PRP Records

Probable Primes Top 10000

(181746 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 ?
42513^181551+3286622Robert Price11/2013
42522^287735-52134786617Paul Bourdelais05/2013
4253(1017*2^287600-1)/9186578Lelio R Paula04/2015
42542^287540-11296786559Enzo Doria06/2014
42553^181407+2086554Robert Price10/2013
4256(13*10^86546+83)/386547Robert Price09/2016
42573^181378-2^(181378-1)86540Robert Price01/2016
425883^45080-286513Lelio R Paula08/2013
4259(78557*2^287351+1)/61186504Lelio R Paula06/2014
426025*29^59147+2093686498Curtis Bright05/2015
42612^287298+187135986486Enzo Doria05/2016
42623*10^86478+8986479Robert Price03/2017
42632^287272-7904986478Paul Bourdelais02/2012
4264906705*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4265811824*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4266779064*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4267768385*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4268700891*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4269652320*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4270377920*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4271255060*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4272187111*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4273(10^86453-1)/986453Lew Baxter10/2000
427487^44563-86^4456386431Robert Price05/2015
42756^111057+6186420Lelio R Paula12/2015
42762^287057-10990986413Enzo Doria04/2014
42775^123608+2286399Lelio R Paula10/2015
4278(31*10^86364-121)/986365Robert Price06/2016
42792^286859+7166386354Enzo Doria04/2016
42802^286740+2983586318Lelio R Paula10/2013
42812*10^86310+9^8631086311Mike Oakes05/2011
428211^82878-186086309Enzo Doria12/2012
42832^286547+1609586260Lelio R Paula10/2013
42842^286455-11042786232Enzo Doria05/2014
4285(37*10^86230+53)/986231Robert Price05/2015
42868*3^180700+586217Lelio R Paula08/2014
42873^180697-4086215Lelio R Paula12/2015
4288(13*2^286318-1)/1325786188Lelio R Paula02/2014
42892^286165+7786145Lelio R Paula08/2012
42909*2^286140+786138Lelio R Paula08/2014
4291(29*2^286108-1)/200236786123Lelio R Paula02/2014
429210^86110+16111386111Patrick De Geest07/2013
429310^86110-6986110Robert Price05/2011
42942^286036-86968810586106Lelio R Paula07/2016
4295(77*10^86072+31)/986073Robert Price10/2015
42962^285923+34586072Lelio R Paula09/2013
429713^77266-9086070Lelio R Paula11/2015
42982^285910-45890386068Enzo Doria04/2015
42992^285904-12586066Lelio R Paula08/2012
43002^285836+6583586046Lelio R Paula09/2013
4301(2^285766+78557)/386024Lelio R Paula01/2013
4302(5*10^86011-107)/386012Robert Price01/2017
43036^110522+16386003Lelio R Paula12/2015
430441^53323-40^5332385999Robert Price07/2012
43052^285678-10961785998Enzo Doria04/2014
43066^110506-1667385991Enzo Doria02/2013
43082^285569-74185965Lelio R Paula09/2013
4307(32*10^85964+31)/985965Robert Price05/2015
43096*10^85910-785911Dmitry Domanov11/2010
43104*10^85881+6385882Robert Price06/2016
4311(10^85864+53)/985864Robert Price01/2015
43122^285230+34585863Lelio R Paula09/2013
43132^285199+7568385854Enzo Doria04/2016
4314p(17832)#/2+51285845Robert Price05/2017
431511^82426-123085838Enzo Doria11/2012
43162^285113-10988185828Enzo Doria04/2014
43175^122746-9285796Lelio R Paula10/2015
43182^285001-11346185794Enzo Doria08/2014
4319(11*10^85782-131)/385783Robert Price02/2017
43202^284913-11049185768Enzo Doria05/2014
43216^110220+4785768Lelio R Paula12/2015
43223*6^110202-585755Lelio R Paula10/2014
4323(157^39047-1)/15685742Alexander Zhirkov06/2016
4324(3^179705+7)/25085739Lelio R Paula12/2012
43252^284734-655585714Lelio R Paula09/2013
4326(10^85712+53)/985712Robert Price01/2015
4327(6883*2^284668-1)/385697Lelio R Paula04/2015
432820^65855+8385680Lelio R Paula01/2016
43296^110105+5385679Lelio R Paula12/2015
43312^284567-760585664Lelio R Paula09/2013
43309*5^122555-285664Lelio R Paula10/2014
