio R Paula01/2013
483293^44541-287679Lelio R Paula09/2013
48332^291261-10956187679Enzo Doria04/2014
4834(4*10^87669+149)/987669Robert Price03/2017
48352^291217+425787666Lelio R Paula10/2013
48362*12^81214-5^8121487645Mike Oakes12/2010
4837(5*10^87622-473)/987622Robert Price12/2017
483812^81188+8587617Lelio R Paula11/2015
4839(21*2^290980-1)/587595Lelio R Paula02/2014
48402^290958+12787588Lelio R Paula09/2012
48412^290923-6787577Lelio R Paula09/2012
48423*10^87573-9787574Robert Price08/2017
4843(13*10^87565+11)/387566Robert Price05/2015
4844(2^290857-7)/5587555Lelio R Paula01/2013
48452^290802+8287587541Lelio R Paula10/2013
4846(509203*2^290792-1)/756098787536Lelio R Paula04/2015
48473^183441+23687524Lelio R Paula12/2015
48482^290618-3387485Lelio R Paula09/2012
4849(184*10^87473-1)/387475Robert Price02/2017
48502^290534-11515187460Enzo Doria06/2015
48512^290512-10975787453Enzo Doria04/2014
4852(32*10^87448-41)/987449Robert Price05/2015
4853(2^290491+9)/317987444Lelio R Paula01/2013
4854(25*2^290489-1)/5180987443Lelio R Paula02/2014
48552^290426+8287587427Lelio R Paula11/2013
48563*2^290415-787425Lelio R Paula08/2014
485810^87408+5787409Robert Price03/2011
48572^290366+7477987409Enzo Doria04/2016
485910^87408-12356987408Patrick De Geest07/2013
48602^290265+5890587379Lelio R Paula10/2013
48617^103391+1687376Lelio R Paula10/2015
4862(115*10^87368-7)/987370Robert Price11/2017
4863(92^44491-1)/9187369Paul Bourdelais08/2017
48648*7^103379+387367Lelio R Paula10/2014
4865(2^290226+7)/7187365Lelio R Paula01/2013
486613^78407-3087341Lelio R Paula11/2015
48674*10^87337-9987338Robert Price12/2016
48687*10^87319+3987320Robert Price07/2016
48693*5^124921+287317Lelio R Paula10/2014
48703^182984+8887306Lelio R Paula12/2015
48714*10^87287-9987288Robert Price12/2016
487211^83813-186087283Enzo Doria12/2012
4873734^30453+30453^73487270Norbert Schneider04/2017
487412^80855+2987258Lelio R Paula11/2015
48753*6^112119-587247Lelio R Paula10/2014
487612^80806+7987205Lelio R Paula11/2015
487791382^9+9^9138287201Andrey Kulsha11/2004
4878(21181*2^289657+1)/8187198Lelio R Paula06/2014
48796^112054-4787195Lelio R Paula12/2015
4880(55459*2^289632+1)/5587191Lelio R Paula06/2014
488115^74131-6887185Lelio R Paula11/2015
48822^289583-74187174Lelio R Paula10/2013
48837^103146+1287169Lelio R Paula10/2015
48845*2^289556-387166Lelio R Paula08/2014
48852^289543-11273587162Enzo Doria06/2014
48868*3^182655-787150Lelio R Paula08/2014
48872*10^87144+8187145Robert Price01/2017
48887^103106+2*3^10310687135Mike Oakes08/2010
48898*3^182614+787130Lelio R Paula08/2014
4890(2^289368-509203)/987108Lelio R Paula01/2013
48913^182566+1487107Robert Price09/2013
4892(3^182385-5)/287020Lelio R Paula01/2013
489311^83534-886992Lelio R Paula11/2015
48944^144479-1426786986Mike Oakes03/2011
4895(145*10^86982-1)/986984Serge Batalov12/2014
4896(151*10^86963-1)/386965Robert Price04/2017
489715^73940-5886961Lelio R Paula11/2015
48982^288761-11314386926Enzo Doria07/2014
48992^288747+308386922Yves Minet03/2011
490030^58842+2986917Norbert Schneider03/2017
4901(10^86906-13)/386906Robert Price02/2017
49022^288692-11002786905Enzo Doria04/2014
4903(2^288682+7)/25989544986894Lelio R Paula01/2013
4904(2^288636+47)/129386885Lelio R Paula01/2013
49053^182089-3486879Robert Price11/2013
49062^288543-10980186861Enzo Doria04/2014
490760^48847-5986858Norbert Schneider10/2014
49082^288470-6487586839Lelio R Paula10/2013
490910^86816+3299786817Patrick De Geest07/2013
491010^86816-9986816Robert Price05/2011
4911(89*10^86802-539)/986803Robert Price11/2017
491241487!2+25686786Robert Price01/2015
4913(5*2^288301-1)/99986785Lelio R Paula02/2014
49142^288243+7604386770Enzo Doria04/2016
4915(29*2^288232+1)/1586767Lelio R Paula01/2013
49169*6^111495+586761Lelio R Paula10/2014
4917(5*2^288202+1)/8186757Lelio R Paula01/2013
49189*7^102654-286754Lelio R Paula10/2014
49192^288122-11284186734Enzo Doria06/2014
