PRP Records

Probable Primes Top 10000

(172742 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 ?
4001(3^183915+5)/12887748Lelio R Paula01/2013
400219^68619+2487747Lelio R Paula12/2015
40042^291480+118587745Lelio R Paula10/2013
40032^291482+186736987745Enzo Doria03/2016
40052^291467-93787741Yves Minet05/2013
4006(25*10^87726+161)/387727Robert Price01/2017
400711^84239-285087726Enzo Doria12/2012
400810^87720+21554187721Patrick De Geest01/2011
400910^87720-387720Markus Tervooren07/2010
4010(2^291357+5)/684787704Lelio R Paula01/2013
401193^44541-287679Lelio R Paula09/2013
40122^291261-10956187679Enzo Doria04/2014
4013(4*10^87669+149)/987669Robert Price03/2017
40142^291217+425787666Lelio R Paula10/2013
40152*12^81214-5^8121487645Mike Oakes12/2010
401612^81188+8587617Lelio R Paula11/2015
4017(21*2^290980-1)/587595Lelio R Paula02/2014
40182^290958+12787588Lelio R Paula09/2012
40192^290923-6787577Lelio R Paula09/2012
4020(13*10^87565+11)/387566Robert Price05/2015
4021(2^290857-7)/5587555Lelio R Paula01/2013
40222^290802+8287587541Lelio R Paula10/2013
4023(509203*2^290792-1)/756098787536Lelio R Paula04/2015
40243^183441+23687524Lelio R Paula12/2015
40252^290618-3387485Lelio R Paula09/2012
4026(184*10^87473-1)/387475Robert Price02/2017
40272^290534-11515187460Enzo Doria06/2015
40282^290512-10975787453Enzo Doria04/2014
4029(32*10^87448-41)/987449Robert Price05/2015
4030(2^290491+9)/317987444Lelio R Paula01/2013
4031(25*2^290489-1)/5180987443Lelio R Paula02/2014
40322^290426+8287587427Lelio R Paula11/2013
40333*2^290415-787425Lelio R Paula08/2014
403510^87408+5787409Robert Price03/2011
40342^290366+7477987409Enzo Doria04/2016
403610^87408-12356987408Patrick De Geest07/2013
40372^290265+5890587379Lelio R Paula10/2013
40387^103391+1687376Lelio R Paula10/2015
40398*7^103379+387367Lelio R Paula10/2014
4040(2^290226+7)/7187365Lelio R Paula01/2013
404113^78407-3087341Lelio R Paula11/2015
40424*10^87337-9987338Robert Price12/2016
40437*10^87319+3987320Robert Price07/2016
40443*5^124921+287317Lelio R Paula10/2014
40453^182984+8887306Lelio R Paula12/2015
40464*10^87287-9987288Robert Price12/2016
404711^83813-186087283Enzo Doria12/2012
404812^80855+2987258Lelio R Paula11/2015
40493*6^112119-587247Lelio R Paula10/2014
405012^80806+7987205Lelio R Paula11/2015
405191382^9+9^9138287201Andrey Kulsha11/2004
4052(21181*2^289657+1)/8187198Lelio R Paula06/2014
40536^112054-4787195Lelio R Paula12/2015
4054(55459*2^289632+1)/5587191Lelio R Paula06/2014
405515^74131-6887185Lelio R Paula11/2015
40562^289583-74187174Lelio R Paula10/2013
40577^103146+1287169Lelio R Paula10/2015
40585*2^289556-387166Lelio R Paula08/2014
40592^289543-11273587162Enzo Doria06/2014
40608*3^182655-787150Lelio R Paula08/2014
40612*10^87144+8187145Robert Price01/2017
40627^103106+2*3^10310687135Mike Oakes08/2010
40638*3^182614+787130Lelio R Paula08/2014
4064(2^289368-509203)/987108Lelio R Paula01/2013
40653^182566+1487107Robert Price09/2013
4066(3^182385-5)/287020Lelio R Paula01/2013
406711^83534-886992Lelio R Paula11/2015
40684^144479-1426786986Mike Oakes03/2011
4069(145*10^86982-1)/986984Serge Batalov12/2014
4070(151*10^86963-1)/386965Robert Price04/2017
407115^73940-5886961Lelio R Paula11/2015
40722^288761-11314386926Enzo Doria07/2014
40732^288747+308386922Yves Minet03/2011
407430^58842+2986917Norbert Schneider03/2017
4075(10^86906-13)/386906Robert Price02/2017
40762^288692-11002786905Enzo Doria04/2014
4077(2^288682+7)/25989544986894Lelio R Paula01/2013
4078(2^288636+47)/129386885Lelio R Paula01/2013
40793^182089-3486879Robert Price11/2013
40802^288543-10980186861Enzo Doria04/2014
408160^48847-5986858Norbert Schneider10/2014
40822^288470-6487586839Lelio R Paula10/2013
408310^86816+3299786817Patrick De Geest07/2013
408410^86816-9986816Robert Price05/2011
408541487!2+25686786Robert Price01/2015