43325^122554-1485662Lelio R Paula10/2015
43339*5^122543+485655Lelio R Paula10/2014
43343^179489-2^(179489-1)85639Robert Price01/2016
43352^284429+17785622Lelio R Paula08/2012
43362*3^179452+585621Lelio R Paula07/2014
4337(19^66919+3^66919)/2285572Robert Price07/2013
433866^47023-6585561Norbert Schneider11/2014
43396^109943+1385553Lelio R Paula12/2015
4340(2^284167-509203)/3456477585536Lelio R Paula01/2013
43412^284133-385533M. Frind & P. Underwood07/2002
43422^284113+31585527Lelio R Paula09/2013
4343(16*10^85495-19)/385496Robert Price03/2016
43442^284004+17785494Lelio R Paula08/2012
4345(16*10^85473-91)/385474Robert Price06/2016
43463^179120+2285462Robert Price12/2013
43472^283872-279224985454Enzo Doria03/2016
4348(29*10^85438+259)/985439Robert Price04/2017
43492^283817+8287585438Lelio R Paula09/2013
4350(2^283815-5)/20185435Lelio R Paula01/2013
43512^283796-12585432Lelio R Paula08/2012
4352(29*2^283784-1)/1385428Lelio R Paula02/2014
435315^72592-2885375Lelio R Paula11/2015
43542^283604-5869585374Lelio R Paula09/2013
4355496^31671+31671^49685369Norbert Schneider07/2017
4356(15*2^283583-1)/10305185364Lelio R Paula02/2014
435715^72572+9285352Lelio R Paula11/2015
43582^283473-161585334Lelio R Paula09/2013
43592^283466-1585332Lelio R Paula08/2012
436011^81916-702085307Enzo Doria02/2013
43616^109626-785306Lelio R Paula11/2014
43622^283374-11032785305Enzo Doria05/2014
436333*10^85297+785299Robert Price07/2016
436418^67933+4185275Lelio R Paula11/2015
43652^283271-10934185274Enzo Doria04/2014
4366(25*10^85249-73)/385250Robert Price09/2016
43672*5^121959+385246Lelio R Paula10/2014
436819834^19834+894785235Henri Lifchitz11/2004
43692^283140+191585234Lelio R Paula09/2013
43703*10^85227-9785228Robert Price08/2017
4371(16*10^85221-31)/385222Robert Price03/2016
43722^283083+186938385217Enzo Doria05/2016
4373(24737*2^283051+1)/1785211Lelio R Paula06/2014
4374(2^283032+78557)/385201Lelio R Paula01/2013
43752^283026-10989385200Enzo Doria04/2014
4376(2^283012+78557)/12985193Lelio R Paula01/2013
43772^282860-10972785150Enzo Doria04/2014
43782^282819+186941385138Enzo Doria05/2016
43793^178428+285132Ray Chandler07/2011
4380(22699*2^282742+1)/7385117Lelio R Paula06/2014
4381(16^70687+5^70687)/2185115Robert Price07/2013
4382(3^178352-2)/785095Lelio R Paula12/2012
438311^81699-279085081Enzo Doria12/2012
43842^282612-9585075Lelio R Paula08/2012
438575^45366-285065Lelio R Paula08/2013
43862^282511+6985045Lelio R Paula08/2012
438769^46249+285045Lelio R Paula06/2013
43883^178226+1085036Robert Price10/2013
4389(14*10^85010+73)/385011Robert Price04/2016
43909*2^282338-784994Lelio R Paula08/2014
4391(9913*2^282330-1)/157800384988Lelio R Paula04/2015
43922^282203+584952Lelio R Paula08/2012
43932^282184+1384946Lelio R Paula08/2012
439411^81568-240084945Enzo Doria12/2012
439511^81562-234084939Enzo Doria12/2012
4396(41*10^84927+31)/984928Robert Price05/2015
4397(2*10^84904-17)/384904Robert Price08/2014
4398(4^141017+23)/384901Robert Price02/2017
43996^109100-1865384897Enzo Doria03/2013
44002^281973+102584883Lelio R Paula09/2013
44012^281951-10965184876Enzo Doria04/2014
440211^81491-543084865Enzo Doria01/2013
4403((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
44042^281825-186148384838Enzo Doria03/2016
44052^281809-9730584833Lelio R Paula09/2013
44062^281780-11489384825Enzo Doria05/2015
44073^177719+6484794Lelio R Paula12/2015
44092^281675-19984793Lelio R Paula08/2012
44082^281673-11122384793Enzo Doria05/2014
4410(4*10^84779+149)/984779Robert Price03/2017
4411(72*10^84772-27)/984773Ray Chandler01/2011
441211^81398-63084768Enzo Doria11/2012
4413(25*2^281577-1)/2384764Lelio R Paula02/2014
44142^281500-45584740Yves Minet03/2012
441510^84725+114514191984726Marisa Kirisame03/2015
441610^84725+14204184726Patrick De Geest10/2015
441710^84725-13867784725Patrick De Geest02/2016
