PRP Records

Probable Primes Top 10000

(225451 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 ?
4751734^30453+30453^73487270Norbert Schneider04/2017
475212^80855+2987258Lelio R Paula11/2015
47533*6^112119-587247Lelio R Paula10/2014
475412^80806+7987205Lelio R Paula11/2015
475591382^9+9^9138287201Andrey Kulsha11/2004
4756(21181*2^289657+1)/8187198Lelio R Paula06/2014
47576^112054-4787195Lelio R Paula12/2015
4758(55459*2^289632+1)/5587191Lelio R Paula06/2014
475915^74131-6887185Lelio R Paula11/2015
47602^289583-74187174Lelio R Paula10/2013
47617^103146+1287169Lelio R Paula10/2015
47625*2^289556-387166Lelio R Paula08/2014
47632^289543-11273587162Enzo Doria06/2014
47648*3^182655-787150Lelio R Paula08/2014
47652*10^87144+8187145Robert Price01/2017
47667^103106+2*3^10310687135Mike Oakes08/2010
47678*3^182614+787130Lelio R Paula08/2014
4768(2^289368-509203)/987108Lelio R Paula01/2013
47693^182566+1487107Robert Price09/2013
4770(3^182385-5)/287020Lelio R Paula01/2013
477111^83534-886992Lelio R Paula11/2015
47724^144479-1426786986Mike Oakes03/2011
4773(145*10^86982-1)/986984Serge Batalov12/2014
4774(151*10^86963-1)/386965Robert Price04/2017
477515^73940-5886961Lelio R Paula11/2015
47762^288761-11314386926Enzo Doria07/2014
47772^288747+308386922Yves Minet03/2011
477830^58842+2986917Norbert Schneider03/2017
4779(10^86906-13)/386906Robert Price02/2017
47802^288692-11002786905Enzo Doria04/2014
4781(2^288682+7)/25989544986894Lelio R Paula01/2013
4782(2^288636+47)/129386885Lelio R Paula01/2013
47833^182089-3486879Robert Price11/2013
47842^288543-10980186861Enzo Doria04/2014
478560^48847-5986858Norbert Schneider10/2014
47862^288470-6487586839Lelio R Paula10/2013
478710^86816+3299786817Patrick De Geest07/2013
478810^86816-9986816Robert Price05/2011
4789(89*10^86802-539)/986803Robert Price11/2017
479041487!2+25686786Robert Price01/2015
4791(5*2^288301-1)/99986785Lelio R Paula02/2014
47922^288243+7604386770Enzo Doria04/2016
4793(29*2^288232+1)/1586767Lelio R Paula01/2013
47949*6^111495+586761Lelio R Paula10/2014
4795(5*2^288202+1)/8186757Lelio R Paula01/2013
47969*7^102654-286754Lelio R Paula10/2014
47972^288122-11284186734Enzo Doria06/2014
47985^124062-6886716Lelio R Paula10/2015
4799(2^288007-3)/12586697Lelio R Paula01/2013
4800379*10^86691+986694Arkadiusz Wesolowski10/2011
48017^102555+4886670Lelio R Paula10/2015
480277779!4+286660Robert Price08/2017
48032^287809-11135586640Enzo Doria05/2014
4804(47*2^287795+1)/786636Lelio R Paula04/2015
48059*7^102504+886627Lelio R Paula10/2014
48063^181551+3286622Robert Price11/2013
48072^287735-52134786617Paul Bourdelais05/2013
4808(1017*2^287600-1)/9186578Lelio R Paula04/2015
48092^287540-11296786559Enzo Doria06/2014
48103^181407+2086554Robert Price10/2013
4811(13*10^86546+83)/386547Robert Price09/2016
48123^181378-2^(181378-1)86540Robert Price01/2016
481383^45080-286513Lelio R Paula08/2013
4814(78557*2^287351+1)/61186504Lelio R Paula06/2014
481525*29^59147+2093686498Curtis Bright05/2015
48162^287298+187135986486Enzo Doria05/2016
4817118^41740-11786481Norbert Schneider08/2018
48183*10^86478+8986479Robert Price03/2017
48192^287272-7904986478Paul Bourdelais02/2012
4820906705*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4821811824*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4822779064*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4823768385*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4824700891*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4825652320*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4826377920*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4827255060*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4828187111*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4829(10^86453-1)/986453Lew Baxter10/2000
483087^44563-86^4456386431Robert Price05/2015
48316^111057+6186420Lelio R Paula12/2015
