PRP Records

Probable Primes Top 10000

(202632 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 ?
4251(17*10^88761-41)/388762Robert Price09/2017
42522^294754+1501588730Lelio R Paula10/2013
4253(3^185951-7)/2088720Lelio R Paula01/2013
4254(2^294661+5)/44369338388694Lelio R Paula01/2013
4255(10^88680+11)/388680Robert Price11/2014
42562*7^104928-988675Lelio R Paula10/2014
425711^85150+1288675Lelio R Paula11/2015
42588*6^113951+588673Lelio R Paula10/2014
42596^113940-1856388663Enzo Doria03/2013
426038^56123-56123^3888663Norbert Schneider02/2017
42612^294492-6588651Lelio R Paula10/2012
426220^68120-5388627Lelio R Paula01/2016
42632^294391-11325788621Enzo Doria07/2014
42645^126784-1547688619Enzo Doria02/2013
42652^294327+988602Lelio R Paula10/2012
42662^294320+1891588600Lelio R Paula10/2013
4267(98*10^88595-89)/9988595Ray Chandler07/2011
4268(17*2^294262-1)/1388582Lelio R Paula02/2014
4270(2*10^88545+7)/988545Erik Branger03/2011
42692^294137-13388545Lelio R Paula10/2012
4271(2^294092-1017)/117188528Lelio R Paula01/2013
42724^147036+147036^4+188525Robert Price04/2014
4273(14^77213-5^77213)/988496Robert Price04/2013
42742^293965+279337788493Enzo Doria03/2016
427511^84971-15088489Enzo Doria08/2012
4276(2^293956-1017)/3985137669667788476Lelio R Paula01/2013
427711^84958-219088475Enzo Doria12/2012
42782^293880-11134788467Enzo Doria05/2014
4279(106*10^88459-1)/388461Serge Batalov12/2014
428010^88457+27873388458Patrick De Geest07/2017
428110^88457-40188457Robert Price06/2017
428211^84908-168088423Enzo Doria12/2012
42832^293679-11207588407Enzo Doria06/2014
42846^113608-6588405Lelio R Paula12/2015
42852^293624+8287588390Lelio R Paula10/2013
42862^293612-11233788387Enzo Doria06/2014
4287758^30693+30693^75888386Norbert Schneider05/2017
4288gcd(V(1062695),5*F(212539)*(F(212539)-1)+1)88383Serge Batalov04/2015
42895*10^88377+7788378Robert Price06/2016
4290(5*2^293526+1)/30388359Lelio R Paula01/2013
42912^293461-278584388341Enzo Doria03/2016
42922^293416-103788328Yves Minet11/2012
4293(2^293384-7)/388317Lelio R Paula01/2013
4294(3^185092-5)/488311Lelio R Paula01/2013
4295(5*10^88303-173)/388304Robert Price11/2017
429614^77039-5788297Lelio R Paula11/2015
42973*10^88293-5988294Robert Price10/2017
42985^126303+4288283Lelio R Paula10/2015
429919^69025-1888266Theodore Burton01/2006
43005*10^88261-388262Dmitry Domanov11/2010
43018^97731-7^(97731-1)88260Robert Price04/2016
43025*10^88254+5988255Robert Price09/2016
43034*3^184968-788253Lelio R Paula08/2014
43047^104426+8888251Lelio R Paula10/2015
43052^293142+9988245Lelio R Paula10/2012
430611^84736-213088244Enzo Doria12/2012
43072^293068-8988223Lelio R Paula10/2012
43082^293014-10965588207Enzo Doria04/2014
43098*7^104371-388205Lelio R Paula10/2014
43102^292995-214588201Lelio R Paula10/2013
43115*10^88182+7788183Robert Price06/2016
43132^292929+4387788181Donovan Johnson04/2005
43126^113321+13188181Lelio R Paula12/2015
43142^292904-58394988173Paul Bourdelais04/2013
43152^292894-11185188170Enzo Doria05/2014
43162^292872-279734988164Enzo Doria03/2016
43172^292860-10968588160Enzo Doria04/2014
43189*6^113288-588157Lelio R Paula10/2014
4319(2*10^88112-23)/388112Robert Price09/2017
4320(73*10^88105+17)/988106Robert Price10/2015
432111^84588+7888090Lelio R Paula11/2015
4322(265*10^88077+11)/388079Robert Price03/2017
432391^44959-90^4495988077Robert Price07/2015
43246^113177-5^11317788069Jean-Louis Charton01/2009
4325(10^88020+101)/388020Robert Price04/2016
4326(10^(2*43982+1)-6*10^43982-1)/387965Robert Price02/2016
4327(424*10^87930-1)/987932Robert Price11/2017
4328p(18225)#/2+12887929Robert Price04/2017
43294*6^112977+787914Lelio R Paula10/2014
433014^76677+6987882Lelio R Paula11/2015
4331(22*10^87863-1)/387864Robert Price12/2014
43322^291822-279781187848Enzo Doria04/2016
43332^291716-11138987816Enzo Doria05/2014
