PRP Records

Probable Primes Top 10000

(252675 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 ?
50012^292894-11185188170Enzo Doria05/2014
50022^292872-279734988164Enzo Doria03/2016
50032^292860-10968588160Enzo Doria04/2014
50049*6^113288-588157Lelio R Paula10/2014
5005(2*10^88112-23)/388112Robert Price09/2017
5006(73*10^88105+17)/988106Robert Price10/2015
500711^84588+7888090Lelio R Paula11/2015
5008(265*10^88077+11)/388079Robert Price03/2017
500991^44959-90^4495988077Robert Price07/2015
50106^113177-5^11317788069Jean-Louis Charton01/2009
5011(10^88020+101)/388020Robert Price04/2016
501252^51285-5188006Norbert Schneider09/2018
5013(10^(2*43982+1)-6*10^43982-1)/387965Robert Price02/2016
5014(424*10^87930-1)/987932Robert Price11/2017
5015p(18225)#/2+12887929Robert Price04/2017
50164*6^112977+787914Lelio R Paula10/2014
501714^76677+6987882Lelio R Paula11/2015
5018(22*10^87863-1)/387864Robert Price12/2014
50192^291822-279781187848Enzo Doria04/2016
50202^291716-11138987816Enzo Doria05/2014
5021(782*10^87809-71)/987811Robert Price06/2017
50223^184039+182087809Lelio R Paula12/2015
502312^81356+4187798Lelio R Paula11/2015
50246^112792-1898387770Enzo Doria03/2013
50253*6^112787-587766Lelio R Paula10/2014
50267^103848+8287762Lelio R Paula10/2015
5027(19*2^291534-1)/17869639587754Lelio R Paula02/2014
5028(3^183915+5)/12887748Lelio R Paula01/2013
502919^68619+2487747Lelio R Paula12/2015
50312^291480+118587745Lelio R Paula10/2013
50302^291482+186736987745Enzo Doria03/2016
50322^291467-93787741Yves Minet05/2013
5033(25*10^87726+161)/387727Robert Price01/2017
503411^84239-285087726Enzo Doria12/2012
503510^87720+21554187721Patrick De Geest01/2011
503610^87720-387720Markus Tervooren07/2010
5037(5*10^87712-473)/987712Robert Price12/2017
5038(2^291357+5)/684787704Lelio R Paula01/2013
503993^44541-287679Lelio R Paula09/2013
50402^291261-10956187679Enzo Doria04/2014
5041(4*10^87669+149)/987669Robert Price03/2017
50422^291217+425787666Lelio R Paula10/2013
50432*12^81214-5^8121487645Mike Oakes12/2010
5044(5*10^87622-473)/987622Robert Price12/2017
504512^81188+8587617Lelio R Paula11/2015
5046(21*2^290980-1)/587595Lelio R Paula02/2014
50472^290958+12787588Lelio R Paula09/2012
50482^290923-6787577Lelio R Paula09/2012
50493*10^87573-9787574Robert Price08/2017
5050(13*10^87565+11)/387566Robert Price05/2015
5051(2^290857-7)/5587555Lelio R Paula01/2013
50522^290802+8287587541Lelio R Paula10/2013
5053(509203*2^290792-1)/756098787536Lelio R Paula04/2015
50543^183441+23687524Lelio R Paula12/2015
50552^290618-3387485Lelio R Paula09/2012
5056(184*10^87473-1)/387475Robert Price02/2017
50572^290534-11515187460Enzo Doria06/2015
50582^290512-10975787453Enzo Doria04/2014
5059(32*10^87448-41)/987449Robert Price05/2015
5060(2^290491+9)/317987444Lelio R Paula01/2013
5061(25*2^290489-1)/5180987443Lelio R Paula02/2014
50622^290426+8287587427Lelio R Paula11/2013
50633*2^290415-787425Lelio R Paula08/2014
506510^87408+5787409Robert Price03/2011
50642^290366+7477987409Enzo Doria04/2016
506610^87408-12356987408Patrick De Geest07/2013
50672^290265+5890587379Lelio R Paula10/2013
50687^103391+1687376Lelio R Paula10/2015
5069(115*10^87368-7)/987370Robert Price11/2017
5070(92^44491-1)/9187369Paul Bourdelais08/2017
50718*7^103379+387367Lelio R Paula10/2014
5072(2^290226+7)/7187365Lelio R Paula01/2013
507313^78407-3087341Lelio R Paula11/2015
50744*10^87337-9987338Robert Price12/2016
50757*10^87319+3987320Robert Price07/2016
50763*5^124921+287317Lelio R Paula10/2014
50773^182984+8887306Lelio R Paula12/2015
5078(10^87323-1)/(9*33909262597306826117)87303Alfred Reich02/2019
50794*10^87287-9987288Robert Price12/2016
508011^83813-186087283Enzo Doria12/2012
5081734^30453+30453^73487270Norbert Schneider04/2017
508212^80855+2987258Lelio R Paula11/2015
50833*6^112119-587247Lelio R Paula10/2014
508412^80806+7987205Lelio R Paula11/2015
