PRP Records

Probable Primes Top 10000

(173006 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 ?
40012^293416-103788328Yves Minet11/2012
4002(2^293384-7)/388317Lelio R Paula01/2013
4003(3^185092-5)/488311Lelio R Paula01/2013
400414^77039-5788297Lelio R Paula11/2015
40055^126303+4288283Lelio R Paula10/2015
400619^69025-1888266Theodore Burton01/2006
40075*10^88261-388262Dmitry Domanov11/2010
40088^97731-7^(97731-1)88260Robert Price04/2016
40095*10^88254+5988255Robert Price09/2016
40104*3^184968-788253Lelio R Paula08/2014
40117^104426+8888251Lelio R Paula10/2015
40122^293142+9988245Lelio R Paula10/2012
401311^84736-213088244Enzo Doria12/2012
40142^293068-8988223Lelio R Paula10/2012
40152^293014-10965588207Enzo Doria04/2014
40168*7^104371-388205Lelio R Paula10/2014
40172^292995-214588201Lelio R Paula10/2013
40185*10^88182+7788183Robert Price06/2016
40192^292929+4387788181Donovan Johnson04/2005
40206^113321+13188181Lelio R Paula12/2015
40212^292904-58394988173Paul Bourdelais04/2013
40222^292894-11185188170Enzo Doria05/2014
40232^292872-279734988164Enzo Doria03/2016
40242^292860-10968588160Enzo Doria04/2014
40259*6^113288-588157Lelio R Paula10/2014
4026(73*10^88105+17)/988106Robert Price10/2015
402711^84588+7888090Lelio R Paula11/2015
4028(265*10^88077+11)/388079Robert Price03/2017
402991^44959-90^4495988077Robert Price07/2015
40306^113177-5^11317788069Jean-Louis Charton01/2009
4031(10^88020+101)/388020Robert Price04/2016
4032(10^(2*43982+1)-6*10^43982-1)/387965Robert Price02/2016
4033p(18225)#/2+12887929Robert Price04/2017
40344*6^112977+787914Lelio R Paula10/2014
403514^76677+6987882Lelio R Paula11/2015
4036(22*10^87863-1)/387864Robert Price12/2014
40372^291822-279781187848Enzo Doria04/2016
40382^291716-11138987816Enzo Doria05/2014
40393^184039+182087809Lelio R Paula12/2015
404012^81356+4187798Lelio R Paula11/2015
40416^112792-1898387770Enzo Doria03/2013
40423*6^112787-587766Lelio R Paula10/2014
40437^103848+8287762Lelio R Paula10/2015
4044(19*2^291534-1)/17869639587754Lelio R Paula02/2014
4045(3^183915+5)/12887748Lelio R Paula01/2013
404619^68619+2487747Lelio R Paula12/2015
40482^291480+118587745Lelio R Paula10/2013
40472^291482+186736987745Enzo Doria03/2016
40492^291467-93787741Yves Minet05/2013
4050(25*10^87726+161)/387727Robert Price01/2017
405111^84239-285087726Enzo Doria12/2012
405210^87720+21554187721Patrick De Geest01/2011
405310^87720-387720Markus Tervooren07/2010
4054(2^291357+5)/684787704Lelio R Paula01/2013
405593^44541-287679Lelio R Paula09/2013
40562^291261-10956187679Enzo Doria04/2014
4057(4*10^87669+149)/987669Robert Price03/2017
40582^291217+425787666Lelio R Paula10/2013
40592*12^81214-5^8121487645Mike Oakes12/2010
406012^81188+8587617Lelio R Paula11/2015
4061(21*2^290980-1)/587595Lelio R Paula02/2014
40622^290958+12787588Lelio R Paula09/2012
40632^290923-6787577Lelio R Paula09/2012
4064(13*10^87565+11)/387566Robert Price05/2015
4065(2^290857-7)/5587555Lelio R Paula01/2013
40662^290802+8287587541Lelio R Paula10/2013
4067(509203*2^290792-1)/756098787536Lelio R Paula04/2015
40683^183441+23687524Lelio R Paula12/2015
40692^290618-3387485Lelio R Paula09/2012
4070(184*10^87473-1)/387475Robert Price02/2017
40712^290534-11515187460Enzo Doria06/2015
40722^290512-10975787453Enzo Doria04/2014
4073(32*10^87448-41)/987449Robert Price05/2015
4074(2^290491+9)/317987444Lelio R Paula01/2013
4075(25*2^290489-1)/5180987443Lelio R Paula02/2014
40762^290426+8287587427Lelio R Paula11/2013
40773*2^290415-787425Lelio R Paula08/2014
407910^87408+5787409Robert Price03/2011
40782^290366+7477987409Enzo Doria04/2016
408010^87408-12356987408Patrick De Geest07/2013
40812^290265+5890587379Lelio R Paula10/2013
40827^103391+1687376Lelio R Paula10/2015
40838*7^103379+387367Lelio R Paula10/2014
4084(2^290226+7)/7187365Lelio R Paula01/2013
