PRP Records

Probable Primes Top 10000

(218736 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 ?
45012*7^104928-988675Lelio R Paula10/2014
450211^85150+1288675Lelio R Paula11/2015
45038*6^113951+588673Lelio R Paula10/2014
45056^113940-1856388663Enzo Doria03/2013
450438^56123-56123^3888663Norbert Schneider02/2017
45062^294492-6588651Lelio R Paula10/2012
450720^68120-5388627Lelio R Paula01/2016
45082^294391-11325788621Enzo Doria07/2014
45095^126784-1547688619Enzo Doria02/2013
45102^294327+988602Lelio R Paula10/2012
45112^294320+1891588600Lelio R Paula10/2013
4512(98*10^88595-89)/9988595Ray Chandler07/2011
4513(17*2^294262-1)/1388582Lelio R Paula02/2014
4515(2*10^88545+7)/988545Erik Branger03/2011
45142^294137-13388545Lelio R Paula10/2012
4516(2^294092-1017)/117188528Lelio R Paula01/2013
45174^147036+147036^4+188525Robert Price04/2014
4518(14^77213-5^77213)/988496Robert Price04/2013
45192^293965+279337788493Enzo Doria03/2016
452011^84971-15088489Enzo Doria08/2012
4521(2^293956-1017)/3985137669667788476Lelio R Paula01/2013
452211^84958-219088475Enzo Doria12/2012
45232^293880-11134788467Enzo Doria05/2014
4524(106*10^88459-1)/388461Serge Batalov12/2014
452510^88457+27873388458Patrick De Geest07/2017
452610^88457-40188457Robert Price06/2017
452711^84908-168088423Enzo Doria12/2012
45282^293679-11207588407Enzo Doria06/2014
45296^113608-6588405Lelio R Paula12/2015
45302^293624+8287588390Lelio R Paula10/2013
45312^293612-11233788387Enzo Doria06/2014
4532758^30693+30693^75888386Norbert Schneider05/2017
4533gcd(V(1062695),5*F(212539)*(F(212539)-1)+1)88383Serge Batalov04/2015
45345*10^88377+7788378Robert Price06/2016
4535(5*2^293526+1)/30388359Lelio R Paula01/2013
45362^293461-278584388341Enzo Doria03/2016
45372^293416-103788328Yves Minet11/2012
4538(2^293384-7)/388317Lelio R Paula01/2013
4539(3^185092-5)/488311Lelio R Paula01/2013
4540(5*10^88303-173)/388304Robert Price11/2017
454114^77039-5788297Lelio R Paula11/2015
45423*10^88293-5988294Robert Price10/2017
45435^126303+4288283Lelio R Paula10/2015
454419^69025-1888266Theodore Burton01/2006
45455*10^88261-388262Dmitry Domanov11/2010
45468^97731-7^(97731-1)88260Robert Price04/2016
45475*10^88254+5988255Robert Price09/2016
45484*3^184968-788253Lelio R Paula08/2014
45497^104426+8888251Lelio R Paula10/2015
45502^293142+9988245Lelio R Paula10/2012
455111^84736-213088244Enzo Doria12/2012
45522^293068-8988223Lelio R Paula10/2012
45532^293014-10965588207Enzo Doria04/2014
45548*7^104371-388205Lelio R Paula10/2014
45552^292995-214588201Lelio R Paula10/2013
45565*10^88182+7788183Robert Price06/2016
45582^292929+4387788181Donovan Johnson04/2005
45576^113321+13188181Lelio R Paula12/2015
45592^292904-58394988173Paul Bourdelais04/2013
45602^292894-11185188170Enzo Doria05/2014
45612^292872-279734988164Enzo Doria03/2016
45622^292860-10968588160Enzo Doria04/2014
45639*6^113288-588157Lelio R Paula10/2014
4564(2*10^88112-23)/388112Robert Price09/2017
4565(73*10^88105+17)/988106Robert Price10/2015
456611^84588+7888090Lelio R Paula11/2015
4567(265*10^88077+11)/388079Robert Price03/2017
456891^44959-90^4495988077Robert Price07/2015
45696^113177-5^11317788069Jean-Louis Charton01/2009
4570(10^88020+101)/388020Robert Price04/2016
4571(10^(2*43982+1)-6*10^43982-1)/387965Robert Price02/2016
4572(424*10^87930-1)/987932Robert Price11/2017
4573p(18225)#/2+12887929Robert Price04/2017
45744*6^112977+787914Lelio R Paula10/2014
457514^76677+6987882Lelio R Paula11/2015
4576(22*10^87863-1)/387864Robert Price12/2014
45772^291822-279781187848Enzo Doria04/2016
45782^291716-11138987816Enzo Doria05/2014
4579(782*10^87809-71)/987811Robert Price06/2017
45803^184039+182087809Lelio R Paula12/2015
458112^81356+4187798Lelio R Paula11/2015
45826^112792-1898387770Enzo Doria03/2013
45833*6^112787-587766Lelio R Paula10/2014
45847^103848+8287762Lelio R Paula10/2015
