PRP Records

Probable Primes Top 10000

(180278 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 ?
400115^75619-8888935Lelio R Paula11/2015
40022^295385-8588920Lelio R Paula10/2012
40032^295385-1633388920Enzo Doria04/2013
40042^295309+5988897Lelio R Paula10/2012
40052^295288-10979988891Enzo Doria04/2014
40062^295245+6588878Lelio R Paula10/2012
4007Padovan(727734)88874Eric W. Weisstein04/2011
400818^70793-1788865Lelio R Paula11/2015
40096^114196-1757388862Enzo Doria02/2013
4010302^35829+35829^30288857Norbert Schneider12/2014
40113^186223+1688851Robert Price10/2013
40123*2^295139+788847Lelio R Paula08/2014
40133^186212-11300888846Enzo Doria07/2014
401487^45803-8688836Norbert Schneider11/2015
40152^295094-11027388833Enzo Doria05/2014
40162^295080+186915188828Enzo Doria05/2016
40172^295027-11340788812Enzo Doria07/2014
4018(2*10^88808-71)/388808Robert Price01/2017
401913^79722-8088806Lelio R Paula11/2015
40203^186103+10488794Lelio R Paula12/2015
4021(3*2^294971+1)/2556588792Lelio R Paula01/2013
40222^294937-11500388785Enzo Doria06/2015
40232^294868-10970988765Enzo Doria04/2014
40242^294864-298588763Yves Minet09/2014
40252^294754+1501588730Lelio R Paula10/2013
4026(3^185951-7)/2088720Lelio R Paula01/2013
4027(2^294661+5)/44369338388694Lelio R Paula01/2013
4028(10^88680+11)/388680Robert Price11/2014
40292*7^104928-988675Lelio R Paula10/2014
403011^85150+1288675Lelio R Paula11/2015
40318*6^113951+588673Lelio R Paula10/2014
40326^113940-1856388663Enzo Doria03/2013
403338^56123-56123^3888663Norbert Schneider02/2017
40342^294492-6588651Lelio R Paula10/2012
403520^68120-5388627Lelio R Paula01/2016
40362^294391-11325788621Enzo Doria07/2014
40375^126784-1547688619Enzo Doria02/2013
40382^294327+988602Lelio R Paula10/2012
40392^294320+1891588600Lelio R Paula10/2013
4040(98*10^88595-89)/9988595Ray Chandler07/2011
4041(17*2^294262-1)/1388582Lelio R Paula02/2014
4042(2*10^88545+7)/988545Erik Branger03/2011
40432^294137-13388545Lelio R Paula10/2012
4044(2^294092-1017)/117188528Lelio R Paula01/2013
40454^147036+147036^4+188525Robert Price04/2014
4046(14^77213-5^77213)/988496Robert Price04/2013
40472^293965+279337788493Enzo Doria03/2016
404811^84971-15088489Enzo Doria08/2012
4049(2^293956-1017)/3985137669667788476Lelio R Paula01/2013
405011^84958-219088475Enzo Doria12/2012
40512^293880-11134788467Enzo Doria05/2014
4052(106*10^88459-1)/388461Serge Batalov12/2014
405310^88457+27873388458Patrick De Geest07/2017
405410^88457-40188457Robert Price06/2017
405511^84908-168088423Enzo Doria12/2012
40562^293679-11207588407Enzo Doria06/2014
40576^113608-6588405Lelio R Paula12/2015
40582^293624+8287588390Lelio R Paula10/2013
40592^293612-11233788387Enzo Doria06/2014
4060758^30693+30693^75888386Norbert Schneider05/2017
4061gcd(V(1062695),5*F(212539)*(F(212539)-1)+1)88383Serge Batalov04/2015
40625*10^88377+7788378Robert Price06/2016
4063(5*2^293526+1)/30388359Lelio R Paula01/2013
40642^293461-278584388341Enzo Doria03/2016
40652^293416-103788328Yves Minet11/2012
4066(2^293384-7)/388317Lelio R Paula01/2013
4067(3^185092-5)/488311Lelio R Paula01/2013
406814^77039-5788297Lelio R Paula11/2015
40695^126303+4288283Lelio R Paula10/2015
407019^69025-1888266Theodore Burton01/2006
40715*10^88261-388262Dmitry Domanov11/2010
40728^97731-7^(97731-1)88260Robert Price04/2016
40735*10^88254+5988255Robert Price09/2016
40744*3^184968-788253Lelio R Paula08/2014
40757^104426+8888251Lelio R Paula10/2015
40762^293142+9988245Lelio R Paula10/2012
407711^84736-213088244Enzo Doria12/2012
40782^293068-8988223Lelio R Paula10/2012
40792^293014-10965588207Enzo Doria04/2014
40808*7^104371-388205Lelio R Paula10/2014
40812^292995-214588201Lelio R Paula10/2013
40825*10^88182+7788183Robert Price06/2016
40832^292929+4387788181Donovan Johnson04/2005
40846^113321+13188181Lelio R Paula12/2015