441876^45044+7584720Norbert Schneider02/2015
441954^48897-5384709Norbert Schneider08/2014
4420(9913*2^281377-1)/6584706Lelio R Paula04/2015
4421Phi(171124,10)/29946701/7761329021/5856034404184700Maksym Voznyy11/2015
44222^281337-11122384691Enzo Doria05/2014
44232^281308+5461584683Lelio R Paula09/2013
44247*5^121144-684677Lelio R Paula10/2014
4425(2^281252+47)/384665Lelio R Paula01/2013
442611^81297-315084663Enzo Doria12/2012
44272^281208-30384653Yves Minet02/2012
4428(21*2^281187+1)/248384644Lelio R Paula01/2013
442911^81247-8484611Lelio R Paula10/2015
443017^68747-6484590Lelio R Paula11/2015
44315^121018-1559684588Enzo Doria02/2013
44326^108702+784587Lelio R Paula11/2014
443310^84582+10067784583Patrick De Geest05/2016
443410^84582-800184582Robert Price03/2016
44353*5^121004-884579Lelio R Paula10/2014
44365^120996-8484573Lelio R Paula10/2015
4437(10223*2^280881+1)/6841984553Lelio R Paula06/2014
44382^280852+9768184545Yves Minet08/2004
44392^280848-120384544Lelio R Paula09/2013
44405^120946-2484538Lelio R Paula10/2015
44412^280810-211184533Yves Minet08/2013
444211^81161-516084521Enzo Doria01/2013
44432^280737-9384511Lelio R Paula08/2012
44442^280698+31584499Lelio R Paula09/2013
44453^177099-34084498Lelio R Paula12/2015
4446(5*10^84469-107)/384470Robert Price01/2017
4447(3^177002+7)/669602227216174484436Lelio R Paula12/2012
4448(2^280500-1017)/82384436Lelio R Paula01/2013
444914^73660-584424Lelio R Paula11/2015
4450(19*10^84409-61)/384410Robert Price04/2017
44512^280388+11784406Lelio R Paula08/2012
44522^280389-56653384406Paul Bourdelais03/2013
4453(141584^16384+1)/6553784390Syoichiro Yamada06/2008
44542^280240-17384361Lelio R Paula08/2012
4455(184*10^84348-1)/384350Robert Price02/2017
44564*10^84346+9384347Robert Price01/2017
44577*2^280156-584337Lelio R Paula08/2014
44588*7^99782-384327Lelio R Paula10/2014
44592^280116+13384324Lelio R Paula08/2012
44602^280118+5461584324Lelio R Paula09/2013
4461(509203*2^280090-1)/384321Lelio R Paula04/2015
44626^108354+4784316Lelio R Paula12/2015
446310^84305+14196384306Patrick De Geest07/2013
446410^84305-5784305Robert Price05/2011
44659^88339+3*8^88339-2*4^88339-3*2^8833984297Mike Oakes01/2011
44663^176648-11280484283Enzo Doria06/2014
44676^108310+11584282Lelio R Paula12/2015
4468(11*2^279968-1)/584280Lelio R Paula02/2014
44696^108288-1664384265Enzo Doria02/2013
44702^279917-5869584264Lelio R Paula08/2013
447165^46477+3684259Lelio R Paula01/2016
44722^279866-190784249Yves Minet05/2013
4473(3^176580-5)/2807684246Lelio R Paula12/2012
4474(2*10^84239+1)/384239Serge Batalov07/2009
447618^67103-4184233Lelio R Paula11/2015
447520^64743-4384233Lelio R Paula01/2016
4477143^39070+39070^14384209Serge Batalov05/2014
447811^80857-540084204Enzo Doria01/2013
4479(13*10^84179+161)/384180Robert Price04/2017
44802^279634-11040584179Enzo Doria05/2014
44812^279582-101784163Lelio R Paula08/2013
4482(22*10^84159-19)/384160Robert Price02/2017
4483p(17513)#/2+51284156Robert Price05/2017
4484(9*2^279507-1)/13784139Lelio R Paula02/2014
448511^80792-81084137Enzo Doria11/2012
4486(97*10^84134-1)/384136Serge Batalov12/2014
4487p(17507)#/2+3284125Robert Price12/2016
448821485^8224+8224^2148584116Hans Havermann04/2017
44893^176294-34084114Lelio R Paula12/2015
4490(3^176287+4)/219184107Lelio R Paula12/2012
44912^279388-71984105Yves Minet05/2012
4492(22699*2^279378+1)/22184104Lelio R Paula06/2014
44932^279332-11044784088Enzo Doria05/2014
44942^279320+784084Lelio R Paula06/2012
4495(11*2^279240-1)/9584059Lelio R Paula02/2014
44962^279218-11134784053Enzo Doria05/2014
449735^54435+284052Lelio R Paula05/2013
4498(31*2^279191-1)/1251152384040Lelio R Paula02/2014
449920996^10059+10059^2099684038Hans Havermann05/2017
450097*10^84033-384035Robert Price01/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 14 2017 17:05 (Time in France)

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