4585(19*2^291534-1)/17869639587754Lelio R Paula02/2014
4586(3^183915+5)/12887748Lelio R Paula01/2013
458719^68619+2487747Lelio R Paula12/2015
45892^291480+118587745Lelio R Paula10/2013
45882^291482+186736987745Enzo Doria03/2016
45902^291467-93787741Yves Minet05/2013
4591(25*10^87726+161)/387727Robert Price01/2017
459211^84239-285087726Enzo Doria12/2012
459310^87720+21554187721Patrick De Geest01/2011
459410^87720-387720Markus Tervooren07/2010
4595(5*10^87712-473)/987712Robert Price12/2017
4596(2^291357+5)/684787704Lelio R Paula01/2013
459793^44541-287679Lelio R Paula09/2013
45982^291261-10956187679Enzo Doria04/2014
4599(4*10^87669+149)/987669Robert Price03/2017
46002^291217+425787666Lelio R Paula10/2013
46012*12^81214-5^8121487645Mike Oakes12/2010
4602(5*10^87622-473)/987622Robert Price12/2017
460312^81188+8587617Lelio R Paula11/2015
4604(21*2^290980-1)/587595Lelio R Paula02/2014
46052^290958+12787588Lelio R Paula09/2012
46062^290923-6787577Lelio R Paula09/2012
46073*10^87573-9787574Robert Price08/2017
4608(13*10^87565+11)/387566Robert Price05/2015
4609(2^290857-7)/5587555Lelio R Paula01/2013
46102^290802+8287587541Lelio R Paula10/2013
4611(509203*2^290792-1)/756098787536Lelio R Paula04/2015
46123^183441+23687524Lelio R Paula12/2015
46132^290618-3387485Lelio R Paula09/2012
4614(184*10^87473-1)/387475Robert Price02/2017
46152^290534-11515187460Enzo Doria06/2015
46162^290512-10975787453Enzo Doria04/2014
4617(32*10^87448-41)/987449Robert Price05/2015
4618(2^290491+9)/317987444Lelio R Paula01/2013
4619(25*2^290489-1)/5180987443Lelio R Paula02/2014
46202^290426+8287587427Lelio R Paula11/2013
46213*2^290415-787425Lelio R Paula08/2014
462310^87408+5787409Robert Price03/2011
46222^290366+7477987409Enzo Doria04/2016
462410^87408-12356987408Patrick De Geest07/2013
46252^290265+5890587379Lelio R Paula10/2013
46267^103391+1687376Lelio R Paula10/2015
4627(115*10^87368-7)/987370Robert Price11/2017
4628(92^44491-1)/9187369Paul Bourdelais08/2017
46298*7^103379+387367Lelio R Paula10/2014
4630(2^290226+7)/7187365Lelio R Paula01/2013
463113^78407-3087341Lelio R Paula11/2015
46324*10^87337-9987338Robert Price12/2016
46337*10^87319+3987320Robert Price07/2016
46343*5^124921+287317Lelio R Paula10/2014
46353^182984+8887306Lelio R Paula12/2015
46364*10^87287-9987288Robert Price12/2016
463711^83813-186087283Enzo Doria12/2012
4638734^30453+30453^73487270Norbert Schneider04/2017
463912^80855+2987258Lelio R Paula11/2015
46403*6^112119-587247Lelio R Paula10/2014
464112^80806+7987205Lelio R Paula11/2015
464291382^9+9^9138287201Andrey Kulsha11/2004
4643(21181*2^289657+1)/8187198Lelio R Paula06/2014
46446^112054-4787195Lelio R Paula12/2015
4645(55459*2^289632+1)/5587191Lelio R Paula06/2014
464615^74131-6887185Lelio R Paula11/2015
46472^289583-74187174Lelio R Paula10/2013
46487^103146+1287169Lelio R Paula10/2015
46495*2^289556-387166Lelio R Paula08/2014
46502^289543-11273587162Enzo Doria06/2014
46518*3^182655-787150Lelio R Paula08/2014
46522*10^87144+8187145Robert Price01/2017
46537^103106+2*3^10310687135Mike Oakes08/2010
46548*3^182614+787130Lelio R Paula08/2014
4655(2^289368-509203)/987108Lelio R Paula01/2013
46563^182566+1487107Robert Price09/2013
4657(3^182385-5)/287020Lelio R Paula01/2013
465811^83534-886992Lelio R Paula11/2015
46594^144479-1426786986Mike Oakes03/2011
4660(145*10^86982-1)/986984Serge Batalov12/2014
4661(151*10^86963-1)/386965Robert Price04/2017
466215^73940-5886961Lelio R Paula11/2015
46632^288761-11314386926Enzo Doria07/2014
46642^288747+308386922Yves Minet03/2011
466530^58842+2986917Norbert Schneider03/2017
4666(10^86906-13)/386906Robert Price02/2017
46672^288692-11002786905Enzo Doria04/2014
4668(2^288682+7)/25989544986894Lelio R Paula01/2013
4669(2^288636+47)/129386885Lelio R Paula01/2013
46703^182089-3486879Robert Price11/2013
46712^288543-10980186861Enzo Doria04/2014