4086(5*2^288301-1)/99986785Lelio R Paula02/2014
40872^288243+7604386770Enzo Doria04/2016
4088(29*2^288232+1)/1586767Lelio R Paula01/2013
40899*6^111495+586761Lelio R Paula10/2014
4090(5*2^288202+1)/8186757Lelio R Paula01/2013
40919*7^102654-286754Lelio R Paula10/2014
40922^288122-11284186734Enzo Doria06/2014
40935^124062-6886716Lelio R Paula10/2015
4094(2^288007-3)/12586697Lelio R Paula01/2013
4095379*10^86691+986694Arkadiusz Wesolowski10/2011
40967^102555+4886670Lelio R Paula10/2015
40972^287809-11135586640Enzo Doria05/2014
4098(47*2^287795+1)/786636Lelio R Paula04/2015
40999*7^102504+886627Lelio R Paula10/2014
41003^181551+3286622Robert Price11/2013
41012^287735-52134786617Paul Bourdelais05/2013
4102(1017*2^287600-1)/9186578Lelio R Paula04/2015
41032^287540-11296786559Enzo Doria06/2014
41043^181407+2086554Robert Price10/2013
4105(13*10^86546+83)/386547Robert Price09/2016
41063^181378-2^(181378-1)86540Robert Price01/2016
410783^45080-286513Lelio R Paula08/2013
4108(78557*2^287351+1)/61186504Lelio R Paula06/2014
410925*29^59147+2093686498Curtis Bright05/2015
41102^287298+187135986486Enzo Doria05/2016
41113*10^86478+8986479Robert Price03/2017
41122^287272-7904986478Paul Bourdelais02/2012
4113906705*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4114811824*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4115779064*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4116768385*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4117700891*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4118652320*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4119377920*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4120255060*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4121187111*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4122(10^86453-1)/986453Lew Baxter10/2000
412387^44563-86^4456386431Robert Price05/2015
41246^111057+6186420Lelio R Paula12/2015
41252^287057-10990986413Enzo Doria04/2014
41265^123608+2286399Lelio R Paula10/2015
4127(31*10^86364-121)/986365Robert Price06/2016
41282^286859+7166386354Enzo Doria04/2016
41292^286740+2983586318Lelio R Paula10/2013
41302*10^86310+9^8631086311Mike Oakes05/2011
413111^82878-186086309Enzo Doria12/2012
41322^286547+1609586260Lelio R Paula10/2013
41332^286455-11042786232Enzo Doria05/2014
4134(37*10^86230+53)/986231Robert Price05/2015
41358*3^180700+586217Lelio R Paula08/2014
41363^180697-4086215Lelio R Paula12/2015
4137(13*2^286318-1)/1325786188Lelio R Paula02/2014
41382^286165+7786145Lelio R Paula08/2012
41399*2^286140+786138Lelio R Paula08/2014
4140(29*2^286108-1)/200236786123Lelio R Paula02/2014
414110^86110+16111386111Patrick De Geest07/2013
414210^86110-6986110Robert Price05/2011
41432^286036-86968810586106Lelio R Paula07/2016
4144(77*10^86072+31)/986073Robert Price10/2015
41452^285923+34586072Lelio R Paula09/2013
414613^77266-9086070Lelio R Paula11/2015
41472^285910-45890386068Enzo Doria04/2015
41482^285904-12586066Lelio R Paula08/2012
41492^285836+6583586046Lelio R Paula09/2013
4150(2^285766+78557)/386024Lelio R Paula01/2013
4151(5*10^86011-107)/386012Robert Price01/2017
41526^110522+16386003Lelio R Paula12/2015
415341^53323-40^5332385999Robert Price07/2012
41542^285678-10961785998Enzo Doria04/2014
41556^110506-1667385991Enzo Doria02/2013
41572^285569-74185965Lelio R Paula09/2013
4156(32*10^85964+31)/985965Robert Price05/2015
41586*10^85910-785911Dmitry Domanov11/2010
41594*10^85881+6385882Robert Price06/2016
4160(10^85864+53)/985864Robert Price01/2015
41612^285230+34585863Lelio R Paula09/2013
41622^285199+7568385854Enzo Doria04/2016
416311^82426-123085838Enzo Doria11/2012
41642^285113-10988185828Enzo Doria04/2014
41655^122746-9285796Lelio R Paula10/2015
41662^285001-11346185794Enzo Doria08/2014
4167(11*10^85782-131)/385783Robert Price02/2017
41682^284913-11049185768Enzo Doria05/2014