4334(782*10^87809-71)/987811Robert Price06/2017
43353^184039+182087809Lelio R Paula12/2015
433612^81356+4187798Lelio R Paula11/2015
43376^112792-1898387770Enzo Doria03/2013
43383*6^112787-587766Lelio R Paula10/2014
43397^103848+8287762Lelio R Paula10/2015
4340(19*2^291534-1)/17869639587754Lelio R Paula02/2014
4341(3^183915+5)/12887748Lelio R Paula01/2013
434219^68619+2487747Lelio R Paula12/2015
43442^291480+118587745Lelio R Paula10/2013
43432^291482+186736987745Enzo Doria03/2016
43452^291467-93787741Yves Minet05/2013
4346(25*10^87726+161)/387727Robert Price01/2017
434711^84239-285087726Enzo Doria12/2012
434810^87720+21554187721Patrick De Geest01/2011
434910^87720-387720Markus Tervooren07/2010
4350(5*10^87712-473)/987712Robert Price12/2017
4351(2^291357+5)/684787704Lelio R Paula01/2013
435293^44541-287679Lelio R Paula09/2013
43532^291261-10956187679Enzo Doria04/2014
4354(4*10^87669+149)/987669Robert Price03/2017
43552^291217+425787666Lelio R Paula10/2013
43562*12^81214-5^8121487645Mike Oakes12/2010
4357(5*10^87622-473)/987622Robert Price12/2017
435812^81188+8587617Lelio R Paula11/2015
4359(21*2^290980-1)/587595Lelio R Paula02/2014
43602^290958+12787588Lelio R Paula09/2012
43612^290923-6787577Lelio R Paula09/2012
43623*10^87573-9787574Robert Price08/2017
4363(13*10^87565+11)/387566Robert Price05/2015
4364(2^290857-7)/5587555Lelio R Paula01/2013
43652^290802+8287587541Lelio R Paula10/2013
4366(509203*2^290792-1)/756098787536Lelio R Paula04/2015
43673^183441+23687524Lelio R Paula12/2015
43682^290618-3387485Lelio R Paula09/2012
4369(184*10^87473-1)/387475Robert Price02/2017
43702^290534-11515187460Enzo Doria06/2015
43712^290512-10975787453Enzo Doria04/2014
4372(32*10^87448-41)/987449Robert Price05/2015
4373(2^290491+9)/317987444Lelio R Paula01/2013
4374(25*2^290489-1)/5180987443Lelio R Paula02/2014
43752^290426+8287587427Lelio R Paula11/2013
43763*2^290415-787425Lelio R Paula08/2014
437810^87408+5787409Robert Price03/2011
43772^290366+7477987409Enzo Doria04/2016
437910^87408-12356987408Patrick De Geest07/2013
43802^290265+5890587379Lelio R Paula10/2013
43817^103391+1687376Lelio R Paula10/2015
4382(115*10^87368-7)/987370Robert Price11/2017
4383(92^44491-1)/9187369Paul Bourdelais08/2017
43848*7^103379+387367Lelio R Paula10/2014
4385(2^290226+7)/7187365Lelio R Paula01/2013
438613^78407-3087341Lelio R Paula11/2015
43874*10^87337-9987338Robert Price12/2016
43887*10^87319+3987320Robert Price07/2016
43893*5^124921+287317Lelio R Paula10/2014
43903^182984+8887306Lelio R Paula12/2015
43914*10^87287-9987288Robert Price12/2016
439211^83813-186087283Enzo Doria12/2012
4393734^30453+30453^73487270Norbert Schneider04/2017
439412^80855+2987258Lelio R Paula11/2015
43953*6^112119-587247Lelio R Paula10/2014
439612^80806+7987205Lelio R Paula11/2015
439791382^9+9^9138287201Andrey Kulsha11/2004
4398(21181*2^289657+1)/8187198Lelio R Paula06/2014
43996^112054-4787195Lelio R Paula12/2015
4400(55459*2^289632+1)/5587191Lelio R Paula06/2014
440115^74131-6887185Lelio R Paula11/2015
44022^289583-74187174Lelio R Paula10/2013
44037^103146+1287169Lelio R Paula10/2015
44045*2^289556-387166Lelio R Paula08/2014
44052^289543-11273587162Enzo Doria06/2014
44068*3^182655-787150Lelio R Paula08/2014
44072*10^87144+8187145Robert Price01/2017
44087^103106+2*3^10310687135Mike Oakes08/2010
44098*3^182614+787130Lelio R Paula08/2014
4410(2^289368-509203)/987108Lelio R Paula01/2013
44113^182566+1487107Robert Price09/2013
4412(3^182385-5)/287020Lelio R Paula01/2013
441311^83534-886992Lelio R Paula11/2015
44144^144479-1426786986Mike Oakes03/2011
4415(145*10^86982-1)/986984Serge Batalov12/2014
4416(151*10^86963-1)/386965Robert Price04/2017
441715^73940-5886961Lelio R Paula11/2015
44182^288761-11314386926Enzo Doria07/2014
44192^288747+308386922Yves Minet03/2011
442030^58842+2986917Norbert Schneider03/2017
4421(10^86906-13)/386906Robert Price02/2017