508591382^9+9^9138287201Andrey Kulsha11/2004
5086(21181*2^289657+1)/8187198Lelio R Paula06/2014
50876^112054-4787195Lelio R Paula12/2015
5088(55459*2^289632+1)/5587191Lelio R Paula06/2014
508915^74131-6887185Lelio R Paula11/2015
50902^289583-74187174Lelio R Paula10/2013
50917^103146+1287169Lelio R Paula10/2015
50925*2^289556-387166Lelio R Paula08/2014
50932^289543-11273587162Enzo Doria06/2014
50948*3^182655-787150Lelio R Paula08/2014
50952*10^87144+8187145Robert Price01/2017
50967^103106+2*3^10310687135Mike Oakes08/2010
50978*3^182614+787130Lelio R Paula08/2014
5098(2^289368-509203)/987108Lelio R Paula01/2013
50993^182566+1487107Robert Price09/2013
5100(3^182385-5)/287020Lelio R Paula01/2013
510111^83534-886992Lelio R Paula11/2015
51024^144479-1426786986Mike Oakes03/2011
5103(145*10^86982-1)/986984Serge Batalov12/2014
5104(151*10^86963-1)/386965Robert Price04/2017
510515^73940-5886961Lelio R Paula11/2015
51062^288761-11314386926Enzo Doria07/2014
51072^288747+308386922Yves Minet03/2011
510830^58842+2986917Norbert Schneider03/2017
5109(10^86906-13)/386906Robert Price02/2017
51102^288692-11002786905Enzo Doria04/2014
5111(2^288682+7)/25989544986894Lelio R Paula01/2013
5112(2^288636+47)/129386885Lelio R Paula01/2013
51133^182089-3486879Robert Price11/2013
51142^288543-10980186861Enzo Doria04/2014
511560^48847-5986858Norbert Schneider10/2014
51162^288470-6487586839Lelio R Paula10/2013
511710^86816+3299786817Patrick De Geest07/2013
511810^86816-9986816Robert Price05/2011
5119(89*10^86802-539)/986803Robert Price11/2017
512041487!2+25686786Robert Price01/2015
5121(5*2^288301-1)/99986785Lelio R Paula02/2014
51222^288243+7604386770Enzo Doria04/2016
5123(29*2^288232+1)/1586767Lelio R Paula01/2013
51249*6^111495+586761Lelio R Paula10/2014
5125(5*2^288202+1)/8186757Lelio R Paula01/2013
51269*7^102654-286754Lelio R Paula10/2014
51272^288122-11284186734Enzo Doria06/2014
51285^124062-6886716Lelio R Paula10/2015
5129(2^288007-3)/12586697Lelio R Paula01/2013
5130379*10^86691+986694Arkadiusz Wesolowski10/2011
51317^102555+4886670Lelio R Paula10/2015
513277779!4+286660Robert Price08/2017
51332^287809-11135586640Enzo Doria05/2014
5134(47*2^287795+1)/786636Lelio R Paula04/2015
51359*7^102504+886627Lelio R Paula10/2014
51363^181551+3286622Robert Price11/2013
51372^287735-52134786617Paul Bourdelais05/2013
5138(1017*2^287600-1)/9186578Lelio R Paula04/2015
51392^287540-11296786559Enzo Doria06/2014
51403^181407+2086554Robert Price10/2013
5141(13*10^86546+83)/386547Robert Price09/2016
51423^181378-2^(181378-1)86540Robert Price01/2016
514383^45080-286513Lelio R Paula08/2013
5144(78557*2^287351+1)/61186504Lelio R Paula06/2014
514525*29^59147+2093686498Curtis Bright05/2015
51462^287298+187135986486Enzo Doria05/2016
5147118^41740-11786481Norbert Schneider08/2018
51483*10^86478+8986479Robert Price03/2017
51492^287272-7904986478Paul Bourdelais02/2012
5150906705*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5151811824*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5152779064*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5153768385*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5154700891*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5155652320*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5156377920*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
5157255060*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
5158187111*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
5159(10^86453-1)/986453Lew Baxter10/2000
516087^44563-86^4456386431Robert Price05/2015
51616^111057+6186420Lelio R Paula12/2015
51622^287057-10990986413Enzo Doria04/2014
51635^123608+2286399Lelio R Paula10/2015
5164(31*10^86364-121)/986365Robert Price06/2016
51652^286859+7166386354Enzo Doria04/2016
51662^286740+2983586318Lelio R Paula10/2013
51672*10^86310+9^8631086311Mike Oakes05/2011
