PRP Records

Probable Primes Top 10000

(252932 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 ?
500110^88888+129204788889Stefano Morozzi07/2018
500210^88888+145602988889Stefano Morozzi07/2018
500310^88888-49028788888Patrick De Geest09/2018
50042^295245+6588878Lelio R Paula10/2012
5005Padovan(727734)88874Eric W. Weisstein04/2011
500618^70793-1788865Lelio R Paula11/2015
50076^114196-1757388862Enzo Doria02/2013
5008302^35829+35829^30288857Norbert Schneider12/2014
50093^186223+1688851Robert Price10/2013
50103*2^295139+788847Lelio R Paula08/2014
50113^186212-11300888846Enzo Doria07/2014
501287^45803-8688836Norbert Schneider11/2015
50132^295094-11027388833Enzo Doria05/2014
50142^295080+186915188828Enzo Doria05/2016
50152^295027-11340788812Enzo Doria07/2014
5016(2*10^88808-71)/388808Robert Price01/2017
501713^79722-8088806Lelio R Paula11/2015
50183^186103+10488794Lelio R Paula12/2015
5019(3*2^294971+1)/2556588792Lelio R Paula01/2013
50202^294937-11500388785Enzo Doria06/2015
50212^294868-10970988765Enzo Doria04/2014
50222^294864-298588763Yves Minet09/2014
5023(17*10^88761-41)/388762Robert Price09/2017
50242^294754+1501588730Lelio R Paula10/2013
5025(3^185951-7)/2088720Lelio R Paula01/2013
5026(2^294661+5)/44369338388694Lelio R Paula01/2013
5027(10^88680+11)/388680Robert Price11/2014
50282*7^104928-988675Lelio R Paula10/2014
502911^85150+1288675Lelio R Paula11/2015
50308*6^113951+588673Lelio R Paula10/2014
50316^113940-1856388663Enzo Doria03/2013
503238^56123-56123^3888663Norbert Schneider02/2017
50332^294492-6588651Lelio R Paula10/2012
503420^68120-5388627Lelio R Paula01/2016
5035122^42477-12188623Norbert Schneider10/2018
50362^294391-11325788621Enzo Doria07/2014
50375^126784-1547688619Enzo Doria02/2013
50382^294327+988602Lelio R Paula10/2012
50392^294320+1891588600Lelio R Paula10/2013
5040(98*10^88595-89)/9988595Ray Chandler07/2011
5041(17*2^294262-1)/1388582Lelio R Paula02/2014
5043(2*10^88545+7)/988545Erik Branger03/2011
50422^294137-13388545Lelio R Paula10/2012
5044(2^294092-1017)/117188528Lelio R Paula01/2013
50454^147036+147036^4+188525Robert Price04/2014
5046(14^77213-5^77213)/988496Robert Price04/2013
50472^293965+279337788493Enzo Doria03/2016
504811^84971-15088489Enzo Doria08/2012
504948^52626-4788478Norbert Schneider08/2018
5050(2^293956-1017)/3985137669667788476Lelio R Paula01/2013
505111^84958-219088475Enzo Doria12/2012
50522^293880-11134788467Enzo Doria05/2014
5053(106*10^88459-1)/388461Serge Batalov12/2014
505410^88457+27873388458Patrick De Geest07/2017
505510^88457-40188457Robert Price06/2017
505611^84908-168088423Enzo Doria12/2012
50572^293679-11207588407Enzo Doria06/2014
50586^113608-6588405Lelio R Paula12/2015
50592^293624+8287588390Lelio R Paula10/2013
50602^293612-11233788387Enzo Doria06/2014
5061758^30693+30693^75888386Norbert Schneider05/2017
5062gcd(V(1062695),5*F(212539)*(F(212539)-1)+1)88383Serge Batalov04/2015
50635*10^88377+7788378Robert Price06/2016
5064(5*2^293526+1)/30388359Lelio R Paula01/2013
50652^293461-278584388341Enzo Doria03/2016
50662^293416-103788328Yves Minet11/2012
5067(2^293384-7)/388317Lelio R Paula01/2013
5068(3^185092-5)/488311Lelio R Paula01/2013
5069(5*10^88303-173)/388304Robert Price11/2017
507014^77039-5788297Lelio R Paula11/2015
50713*10^88293-5988294Robert Price10/2017
50725^126303+4288283Lelio R Paula10/2015
507419^69025-1888266Theodore Burton01/2006
5073140^41128+13988266Norbert Schneider04/2019
50755*10^88261-388262Dmitry Domanov11/2010
50768^97731-7^(97731-1)88260Robert Price04/2016
50775*10^88254+5988255Robert Price09/2016
50784*3^184968-788253Lelio R Paula08/2014
50797^104426+8888251Lelio R Paula10/2015
50802^293142+9988245Lelio R Paula10/2012
508111^84736-213088244Enzo Doria12/2012
5082(10^110315+1)/(10^22063+1)/582481268216764857846028164188225Makoto Kamada04/2019
50832^293068-8988223Lelio R Paula10/2012