467260^48847-5986858Norbert Schneider10/2014
46732^288470-6487586839Lelio R Paula10/2013
467410^86816+3299786817Patrick De Geest07/2013
467510^86816-9986816Robert Price05/2011
4676(89*10^86802-539)/986803Robert Price11/2017
467741487!2+25686786Robert Price01/2015
4678(5*2^288301-1)/99986785Lelio R Paula02/2014
46792^288243+7604386770Enzo Doria04/2016
4680(29*2^288232+1)/1586767Lelio R Paula01/2013
46819*6^111495+586761Lelio R Paula10/2014
4682(5*2^288202+1)/8186757Lelio R Paula01/2013
46839*7^102654-286754Lelio R Paula10/2014
46842^288122-11284186734Enzo Doria06/2014
46855^124062-6886716Lelio R Paula10/2015
4686(2^288007-3)/12586697Lelio R Paula01/2013
4687379*10^86691+986694Arkadiusz Wesolowski10/2011
46887^102555+4886670Lelio R Paula10/2015
468977779!4+286660Robert Price08/2017
46902^287809-11135586640Enzo Doria05/2014
4691(47*2^287795+1)/786636Lelio R Paula04/2015
46929*7^102504+886627Lelio R Paula10/2014
46933^181551+3286622Robert Price11/2013
46942^287735-52134786617Paul Bourdelais05/2013
4695(1017*2^287600-1)/9186578Lelio R Paula04/2015
46962^287540-11296786559Enzo Doria06/2014
46973^181407+2086554Robert Price10/2013
4698(13*10^86546+83)/386547Robert Price09/2016
46993^181378-2^(181378-1)86540Robert Price01/2016
470083^45080-286513Lelio R Paula08/2013
4701(78557*2^287351+1)/61186504Lelio R Paula06/2014
470225*29^59147+2093686498Curtis Bright05/2015
47032^287298+187135986486Enzo Doria05/2016
47043*10^86478+8986479Robert Price03/2017
47052^287272-7904986478Paul Bourdelais02/2012
4706906705*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4707811824*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4708779064*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4709768385*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4710700891*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4711652320*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4712377920*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4713255060*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4714187111*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4715(10^86453-1)/986453Lew Baxter10/2000
471687^44563-86^4456386431Robert Price05/2015
47176^111057+6186420Lelio R Paula12/2015
47182^287057-10990986413Enzo Doria04/2014
47195^123608+2286399Lelio R Paula10/2015
4720(31*10^86364-121)/986365Robert Price06/2016
47212^286859+7166386354Enzo Doria04/2016
47222^286740+2983586318Lelio R Paula10/2013
47232*10^86310+9^8631086311Mike Oakes05/2011
472411^82878-186086309Enzo Doria12/2012
47252^286547+1609586260Lelio R Paula10/2013
4726(58*10^86242+329)/986243Robert Price11/2017
47272^286455-11042786232Enzo Doria05/2014
4728(37*10^86230+53)/986231Robert Price05/2015
47298*3^180700+586217Lelio R Paula08/2014
47303^180697-4086215Lelio R Paula12/2015
4731(13*2^286318-1)/1325786188Lelio R Paula02/2014
47322^286165+7786145Lelio R Paula08/2012
47339*2^286140+786138Lelio R Paula08/2014
4734(29*2^286108-1)/200236786123Lelio R Paula02/2014
473510^86110+16111386111Patrick De Geest07/2013
473610^86110-6986110Robert Price05/2011
47372^286036-86968810586106Lelio R Paula07/2016
4738(77*10^86072+31)/986073Robert Price10/2015
47392^285923+34586072Lelio R Paula09/2013
474013^77266-9086070Lelio R Paula11/2015
47412^285910-45890386068Enzo Doria04/2015
47422^285904-12586066Lelio R Paula08/2012
47432^285836+6583586046Lelio R Paula09/2013
4744(2^285766+78557)/386024Lelio R Paula01/2013
4745(5*10^86011-107)/386012Robert Price01/2017
47466^110522+16386003Lelio R Paula12/2015
474741^53323-40^5332385999Robert Price07/2012
47482^285678-10961785998Enzo Doria04/2014
47496^110506-1667385991Enzo Doria02/2013
4750(32*10^85964+31)/985965Robert Price05/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 14 2018 21:45 (Time in France)

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