40852^292904-58394988173Paul Bourdelais04/2013
40862^292894-11185188170Enzo Doria05/2014
40872^292872-279734988164Enzo Doria03/2016
40882^292860-10968588160Enzo Doria04/2014
40899*6^113288-588157Lelio R Paula10/2014
4090(73*10^88105+17)/988106Robert Price10/2015
409111^84588+7888090Lelio R Paula11/2015
4092(265*10^88077+11)/388079Robert Price03/2017
409391^44959-90^4495988077Robert Price07/2015
40946^113177-5^11317788069Jean-Louis Charton01/2009
4095(10^88020+101)/388020Robert Price04/2016
4096(10^(2*43982+1)-6*10^43982-1)/387965Robert Price02/2016
4097p(18225)#/2+12887929Robert Price04/2017
40984*6^112977+787914Lelio R Paula10/2014
409914^76677+6987882Lelio R Paula11/2015
4100(22*10^87863-1)/387864Robert Price12/2014
41012^291822-279781187848Enzo Doria04/2016
41022^291716-11138987816Enzo Doria05/2014
4103(782*10^87809-71)/987811Robert Price06/2017
41043^184039+182087809Lelio R Paula12/2015
410512^81356+4187798Lelio R Paula11/2015
41066^112792-1898387770Enzo Doria03/2013
41073*6^112787-587766Lelio R Paula10/2014
41087^103848+8287762Lelio R Paula10/2015
4109(19*2^291534-1)/17869639587754Lelio R Paula02/2014
4110(3^183915+5)/12887748Lelio R Paula01/2013
411119^68619+2487747Lelio R Paula12/2015
41132^291480+118587745Lelio R Paula10/2013
41122^291482+186736987745Enzo Doria03/2016
41142^291467-93787741Yves Minet05/2013
4115(25*10^87726+161)/387727Robert Price01/2017
411611^84239-285087726Enzo Doria12/2012
411710^87720+21554187721Patrick De Geest01/2011
411810^87720-387720Markus Tervooren07/2010
4119(2^291357+5)/684787704Lelio R Paula01/2013
412093^44541-287679Lelio R Paula09/2013
41212^291261-10956187679Enzo Doria04/2014
4122(4*10^87669+149)/987669Robert Price03/2017
41232^291217+425787666Lelio R Paula10/2013
41242*12^81214-5^8121487645Mike Oakes12/2010
412512^81188+8587617Lelio R Paula11/2015
4126(21*2^290980-1)/587595Lelio R Paula02/2014
41272^290958+12787588Lelio R Paula09/2012
41282^290923-6787577Lelio R Paula09/2012
41293*10^87573-9787574Robert Price08/2017
4130(13*10^87565+11)/387566Robert Price05/2015
4131(2^290857-7)/5587555Lelio R Paula01/2013
41322^290802+8287587541Lelio R Paula10/2013
4133(509203*2^290792-1)/756098787536Lelio R Paula04/2015
41343^183441+23687524Lelio R Paula12/2015
41352^290618-3387485Lelio R Paula09/2012
4136(184*10^87473-1)/387475Robert Price02/2017
41372^290534-11515187460Enzo Doria06/2015
41382^290512-10975787453Enzo Doria04/2014
4139(32*10^87448-41)/987449Robert Price05/2015
4140(2^290491+9)/317987444Lelio R Paula01/2013
4141(25*2^290489-1)/5180987443Lelio R Paula02/2014
41422^290426+8287587427Lelio R Paula11/2013
41433*2^290415-787425Lelio R Paula08/2014
414410^87408+5787409Robert Price03/2011
41452^290366+7477987409Enzo Doria04/2016
414610^87408-12356987408Patrick De Geest07/2013
41472^290265+5890587379Lelio R Paula10/2013
41487^103391+1687376Lelio R Paula10/2015
41498*7^103379+387367Lelio R Paula10/2014
4150(2^290226+7)/7187365Lelio R Paula01/2013
415113^78407-3087341Lelio R Paula11/2015
41524*10^87337-9987338Robert Price12/2016
41537*10^87319+3987320Robert Price07/2016
41543*5^124921+287317Lelio R Paula10/2014
41553^182984+8887306Lelio R Paula12/2015
41564*10^87287-9987288Robert Price12/2016
415711^83813-186087283Enzo Doria12/2012
4158734^30453+30453^73487270Norbert Schneider04/2017
415912^80855+2987258Lelio R Paula11/2015
41603*6^112119-587247Lelio R Paula10/2014
416112^80806+7987205Lelio R Paula11/2015
416291382^9+9^9138287201Andrey Kulsha11/2004
4163(21181*2^289657+1)/8187198Lelio R Paula06/2014
41646^112054-4787195Lelio R Paula12/2015
4165(55459*2^289632+1)/5587191Lelio R Paula06/2014
416615^74131-6887185Lelio R Paula11/2015
41672^289583-74187174Lelio R Paula10/2013
41687^103146+1287169Lelio R Paula10/2015
41695*2^289556-387166Lelio R Paula08/2014
41702^289543-11273587162Enzo Doria06/2014