50842^293014-10965588207Enzo Doria04/2014
50858*7^104371-388205Lelio R Paula10/2014
50862^292995-214588201Lelio R Paula10/2013
50875*10^88182+7788183Robert Price06/2016
50892^292929+4387788181Donovan Johnson04/2005
50886^113321+13188181Lelio R Paula12/2015
50902^292904-58394988173Paul Bourdelais04/2013
50912^292894-11185188170Enzo Doria05/2014
50922^292872-279734988164Enzo Doria03/2016
50932^292860-10968588160Enzo Doria04/2014
50949*6^113288-588157Lelio R Paula10/2014
5095(2*10^88112-23)/388112Robert Price09/2017
5096(73*10^88105+17)/988106Robert Price10/2015
509711^84588+7888090Lelio R Paula11/2015
5098(265*10^88077+11)/388079Robert Price03/2017
509991^44959-90^4495988077Robert Price07/2015
51006^113177-5^11317788069Jean-Louis Charton01/2009
5101(10^88020+101)/388020Robert Price04/2016
510252^51285-5188006Norbert Schneider09/2018
5103(10^(2*43982+1)-6*10^43982-1)/387965Robert Price02/2016
5104(424*10^87930-1)/987932Robert Price11/2017
5105p(18225)#/2+12887929Robert Price04/2017
51064*6^112977+787914Lelio R Paula10/2014
510714^76677+6987882Lelio R Paula11/2015
5108(22*10^87863-1)/387864Robert Price12/2014
51092^291822-279781187848Enzo Doria04/2016
51102^291716-11138987816Enzo Doria05/2014
5111(782*10^87809-71)/987811Robert Price06/2017
51123^184039+182087809Lelio R Paula12/2015
511312^81356+4187798Lelio R Paula11/2015
51146^112792-1898387770Enzo Doria03/2013
51153*6^112787-587766Lelio R Paula10/2014
51167^103848+8287762Lelio R Paula10/2015
5117(19*2^291534-1)/17869639587754Lelio R Paula02/2014
5118(3^183915+5)/12887748Lelio R Paula01/2013
511919^68619+2487747Lelio R Paula12/2015
51212^291480+118587745Lelio R Paula10/2013
51202^291482+186736987745Enzo Doria03/2016
51222^291467-93787741Yves Minet05/2013
5123(25*10^87726+161)/387727Robert Price01/2017
512411^84239-285087726Enzo Doria12/2012
512510^87720+21554187721Patrick De Geest01/2011
512610^87720-387720Markus Tervooren07/2010
5127(5*10^87712-473)/987712Robert Price12/2017
5128(2^291357+5)/684787704Lelio R Paula01/2013
512993^44541-287679Lelio R Paula09/2013
51302^291261-10956187679Enzo Doria04/2014
5131(4*10^87669+149)/987669Robert Price03/2017
51322^291217+425787666Lelio R Paula10/2013
51332*12^81214-5^8121487645Mike Oakes12/2010
5134(5*10^87622-473)/987622Robert Price12/2017
513512^81188+8587617Lelio R Paula11/2015
5136(21*2^290980-1)/587595Lelio R Paula02/2014
51372^290958+12787588Lelio R Paula09/2012
51382^290923-6787577Lelio R Paula09/2012
51393*10^87573-9787574Robert Price08/2017
5140(13*10^87565+11)/387566Robert Price05/2015
5141(2^290857-7)/5587555Lelio R Paula01/2013
51422^290802+8287587541Lelio R Paula10/2013
5143(509203*2^290792-1)/756098787536Lelio R Paula04/2015
51443^183441+23687524Lelio R Paula12/2015
51452^290618-3387485Lelio R Paula09/2012
5146(184*10^87473-1)/387475Robert Price02/2017
51472^290534-11515187460Enzo Doria06/2015
51482^290512-10975787453Enzo Doria04/2014
5149(32*10^87448-41)/987449Robert Price05/2015
5150(2^290491+9)/317987444Lelio R Paula01/2013
5151(25*2^290489-1)/5180987443Lelio R Paula02/2014
51522^290426+8287587427Lelio R Paula11/2013
51533*2^290415-787425Lelio R Paula08/2014
515410^87408+5787409Robert Price03/2011
51552^290366+7477987409Enzo Doria04/2016
515610^87408-12356987408Patrick De Geest07/2013
51572^290265+5890587379Lelio R Paula10/2013
51587^103391+1687376Lelio R Paula10/2015
5159(115*10^87368-7)/987370Robert Price11/2017
5160(92^44491-1)/9187369Paul Bourdelais08/2017
51618*7^103379+387367Lelio R Paula10/2014
5162(2^290226+7)/7187365Lelio R Paula01/2013
516313^78407-3087341Lelio R Paula11/2015
51644*10^87337-9987338Robert Price12/2016
51657*10^87319+3987320Robert Price07/2016
51663*5^124921+287317Lelio R Paula10/2014
51673^182984+8887306Lelio R Paula12/2015
5168(10^87323-1)/(9*33909262597306826117)87303Alfred Reich02/2019
51694*10^87287-9987288Robert Price12/2016