48322^287057-10990986413Enzo Doria04/2014
48335^123608+2286399Lelio R Paula10/2015
4834(31*10^86364-121)/986365Robert Price06/2016
48352^286859+7166386354Enzo Doria04/2016
48362^286740+2983586318Lelio R Paula10/2013
48372*10^86310+9^8631086311Mike Oakes05/2011
483811^82878-186086309Enzo Doria12/2012
48392^286547+1609586260Lelio R Paula10/2013
4840(58*10^86242+329)/986243Robert Price11/2017
48412^286455-11042786232Enzo Doria05/2014
4842(37*10^86230+53)/986231Robert Price05/2015
48438*3^180700+586217Lelio R Paula08/2014
48443^180697-4086215Lelio R Paula12/2015
4845(13*2^286318-1)/1325786188Lelio R Paula02/2014
48462^286165+7786145Lelio R Paula08/2012
48479*2^286140+786138Lelio R Paula08/2014
4848(29*2^286108-1)/200236786123Lelio R Paula02/2014
484910^86110+16111386111Patrick De Geest07/2013
485010^86110-6986110Robert Price05/2011
48512^286036-86968810586106Lelio R Paula07/2016
4852(77*10^86072+31)/986073Robert Price10/2015
48532^285923+34586072Lelio R Paula09/2013
485413^77266-9086070Lelio R Paula11/2015
48552^285910-45890386068Enzo Doria04/2015
48562^285904-12586066Lelio R Paula08/2012
48572^285836+6583586046Lelio R Paula09/2013
4858(2^285766+78557)/386024Lelio R Paula01/2013
4859(5*10^86011-107)/386012Robert Price01/2017
48606^110522+16386003Lelio R Paula12/2015
486141^53323-40^5332385999Robert Price07/2012
48622^285678-10961785998Enzo Doria04/2014
48636^110506-1667385991Enzo Doria02/2013
48652^285569-74185965Lelio R Paula09/2013
4864(32*10^85964+31)/985965Robert Price05/2015
48666*10^85910-785911Dmitry Domanov11/2010
4867(412*10^85897-7)/985899Robert Price10/2017
48684*10^85881+6385882Robert Price06/2016
4869(10^85864+53)/985864Robert Price01/2015
48702^285230+34585863Lelio R Paula09/2013
4871(5*10^85855-473)/985855Robert Price12/2017
48722^285199+7568385854Enzo Doria04/2016
4873(76*10^85847-211)/985848Robert Price10/2017
4874p(17832)#/2+51285845Robert Price05/2017
4875(16*10^85839+167)/385840Robert Price10/2017
487611^82426-123085838Enzo Doria11/2012
48772^285113-10988185828Enzo Doria04/2014
48785^122746-9285796Lelio R Paula10/2015
48792^285001-11346185794Enzo Doria08/2014
4880(11*10^85782-131)/385783Robert Price02/2017
48812^284913-11049185768Enzo Doria05/2014
48826^110220+4785768Lelio R Paula12/2015
48833*6^110202-585755Lelio R Paula10/2014
4884(157^39047-1)/15685742Alexander Zhirkov06/2016
4885(3^179705+7)/25085739Lelio R Paula12/2012
48862^284734-655585714Lelio R Paula09/2013
4887(10^85712+53)/985712Robert Price01/2015
48883*10^85703+1185704Robert Price11/2017
4889(6883*2^284668-1)/385697Lelio R Paula04/2015
489020^65855+8385680Lelio R Paula01/2016
48916^110105+5385679Lelio R Paula12/2015
4892(10^85666-97)/385666Robert Kinser10/2017
48942^284567-760585664Lelio R Paula09/2013
48939*5^122555-285664Lelio R Paula10/2014
48955^122554-1485662Lelio R Paula10/2015
48969*5^122543+485655Lelio R Paula10/2014
48973^179489-2^(179489-1)85639Robert Price01/2016
48982^284429+17785622Lelio R Paula08/2012
48992*3^179452+585621Lelio R Paula07/2014
4900(19^66919+3^66919)/2285572Robert Price07/2013
490166^47023-6585561Norbert Schneider11/2014
49026^109943+1385553Lelio R Paula12/2015
4903(2^284167-509203)/3456477585536Lelio R Paula01/2013
49042^284133-385533M. Frind & P. Underwood07/2002
49052^284113+31585527Lelio R Paula09/2013
4906(28*10^85500+149)/385501Robert Price10/2017
4907(16*10^85495-19)/385496Robert Price03/2016
49082^284004+17785494Lelio R Paula08/2012
4909(16*10^85473-91)/385474Robert Price06/2016
49103^179120+2285462Robert Price12/2013
49112^283872-279224985454Enzo Doria03/2016
4912(29*10^85438+259)/985439Robert Price04/2017
49132^283817+8287585438Lelio R Paula09/2013
4914(2^283815-5)/20185435Lelio R Paula01/2013
49152^283796-12585432Lelio R Paula08/2012
4916(29*2^283784-1)/1385428Lelio R Paula02/2014
491715^72592-2885375Lelio R Paula11/2015