41696^110220+4785768Lelio R Paula12/2015
41703*6^110202-585755Lelio R Paula10/2014
4171(157^39047-1)/15685742Alexander Zhirkov06/2016
4172(3^179705+7)/25085739Lelio R Paula12/2012
41732^284734-655585714Lelio R Paula09/2013
4174(10^85712+53)/985712Robert Price01/2015
4175(6883*2^284668-1)/385697Lelio R Paula04/2015
417620^65855+8385680Lelio R Paula01/2016
41776^110105+5385679Lelio R Paula12/2015
41792^284567-760585664Lelio R Paula09/2013
41789*5^122555-285664Lelio R Paula10/2014
41805^122554-1485662Lelio R Paula10/2015
41819*5^122543+485655Lelio R Paula10/2014
41823^179489-2^(179489-1)85639Robert Price01/2016
41832^284429+17785622Lelio R Paula08/2012
41842*3^179452+585621Lelio R Paula07/2014
4185(19^66919+3^66919)/2285572Robert Price07/2013
418666^47023-6585561Norbert Schneider11/2014
41876^109943+1385553Lelio R Paula12/2015
4188(2^284167-509203)/3456477585536Lelio R Paula01/2013
41892^284133-385533M. Frind & P. Underwood07/2002
41902^284113+31585527Lelio R Paula09/2013
4191(16*10^85495-19)/385496Robert Price03/2016
41922^284004+17785494Lelio R Paula08/2012
4193(16*10^85473-91)/385474Robert Price06/2016
41943^179120+2285462Robert Price12/2013
41952^283872-279224985454Enzo Doria03/2016
4196(29*10^85438+259)/985439Robert Price04/2017
41972^283817+8287585438Lelio R Paula09/2013
4198(2^283815-5)/20185435Lelio R Paula01/2013
41992^283796-12585432Lelio R Paula08/2012
4200(29*2^283784-1)/1385428Lelio R Paula02/2014
420115^72592-2885375Lelio R Paula11/2015
42022^283604-5869585374Lelio R Paula09/2013
4203(15*2^283583-1)/10305185364Lelio R Paula02/2014
420415^72572+9285352Lelio R Paula11/2015
42052^283473-161585334Lelio R Paula09/2013
42062^283466-1585332Lelio R Paula08/2012
420711^81916-702085307Enzo Doria02/2013
42086^109626-785306Lelio R Paula11/2014
42092^283374-11032785305Enzo Doria05/2014
421033*10^85297+785299Robert Price07/2016
421118^67933+4185275Lelio R Paula11/2015
42122^283271-10934185274Enzo Doria04/2014
4213(25*10^85249-73)/385250Robert Price09/2016
42142*5^121959+385246Lelio R Paula10/2014
421519834^19834+894785235Henri Lifchitz11/2004
42162^283140+191585234Lelio R Paula09/2013
4217(16*10^85221-31)/385222Robert Price03/2016
42182^283083+186938385217Enzo Doria05/2016
4219(24737*2^283051+1)/1785211Lelio R Paula06/2014
4220(2^283032+78557)/385201Lelio R Paula01/2013
42212^283026-10989385200Enzo Doria04/2014
4222(2^283012+78557)/12985193Lelio R Paula01/2013
42232^282860-10972785150Enzo Doria04/2014
42242^282819+186941385138Enzo Doria05/2016
42253^178428+285132Ray Chandler07/2011
4226(22699*2^282742+1)/7385117Lelio R Paula06/2014
4227(16^70687+5^70687)/2185115Robert Price07/2013
4228(3^178352-2)/785095Lelio R Paula12/2012
422911^81699-279085081Enzo Doria12/2012
42302^282612-9585075Lelio R Paula08/2012
423175^45366-285065Lelio R Paula08/2013
42322^282511+6985045Lelio R Paula08/2012
423369^46249+285045Lelio R Paula06/2013
42343^178226+1085036Robert Price10/2013
4235(14*10^85010+73)/385011Robert Price04/2016
42369*2^282338-784994Lelio R Paula08/2014
4237(9913*2^282330-1)/157800384988Lelio R Paula04/2015
42382^282203+584952Lelio R Paula08/2012
42392^282184+1384946Lelio R Paula08/2012
424011^81568-240084945Enzo Doria12/2012
424111^81562-234084939Enzo Doria12/2012
4242(41*10^84927+31)/984928Robert Price05/2015
4243(2*10^84904-17)/384904Robert Price08/2014
4244(4^141017+23)/384901Robert Price02/2017
42456^109100-1865384897Enzo Doria03/2013
42462^281973+102584883Lelio R Paula09/2013
42472^281951-10965184876Enzo Doria04/2014
424811^81491-543084865Enzo Doria01/2013
4249((1+sqrt(3)+sqrt(2))^79357-1)*((1+sqrt(3)-sqrt(2))^79357-1)*((1-sqrt(3)+sqrt(2))^79357-1)*((1-sqrt(384849Mike Oakes04/2009
42502^281825-186148384838Enzo Doria03/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 21 2017 08:01 (Time in France)

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