517011^83813-186087283Enzo Doria12/2012
5171734^30453+30453^73487270Norbert Schneider04/2017
517212^80855+2987258Lelio R Paula11/2015
51733*6^112119-587247Lelio R Paula10/2014
517412^80806+7987205Lelio R Paula11/2015
517591382^9+9^9138287201Andrey Kulsha11/2004
5176(21181*2^289657+1)/8187198Lelio R Paula06/2014
51776^112054-4787195Lelio R Paula12/2015
5178(55459*2^289632+1)/5587191Lelio R Paula06/2014
517915^74131-6887185Lelio R Paula11/2015
51802^289583-74187174Lelio R Paula10/2013
51817^103146+1287169Lelio R Paula10/2015
51825*2^289556-387166Lelio R Paula08/2014
51832^289543-11273587162Enzo Doria06/2014
51848*3^182655-787150Lelio R Paula08/2014
51852*10^87144+8187145Robert Price01/2017
51867^103106+2*3^10310687135Mike Oakes08/2010
51878*3^182614+787130Lelio R Paula08/2014
5188(2^289368-509203)/987108Lelio R Paula01/2013
51893^182566+1487107Robert Price09/2013
5190(3^182385-5)/287020Lelio R Paula01/2013
519111^83534-886992Lelio R Paula11/2015
51924^144479-1426786986Mike Oakes03/2011
5193(145*10^86982-1)/986984Serge Batalov12/2014
5194(151*10^86963-1)/386965Robert Price04/2017
519515^73940-5886961Lelio R Paula11/2015
51962^288761-11314386926Enzo Doria07/2014
51972^288747+308386922Yves Minet03/2011
519830^58842+2986917Norbert Schneider03/2017
5199(10^86906-13)/386906Robert Price02/2017
52002^288692-11002786905Enzo Doria04/2014
5201(2^288682+7)/25989544986894Lelio R Paula01/2013
5202(2^288636+47)/129386885Lelio R Paula01/2013
52033^182089-3486879Robert Price11/2013
52042^288543-10980186861Enzo Doria04/2014
520560^48847-5986858Norbert Schneider10/2014
52062^288470-6487586839Lelio R Paula10/2013
520710^86816+3299786817Patrick De Geest07/2013
520810^86816-9986816Robert Price05/2011
5209(89*10^86802-539)/986803Robert Price11/2017
521041487!2+25686786Robert Price01/2015
5211(5*2^288301-1)/99986785Lelio R Paula02/2014
52122^288243+7604386770Enzo Doria04/2016
5213(29*2^288232+1)/1586767Lelio R Paula01/2013
52149*6^111495+586761Lelio R Paula10/2014
5215(5*2^288202+1)/8186757Lelio R Paula01/2013
52169*7^102654-286754Lelio R Paula10/2014
52172^288122-11284186734Enzo Doria06/2014
52185^124062-6886716Lelio R Paula10/2015
5219(2^288007-3)/12586697Lelio R Paula01/2013
5220379*10^86691+986694Arkadiusz Wesolowski10/2011
52217^102555+4886670Lelio R Paula10/2015
52222^287902-496186668Yves Minet05/2019
522377779!4+286660Robert Price08/2017
52242^287809-11135586640Enzo Doria05/2014
5225(47*2^287795+1)/786636Lelio R Paula04/2015
52269*7^102504+886627Lelio R Paula10/2014
52273^181551+3286622Robert Price11/2013
52282^287735-52134786617Paul Bourdelais05/2013
5229(1017*2^287600-1)/9186578Lelio R Paula04/2015
52302^287540-11296786559Enzo Doria06/2014
52313^181407+2086554Robert Price10/2013
5232(13*10^86546+83)/386547Robert Price09/2016
52332^287482-471586541Yves Minet05/2019
52343^181378-2^(181378-1)86540Robert Price01/2016
523583^45080-286513Lelio R Paula08/2013
5236(78557*2^287351+1)/61186504Lelio R Paula06/2014
523725*29^59147+2093686498Curtis Bright05/2015
52382^287298+187135986486Enzo Doria05/2016
5239118^41740-11786481Norbert Schneider08/2018
52403*10^86478+8986479Robert Price03/2017
52412^287272-7904986478Paul Bourdelais02/2012
5242906705*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5243811824*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5244779064*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5245768385*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5246700891*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5247652320*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5248377920*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
5249255060*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
5250187111*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2019 07:14 (Time in France)

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