41718*3^182655-787150Lelio R Paula08/2014
41722*10^87144+8187145Robert Price01/2017
41737^103106+2*3^10310687135Mike Oakes08/2010
41748*3^182614+787130Lelio R Paula08/2014
4175(2^289368-509203)/987108Lelio R Paula01/2013
41763^182566+1487107Robert Price09/2013
4177(3^182385-5)/287020Lelio R Paula01/2013
417811^83534-886992Lelio R Paula11/2015
41794^144479-1426786986Mike Oakes03/2011
4180(145*10^86982-1)/986984Serge Batalov12/2014
4181(151*10^86963-1)/386965Robert Price04/2017
418215^73940-5886961Lelio R Paula11/2015
41832^288761-11314386926Enzo Doria07/2014
41842^288747+308386922Yves Minet03/2011
418530^58842+2986917Norbert Schneider03/2017
4186(10^86906-13)/386906Robert Price02/2017
41872^288692-11002786905Enzo Doria04/2014
4188(2^288682+7)/25989544986894Lelio R Paula01/2013
4189(2^288636+47)/129386885Lelio R Paula01/2013
41903^182089-3486879Robert Price11/2013
41912^288543-10980186861Enzo Doria04/2014
419260^48847-5986858Norbert Schneider10/2014
41932^288470-6487586839Lelio R Paula10/2013
419410^86816+3299786817Patrick De Geest07/2013
419510^86816-9986816Robert Price05/2011
419641487!2+25686786Robert Price01/2015
4197(5*2^288301-1)/99986785Lelio R Paula02/2014
41982^288243+7604386770Enzo Doria04/2016
4199(29*2^288232+1)/1586767Lelio R Paula01/2013
42009*6^111495+586761Lelio R Paula10/2014
4201(5*2^288202+1)/8186757Lelio R Paula01/2013
42029*7^102654-286754Lelio R Paula10/2014
42032^288122-11284186734Enzo Doria06/2014
42045^124062-6886716Lelio R Paula10/2015
4205(2^288007-3)/12586697Lelio R Paula01/2013
4206379*10^86691+986694Arkadiusz Wesolowski10/2011
42077^102555+4886670Lelio R Paula10/2015
420877779!4+286660Robert Price08/2017
42092^287809-11135586640Enzo Doria05/2014
4210(47*2^287795+1)/786636Lelio R Paula04/2015
42119*7^102504+886627Lelio R Paula10/2014
42123^181551+3286622Robert Price11/2013
42132^287735-52134786617Paul Bourdelais05/2013
4214(1017*2^287600-1)/9186578Lelio R Paula04/2015
42152^287540-11296786559Enzo Doria06/2014
42163^181407+2086554Robert Price10/2013
4217(13*10^86546+83)/386547Robert Price09/2016
42183^181378-2^(181378-1)86540Robert Price01/2016
421983^45080-286513Lelio R Paula08/2013
4220(78557*2^287351+1)/61186504Lelio R Paula06/2014
422125*29^59147+2093686498Curtis Bright05/2015
42222^287298+187135986486Enzo Doria05/2016
42233*10^86478+8986479Robert Price03/2017
42242^287272-7904986478Paul Bourdelais02/2012
4225906705*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4226811824*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4227779064*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4228768385*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4229700891*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4230652320*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4231377920*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4232255060*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4233187111*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4234(10^86453-1)/986453Lew Baxter10/2000
423587^44563-86^4456386431Robert Price05/2015
42366^111057+6186420Lelio R Paula12/2015
42372^287057-10990986413Enzo Doria04/2014
42385^123608+2286399Lelio R Paula10/2015
4239(31*10^86364-121)/986365Robert Price06/2016
42402^286859+7166386354Enzo Doria04/2016
42412^286740+2983586318Lelio R Paula10/2013
42422*10^86310+9^8631086311Mike Oakes05/2011
424311^82878-186086309Enzo Doria12/2012
42442^286547+1609586260Lelio R Paula10/2013
42452^286455-11042786232Enzo Doria05/2014
4246(37*10^86230+53)/986231Robert Price05/2015
42478*3^180700+586217Lelio R Paula08/2014
42483^180697-4086215Lelio R Paula12/2015
4249(13*2^286318-1)/1325786188Lelio R Paula02/2014
42502^286165+7786145Lelio R Paula08/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 20 2017 08:36 (Time in France)

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