516811^82878-186086309Enzo Doria12/2012
51692^286547+1609586260Lelio R Paula10/2013
5170(58*10^86242+329)/986243Robert Price11/2017
51712^286455-11042786232Enzo Doria05/2014
5172(37*10^86230+53)/986231Robert Price05/2015
51738*3^180700+586217Lelio R Paula08/2014
51743^180697-4086215Lelio R Paula12/2015
5175(13*2^286318-1)/1325786188Lelio R Paula02/2014
51762^286165+7786145Lelio R Paula08/2012
51779*2^286140+786138Lelio R Paula08/2014
5178(29*2^286108-1)/200236786123Lelio R Paula02/2014
517910^86110+16111386111Patrick De Geest07/2013
518010^86110-6986110Robert Price05/2011
51812^286036-86968810586106Lelio R Paula07/2016
5182(77*10^86072+31)/986073Robert Price10/2015
51832^285923+34586072Lelio R Paula09/2013
518413^77266-9086070Lelio R Paula11/2015
51852^285910-45890386068Enzo Doria04/2015
51862^285904-12586066Lelio R Paula08/2012
51872^285836+6583586046Lelio R Paula09/2013
5188(2^285766+78557)/386024Lelio R Paula01/2013
5189(5*10^86011-107)/386012Robert Price01/2017
51906^110522+16386003Lelio R Paula12/2015
519141^53323-40^5332385999Robert Price07/2012
51922^285678-10961785998Enzo Doria04/2014
51936^110506-1667385991Enzo Doria02/2013
51952^285569-74185965Lelio R Paula09/2013
5194(32*10^85964+31)/985965Robert Price05/2015
5196133^40466+13285944Norbert Schneider02/2019
51976*10^85910-785911Dmitry Domanov11/2010
5198(412*10^85897-7)/985899Robert Price10/2017
51994*10^85881+6385882Robert Price06/2016
5200(10^85864+53)/985864Robert Price01/2015
52012^285230+34585863Lelio R Paula09/2013
5202(5*10^85855-473)/985855Robert Price12/2017
52032^285199+7568385854Enzo Doria04/2016
5204(76*10^85847-211)/985848Robert Price10/2017
5205p(17832)#/2+51285845Robert Price05/2017
5206(16*10^85839+167)/385840Robert Price10/2017
520711^82426-123085838Enzo Doria11/2012
52082^285113-10988185828Enzo Doria04/2014
52095^122746-9285796Lelio R Paula10/2015
52102^285001-11346185794Enzo Doria08/2014
5211(11*10^85782-131)/385783Robert Price02/2017
52122^284913-11049185768Enzo Doria05/2014
52136^110220+4785768Lelio R Paula12/2015
52143*6^110202-585755Lelio R Paula10/2014
5215(157^39047-1)/15685742Alexander Zhirkov06/2016
5216(3^179705+7)/25085739Lelio R Paula12/2012
52172^284734-655585714Lelio R Paula09/2013
5218(10^85712+53)/985712Robert Price01/2015
52193*10^85703+1185704Robert Price11/2017
5220(6883*2^284668-1)/385697Lelio R Paula04/2015
522120^65855+8385680Lelio R Paula01/2016
52226^110105+5385679Lelio R Paula12/2015
5223(10^85666-97)/385666Robert Kinser10/2017
52252^284567-760585664Lelio R Paula09/2013
52249*5^122555-285664Lelio R Paula10/2014
52265^122554-1485662Lelio R Paula10/2015
52279*5^122543+485655Lelio R Paula10/2014
52283^179489-2^(179489-1)85639Robert Price01/2016
52292^284429+17785622Lelio R Paula08/2012
52302*3^179452+585621Lelio R Paula07/2014
5231(19^66919+3^66919)/2285572Robert Price07/2013
523266^47023-6585561Norbert Schneider11/2014
52336^109943+1385553Lelio R Paula12/2015
5234(2^284167-509203)/3456477585536Lelio R Paula01/2013
52352^284133-385533M. Frind & P. Underwood07/2002
52362^284113+31585527Lelio R Paula09/2013
5237(28*10^85500+149)/385501Robert Price10/2017
5238(16*10^85495-19)/385496Robert Price03/2016
52392^284004+17785494Lelio R Paula08/2012
5240(16*10^85473-91)/385474Robert Price06/2016
52413^179120+2285462Robert Price12/2013
52422^283872-279224985454Enzo Doria03/2016
5243(29*10^85438+259)/985439Robert Price04/2017
52442^283817+8287585438Lelio R Paula09/2013
5245(2^283815-5)/20185435Lelio R Paula01/2013
52462^283796-12585432Lelio R Paula08/2012
5247(29*2^283784-1)/1385428Lelio R Paula02/2014
524815^72592-2885375Lelio R Paula11/2015
52492^283604-5869585374Lelio R Paula09/2013
5250(44*10^85370-503)/985371Robert Price10/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 20 2019 09:21 (Time in France)

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