408513^78407-3087341Lelio R Paula11/2015
40864*10^87337-9987338Robert Price12/2016
40877*10^87319+3987320Robert Price07/2016
40883*5^124921+287317Lelio R Paula10/2014
40893^182984+8887306Lelio R Paula12/2015
40904*10^87287-9987288Robert Price12/2016
409111^83813-186087283Enzo Doria12/2012
4092734^30453+30453^73487270Norbert Schneider04/2017
409312^80855+2987258Lelio R Paula11/2015
40943*6^112119-587247Lelio R Paula10/2014
409512^80806+7987205Lelio R Paula11/2015
409691382^9+9^9138287201Andrey Kulsha11/2004
4097(21181*2^289657+1)/8187198Lelio R Paula06/2014
40986^112054-4787195Lelio R Paula12/2015
4099(55459*2^289632+1)/5587191Lelio R Paula06/2014
410015^74131-6887185Lelio R Paula11/2015
41012^289583-74187174Lelio R Paula10/2013
41027^103146+1287169Lelio R Paula10/2015
41035*2^289556-387166Lelio R Paula08/2014
41042^289543-11273587162Enzo Doria06/2014
41058*3^182655-787150Lelio R Paula08/2014
41062*10^87144+8187145Robert Price01/2017
41077^103106+2*3^10310687135Mike Oakes08/2010
41088*3^182614+787130Lelio R Paula08/2014
4109(2^289368-509203)/987108Lelio R Paula01/2013
41103^182566+1487107Robert Price09/2013
4111(3^182385-5)/287020Lelio R Paula01/2013
411211^83534-886992Lelio R Paula11/2015
41134^144479-1426786986Mike Oakes03/2011
4114(145*10^86982-1)/986984Serge Batalov12/2014
4115(151*10^86963-1)/386965Robert Price04/2017
411615^73940-5886961Lelio R Paula11/2015
41172^288761-11314386926Enzo Doria07/2014
41182^288747+308386922Yves Minet03/2011
411930^58842+2986917Norbert Schneider03/2017
4120(10^86906-13)/386906Robert Price02/2017
41212^288692-11002786905Enzo Doria04/2014
4122(2^288682+7)/25989544986894Lelio R Paula01/2013
4123(2^288636+47)/129386885Lelio R Paula01/2013
41243^182089-3486879Robert Price11/2013
41252^288543-10980186861Enzo Doria04/2014
412660^48847-5986858Norbert Schneider10/2014
41272^288470-6487586839Lelio R Paula10/2013
412810^86816+3299786817Patrick De Geest07/2013
412910^86816-9986816Robert Price05/2011
413041487!2+25686786Robert Price01/2015
4131(5*2^288301-1)/99986785Lelio R Paula02/2014
41322^288243+7604386770Enzo Doria04/2016
4133(29*2^288232+1)/1586767Lelio R Paula01/2013
41349*6^111495+586761Lelio R Paula10/2014
4135(5*2^288202+1)/8186757Lelio R Paula01/2013
41369*7^102654-286754Lelio R Paula10/2014
41372^288122-11284186734Enzo Doria06/2014
41385^124062-6886716Lelio R Paula10/2015
4139(2^288007-3)/12586697Lelio R Paula01/2013
4140379*10^86691+986694Arkadiusz Wesolowski10/2011
41417^102555+4886670Lelio R Paula10/2015
41422^287809-11135586640Enzo Doria05/2014
4143(47*2^287795+1)/786636Lelio R Paula04/2015
41449*7^102504+886627Lelio R Paula10/2014
41453^181551+3286622Robert Price11/2013
41462^287735-52134786617Paul Bourdelais05/2013
4147(1017*2^287600-1)/9186578Lelio R Paula04/2015
41482^287540-11296786559Enzo Doria06/2014
41493^181407+2086554Robert Price10/2013
4150(13*10^86546+83)/386547Robert Price09/2016
41513^181378-2^(181378-1)86540Robert Price01/2016
415283^45080-286513Lelio R Paula08/2013
4153(78557*2^287351+1)/61186504Lelio R Paula06/2014
415425*29^59147+2093686498Curtis Bright05/2015
41552^287298+187135986486Enzo Doria05/2016
41563*10^86478+8986479Robert Price03/2017
41572^287272-7904986478Paul Bourdelais02/2012
4158906705*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4159811824*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4160779064*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4161768385*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4162700891*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4163652320*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4164377920*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4165255060*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4166187111*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4167(10^86453-1)/986453Lew Baxter10/2000