49182^283604-5869585374Lelio R Paula09/2013
4919(44*10^85370-503)/985371Robert Price10/2017
4920496^31671+31671^49685369Norbert Schneider07/2017
4921(15*2^283583-1)/10305185364Lelio R Paula02/2014
492215^72572+9285352Lelio R Paula11/2015
49232^283473-161585334Lelio R Paula09/2013
49242^283466-1585332Lelio R Paula08/2012
492511^81916-702085307Enzo Doria02/2013
49266^109626-785306Lelio R Paula11/2014
49272^283374-11032785305Enzo Doria05/2014
492833*10^85297+785299Robert Price07/2016
492918^67933+4185275Lelio R Paula11/2015
49302^283271-10934185274Enzo Doria04/2014
4931(25*10^85249-73)/385250Robert Price09/2016
49322*5^121959+385246Lelio R Paula10/2014
493319834^19834+894785235Henri Lifchitz11/2004
49342^283140+191585234Lelio R Paula09/2013
49353*10^85227-9785228Robert Price08/2017
4936(16*10^85221-31)/385222Robert Price03/2016
49372^283083+186938385217Enzo Doria05/2016
4938(24737*2^283051+1)/1785211Lelio R Paula06/2014
4939(2^283032+78557)/385201Lelio R Paula01/2013
49402^283026-10989385200Enzo Doria04/2014
4941(2^283012+78557)/12985193Lelio R Paula01/2013
4942(10^(2*42589+1)+72*10^42589-1)/985179Robert Price09/2017
49432^282860-10972785150Enzo Doria04/2014
49442^282819+186941385138Enzo Doria05/2016
49453^178428+285132Ray Chandler07/2011
4946(22699*2^282742+1)/7385117Lelio R Paula06/2014
4947(16^70687+5^70687)/2185115Robert Price07/2013
4948(3^178352-2)/785095Lelio R Paula12/2012
494911^81699-279085081Enzo Doria12/2012
49502^282612-9585075Lelio R Paula08/2012
49512^282609-406985074Yves Minet02/2018
495275^45366-285065Lelio R Paula08/2013
49532^282511+6985045Lelio R Paula08/2012
495469^46249+285045Lelio R Paula06/2013
49553^178226+1085036Robert Price10/2013
4956(182*10^85017+43)/985019Robert Price11/2017
4957(14*10^85010+73)/385011Robert Price04/2016
49589*2^282338-784994Lelio R Paula08/2014
4959(9913*2^282330-1)/157800384988Lelio R Paula04/2015
49602^282203+584952Lelio R Paula08/2012
49612^282184+1384946Lelio R Paula08/2012
496211^81568-240084945Enzo Doria12/2012
496311^81562-234084939Enzo Doria12/2012
4964(41*10^84927+31)/984928Robert Price05/2015
4965(2*10^84904-17)/384904Robert Price08/2014
4966(4^141017+23)/384901Robert Price02/2017
49676^109100-1865384897Enzo Doria03/2013
49682^281973+102584883Lelio R Paula09/2013
49692^281951-10965184876Enzo Doria04/2014
497011^81491-543084865Enzo Doria01/2013
4971((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
49722^281825-186148384838Enzo Doria03/2016
49732^281809-9730584833Lelio R Paula09/2013
49742^281780-11489384825Enzo Doria05/2015
49753^177719+6484794Lelio R Paula12/2015
49772^281675-19984793Lelio R Paula08/2012
49762^281673-11122384793Enzo Doria05/2014
4978(4*10^84779+149)/984779Robert Price03/2017
4979(72*10^84772-27)/984773Ray Chandler01/2011
498011^81398-63084768Enzo Doria11/2012
4981(25*2^281577-1)/2384764Lelio R Paula02/2014
49822^281500-45584740Yves Minet03/2012
498310^84725+114514191984726Marisa Kirisame03/2015
498410^84725+14204184726Patrick De Geest10/2015
498510^84725-13867784725Patrick De Geest02/2016
498676^45044+7584720Norbert Schneider02/2015
498754^48897-5384709Norbert Schneider08/2014
4988(9913*2^281377-1)/6584706Lelio R Paula04/2015
4989Phi(171124,10)/29946701/7761329021/5856034404184700Maksym Voznyy11/2015
49902^281337-11122384691Enzo Doria05/2014
49912^281308+5461584683Lelio R Paula09/2013
49927*5^121144-684677Lelio R Paula10/2014
4993(2^281252+47)/384665Lelio R Paula01/2013
499411^81297-315084663Enzo Doria12/2012
49952^281208-30384653Yves Minet02/2012
4996197^36892-284648Lelio R Paula10/2017
4997(21*2^281187+1)/248384644Lelio R Paula01/2013
499811^81247-8484611Lelio R Paula10/2015
499917^68747-6484590Lelio R Paula11/2015
50005^121018-1559684588Enzo Doria02/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 20 2018 23:15 (Time in France)

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