44222^288692-11002786905Enzo Doria04/2014
4423(2^288682+7)/25989544986894Lelio R Paula01/2013
4424(2^288636+47)/129386885Lelio R Paula01/2013
44253^182089-3486879Robert Price11/2013
44262^288543-10980186861Enzo Doria04/2014
442760^48847-5986858Norbert Schneider10/2014
44282^288470-6487586839Lelio R Paula10/2013
442910^86816+3299786817Patrick De Geest07/2013
443010^86816-9986816Robert Price05/2011
4431(89*10^86802-539)/986803Robert Price11/2017
443241487!2+25686786Robert Price01/2015
4433(5*2^288301-1)/99986785Lelio R Paula02/2014
44342^288243+7604386770Enzo Doria04/2016
4435(29*2^288232+1)/1586767Lelio R Paula01/2013
44369*6^111495+586761Lelio R Paula10/2014
4437(5*2^288202+1)/8186757Lelio R Paula01/2013
44389*7^102654-286754Lelio R Paula10/2014
44392^288122-11284186734Enzo Doria06/2014
44405^124062-6886716Lelio R Paula10/2015
4441(2^288007-3)/12586697Lelio R Paula01/2013
4442379*10^86691+986694Arkadiusz Wesolowski10/2011
44437^102555+4886670Lelio R Paula10/2015
444477779!4+286660Robert Price08/2017
44452^287809-11135586640Enzo Doria05/2014
4446(47*2^287795+1)/786636Lelio R Paula04/2015
44479*7^102504+886627Lelio R Paula10/2014
44483^181551+3286622Robert Price11/2013
44492^287735-52134786617Paul Bourdelais05/2013
4450(1017*2^287600-1)/9186578Lelio R Paula04/2015
44512^287540-11296786559Enzo Doria06/2014
44523^181407+2086554Robert Price10/2013
4453(13*10^86546+83)/386547Robert Price09/2016
44543^181378-2^(181378-1)86540Robert Price01/2016
445583^45080-286513Lelio R Paula08/2013
4456(78557*2^287351+1)/61186504Lelio R Paula06/2014
445725*29^59147+2093686498Curtis Bright05/2015
44582^287298+187135986486Enzo Doria05/2016
44593*10^86478+8986479Robert Price03/2017
44602^287272-7904986478Paul Bourdelais02/2012
4461906705*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4462811824*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4463779064*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4464768385*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4465700891*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4466652320*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4467377920*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4468255060*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4469187111*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4470(10^86453-1)/986453Lew Baxter10/2000
447187^44563-86^4456386431Robert Price05/2015
44726^111057+6186420Lelio R Paula12/2015
44732^287057-10990986413Enzo Doria04/2014
44745^123608+2286399Lelio R Paula10/2015
4475(31*10^86364-121)/986365Robert Price06/2016
44762^286859+7166386354Enzo Doria04/2016
44772^286740+2983586318Lelio R Paula10/2013
44782*10^86310+9^8631086311Mike Oakes05/2011
447911^82878-186086309Enzo Doria12/2012
44802^286547+1609586260Lelio R Paula10/2013
4481(58*10^86242+329)/986243Robert Price11/2017
44822^286455-11042786232Enzo Doria05/2014
4483(37*10^86230+53)/986231Robert Price05/2015
44848*3^180700+586217Lelio R Paula08/2014
44853^180697-4086215Lelio R Paula12/2015
4486(13*2^286318-1)/1325786188Lelio R Paula02/2014
44872^286165+7786145Lelio R Paula08/2012
44889*2^286140+786138Lelio R Paula08/2014
4489(29*2^286108-1)/200236786123Lelio R Paula02/2014
449010^86110+16111386111Patrick De Geest07/2013
449110^86110-6986110Robert Price05/2011
44922^286036-86968810586106Lelio R Paula07/2016
4493(77*10^86072+31)/986073Robert Price10/2015
44942^285923+34586072Lelio R Paula09/2013
449513^77266-9086070Lelio R Paula11/2015
44962^285910-45890386068Enzo Doria04/2015
44972^285904-12586066Lelio R Paula08/2012
44982^285836+6583586046Lelio R Paula09/2013
4499(2^285766+78557)/386024Lelio R Paula01/2013
4500(5*10^86011-107)/386012Robert Price01/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 20 2018 10:36 (Time in France)

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