49205^124062-6886716Lelio R Paula10/2015
4921(2^288007-3)/12586697Lelio R Paula01/2013
4922379*10^86691+986694Arkadiusz Wesolowski10/2011
49237^102555+4886670Lelio R Paula10/2015
492477779!4+286660Robert Price08/2017
49252^287809-11135586640Enzo Doria05/2014
4926(47*2^287795+1)/786636Lelio R Paula04/2015
49279*7^102504+886627Lelio R Paula10/2014
49283^181551+3286622Robert Price11/2013
49292^287735-52134786617Paul Bourdelais05/2013
4930(1017*2^287600-1)/9186578Lelio R Paula04/2015
49312^287540-11296786559Enzo Doria06/2014
49323^181407+2086554Robert Price10/2013
4933(13*10^86546+83)/386547Robert Price09/2016
49343^181378-2^(181378-1)86540Robert Price01/2016
493583^45080-286513Lelio R Paula08/2013
4936(78557*2^287351+1)/61186504Lelio R Paula06/2014
493725*29^59147+2093686498Curtis Bright05/2015
49382^287298+187135986486Enzo Doria05/2016
4939118^41740-11786481Norbert Schneider08/2018
49403*10^86478+8986479Robert Price03/2017
49412^287272-7904986478Paul Bourdelais02/2012
4942906705*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4943811824*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4944779064*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4945768385*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4946700891*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4947652320*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4948377920*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4949255060*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4950187111*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4951(10^86453-1)/986453Lew Baxter10/2000
495287^44563-86^4456386431Robert Price05/2015
49536^111057+6186420Lelio R Paula12/2015
49542^287057-10990986413Enzo Doria04/2014
49555^123608+2286399Lelio R Paula10/2015
4956(31*10^86364-121)/986365Robert Price06/2016
49572^286859+7166386354Enzo Doria04/2016
49582^286740+2983586318Lelio R Paula10/2013
49592*10^86310+9^8631086311Mike Oakes05/2011
496011^82878-186086309Enzo Doria12/2012
49612^286547+1609586260Lelio R Paula10/2013
4962(58*10^86242+329)/986243Robert Price11/2017
49632^286455-11042786232Enzo Doria05/2014
4964(37*10^86230+53)/986231Robert Price05/2015
49658*3^180700+586217Lelio R Paula08/2014
49663^180697-4086215Lelio R Paula12/2015
4967(13*2^286318-1)/1325786188Lelio R Paula02/2014
49682^286165+7786145Lelio R Paula08/2012
49699*2^286140+786138Lelio R Paula08/2014
4970(29*2^286108-1)/200236786123Lelio R Paula02/2014
497110^86110+16111386111Patrick De Geest07/2013
497210^86110-6986110Robert Price05/2011
49732^286036-86968810586106Lelio R Paula07/2016
4974(77*10^86072+31)/986073Robert Price10/2015
49752^285923+34586072Lelio R Paula09/2013
497613^77266-9086070Lelio R Paula11/2015
49772^285910-45890386068Enzo Doria04/2015
49782^285904-12586066Lelio R Paula08/2012
49792^285836+6583586046Lelio R Paula09/2013
4980(2^285766+78557)/386024Lelio R Paula01/2013
4981(5*10^86011-107)/386012Robert Price01/2017
49826^110522+16386003Lelio R Paula12/2015
498341^53323-40^5332385999Robert Price07/2012
49842^285678-10961785998Enzo Doria04/2014
49856^110506-1667385991Enzo Doria02/2013
49872^285569-74185965Lelio R Paula09/2013
4986(32*10^85964+31)/985965Robert Price05/2015
49886*10^85910-785911Dmitry Domanov11/2010
4989(412*10^85897-7)/985899Robert Price10/2017
49904*10^85881+6385882Robert Price06/2016
4991(10^85864+53)/985864Robert Price01/2015
49922^285230+34585863Lelio R Paula09/2013
4993(5*10^85855-473)/985855Robert Price12/2017
49942^285199+7568385854Enzo Doria04/2016
4995(76*10^85847-211)/985848Robert Price10/2017
4996p(17832)#/2+51285845Robert Price05/2017
4997(16*10^85839+167)/385840Robert Price10/2017
499811^82426-123085838Enzo Doria11/2012
49992^285113-10988185828Enzo Doria04/2014
50005^122746-9285796Lelio R Paula10/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 17 2018 20:37 (Time in France)

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