416887^44563-86^4456386431Robert Price05/2015
41696^111057+6186420Lelio R Paula12/2015
41702^287057-10990986413Enzo Doria04/2014
41715^123608+2286399Lelio R Paula10/2015
4172(31*10^86364-121)/986365Robert Price06/2016
41732^286859+7166386354Enzo Doria04/2016
41742^286740+2983586318Lelio R Paula10/2013
41752*10^86310+9^8631086311Mike Oakes05/2011
417611^82878-186086309Enzo Doria12/2012
41772^286547+1609586260Lelio R Paula10/2013
41782^286455-11042786232Enzo Doria05/2014
4179(37*10^86230+53)/986231Robert Price05/2015
41808*3^180700+586217Lelio R Paula08/2014
41813^180697-4086215Lelio R Paula12/2015
4182(13*2^286318-1)/1325786188Lelio R Paula02/2014
41832^286165+7786145Lelio R Paula08/2012
41849*2^286140+786138Lelio R Paula08/2014
4185(29*2^286108-1)/200236786123Lelio R Paula02/2014
418610^86110+16111386111Patrick De Geest07/2013
418710^86110-6986110Robert Price05/2011
41882^286036-86968810586106Lelio R Paula07/2016
4189(77*10^86072+31)/986073Robert Price10/2015
41902^285923+34586072Lelio R Paula09/2013
419113^77266-9086070Lelio R Paula11/2015
41922^285910-45890386068Enzo Doria04/2015
41932^285904-12586066Lelio R Paula08/2012
41942^285836+6583586046Lelio R Paula09/2013
4195(2^285766+78557)/386024Lelio R Paula01/2013
4196(5*10^86011-107)/386012Robert Price01/2017
41976^110522+16386003Lelio R Paula12/2015
419841^53323-40^5332385999Robert Price07/2012
41992^285678-10961785998Enzo Doria04/2014
42006^110506-1667385991Enzo Doria02/2013
42022^285569-74185965Lelio R Paula09/2013
4201(32*10^85964+31)/985965Robert Price05/2015
42036*10^85910-785911Dmitry Domanov11/2010
42044*10^85881+6385882Robert Price06/2016
4205(10^85864+53)/985864Robert Price01/2015
42062^285230+34585863Lelio R Paula09/2013
42072^285199+7568385854Enzo Doria04/2016
4208p(17832)#/2+51285845Robert Price05/2017
420911^82426-123085838Enzo Doria11/2012
42102^285113-10988185828Enzo Doria04/2014
42115^122746-9285796Lelio R Paula10/2015
42122^285001-11346185794Enzo Doria08/2014
4213(11*10^85782-131)/385783Robert Price02/2017
42142^284913-11049185768Enzo Doria05/2014
42156^110220+4785768Lelio R Paula12/2015
42163*6^110202-585755Lelio R Paula10/2014
4217(157^39047-1)/15685742Alexander Zhirkov06/2016
4218(3^179705+7)/25085739Lelio R Paula12/2012
42192^284734-655585714Lelio R Paula09/2013
4220(10^85712+53)/985712Robert Price01/2015
4221(6883*2^284668-1)/385697Lelio R Paula04/2015
422220^65855+8385680Lelio R Paula01/2016
42236^110105+5385679Lelio R Paula12/2015
42252^284567-760585664Lelio R Paula09/2013
42249*5^122555-285664Lelio R Paula10/2014
42265^122554-1485662Lelio R Paula10/2015
42279*5^122543+485655Lelio R Paula10/2014
42283^179489-2^(179489-1)85639Robert Price01/2016
42292^284429+17785622Lelio R Paula08/2012
42302*3^179452+585621Lelio R Paula07/2014
4231(19^66919+3^66919)/2285572Robert Price07/2013
423266^47023-6585561Norbert Schneider11/2014
42336^109943+1385553Lelio R Paula12/2015
4234(2^284167-509203)/3456477585536Lelio R Paula01/2013
42352^284133-385533M. Frind & P. Underwood07/2002
42362^284113+31585527Lelio R Paula09/2013
4237(16*10^85495-19)/385496Robert Price03/2016
42382^284004+17785494Lelio R Paula08/2012
4239(16*10^85473-91)/385474Robert Price06/2016
42403^179120+2285462Robert Price12/2013
42412^283872-279224985454Enzo Doria03/2016
4242(29*10^85438+259)/985439Robert Price04/2017
42432^283817+8287585438Lelio R Paula09/2013
4244(2^283815-5)/20185435Lelio R Paula01/2013
42452^283796-12585432Lelio R Paula08/2012
4246(29*2^283784-1)/1385428Lelio R Paula02/2014
424715^72592-2885375Lelio R Paula11/2015
42482^283604-5869585374Lelio R Paula09/2013
4249(15*2^283583-1)/10305185364Lelio R Paula02/2014
425015^72572+9285352Lelio R Paula11/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

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