PRP Records

Probable Primes Top 10000

(252932 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 ?
5251(10^86453-1)/986453Lew Baxter10/2000
525287^44563-86^4456386431Robert Price05/2015
52536^111057+6186420Lelio R Paula12/2015
52542^287057-10990986413Enzo Doria04/2014
52555^123608+2286399Lelio R Paula10/2015
5256(31*10^86364-121)/986365Robert Price06/2016
52572^286859+7166386354Enzo Doria04/2016
52582^286740+2983586318Lelio R Paula10/2013
52592*10^86310+9^8631086311Mike Oakes05/2011
526011^82878-186086309Enzo Doria12/2012
52612^286547+1609586260Lelio R Paula10/2013
5262(58*10^86242+329)/986243Robert Price11/2017
52632^286455-11042786232Enzo Doria05/2014
5264(37*10^86230+53)/986231Robert Price05/2015
52658*3^180700+586217Lelio R Paula08/2014
52663^180697-4086215Lelio R Paula12/2015
5267(13*2^286318-1)/1325786188Lelio R Paula02/2014
52682^286165+7786145Lelio R Paula08/2012
52699*2^286140+786138Lelio R Paula08/2014
5270(29*2^286108-1)/200236786123Lelio R Paula02/2014
527110^86110+16111386111Patrick De Geest07/2013
527210^86110-6986110Robert Price05/2011
52732^286036-86968810586106Lelio R Paula07/2016
5274(77*10^86072+31)/986073Robert Price10/2015
52752^285923+34586072Lelio R Paula09/2013
527613^77266-9086070Lelio R Paula11/2015
52772^285910-45890386068Enzo Doria04/2015
52782^285904-12586066Lelio R Paula08/2012
52792^285836+6583586046Lelio R Paula09/2013
5280(2^285766+78557)/386024Lelio R Paula01/2013
5281(5*10^86011-107)/386012Robert Price01/2017
52826^110522+16386003Lelio R Paula12/2015
528341^53323-40^5332385999Robert Price07/2012
52842^285678-10961785998Enzo Doria04/2014
52856^110506-1667385991Enzo Doria02/2013
52872^285569-74185965Lelio R Paula09/2013
5286(32*10^85964+31)/985965Robert Price05/2015
5288133^40466+13285944Norbert Schneider02/2019
52896*10^85910-785911Dmitry Domanov11/2010
5290(412*10^85897-7)/985899Robert Price10/2017
52914*10^85881+6385882Robert Price06/2016
5292(10^85864+53)/985864Robert Price01/2015
52932^285230+34585863Lelio R Paula09/2013
5294(5*10^85855-473)/985855Robert Price12/2017
52952^285199+7568385854Enzo Doria04/2016
5296(76*10^85847-211)/985848Robert Price10/2017
5297p(17832)#/2+51285845Robert Price05/2017
5298(16*10^85839+167)/385840Robert Price10/2017
529911^82426-123085838Enzo Doria11/2012
53002^285113-10988185828Enzo Doria04/2014
53015^122746-9285796Lelio R Paula10/2015
53022^285001-11346185794Enzo Doria08/2014
5303(11*10^85782-131)/385783Robert Price02/2017
53042^284913-11049185768Enzo Doria05/2014
53056^110220+4785768Lelio R Paula12/2015
53063*6^110202-585755Lelio R Paula10/2014
5307(157^39047-1)/15685742Alexander Zhirkov06/2016
5308(3^179705+7)/25085739Lelio R Paula12/2012
53092^284734-655585714Lelio R Paula09/2013
5310(10^85712+53)/985712Robert Price01/2015
53113*10^85703+1185704Robert Price11/2017
5312(6883*2^284668-1)/385697Lelio R Paula04/2015
531320^65855+8385680Lelio R Paula01/2016
53146^110105+5385679Lelio R Paula12/2015
5315(10^85666-97)/385666Robert Kinser10/2017
53172^284567-760585664Lelio R Paula09/2013
53169*5^122555-285664Lelio R Paula10/2014
53185^122554-1485662Lelio R Paula10/2015
53199*5^122543+485655Lelio R Paula10/2014
53203^179489-2^(179489-1)85639Robert Price01/2016
53212^284429+17785622Lelio R Paula08/2012
53222*3^179452+585621Lelio R Paula07/2014
5323(19^66919+3^66919)/2285572Robert Price07/2013
532466^47023-6585561Norbert Schneider11/2014
53256^109943+1385553Lelio R Paula12/2015
53262^284183-474785548Yves Minet05/2019
5327(2^284167-509203)/3456477585536Lelio R Paula01/2013
53282^284133-385533M. Frind & P. Underwood07/2002
53292^284113+31585527Lelio R Paula09/2013
5330(28*10^85500+149)/385501Robert Price10/2017
5331(16*10^85495-19)/385496Robert Price03/2016
53322^284004+17785494Lelio R Paula08/2012
5333(16*10^85473-91)/385474Robert Price06/2016
53343^179120+2285462Robert Price12/2013
53352^283872-279224985454Enzo Doria03/2016
5336(29*10^85438+259)/985439Robert Price04/2017
53372^283817+8287585438Lelio R Paula09/2013
5338(2^283815-5)/20185435Lelio R Paula01/2013
53392^283796-12585432Lelio R Paula08/2012
5340(29*2^283784-1)/1385428Lelio R Paula02/2014
534115^72592-2885375Lelio R Paula11/2015
53422^283604-5869585374Lelio R Paula09/2013
5343(44*10^85370-503)/985371Robert Price10/2017
5344496^31671+31671^49685369Norbert Schneider07/2017
5345(15*2^283583-1)/10305185364Lelio R Paula02/2014
534615^72572+9285352Lelio R Paula11/2015
53472^283473-161585334Lelio R Paula09/2013
53482^283466-1585332Lelio R Paula08/2012
534911^81916-702085307Enzo Doria02/2013
53506^109626-785306Lelio R Paula11/2014
53512^283374-11032785305Enzo Doria05/2014
535233*10^85297+785299Robert Price07/2016
535318^67933+4185275Lelio R Paula11/2015
53542^283271-10934185274Enzo Doria04/2014
5355(25*10^85249-73)/385250Robert Price09/2016
53562*5^121959+385246Lelio R Paula10/2014
535719834^19834+894785235Henri Lifchitz11/2004
53582^283140+191585234Lelio R Paula09/2013
53593*10^85227-9785228Robert Price08/2017
5360(16*10^85221-31)/385222Robert Price03/2016
53612^283083+186938385217Enzo Doria05/2016
5362(24737*2^283051+1)/1785211Lelio R Paula06/2014
5363(2^283032+78557)/385201Lelio R Paula01/2013
53642^283026-10989385200Enzo Doria04/2014
5365(2^283012+78557)/12985193Lelio R Paula01/2013
5366(10^(2*42589+1)+72*10^42589-1)/985179Robert Price09/2017
53672^282860-10972785150Enzo Doria04/2014
53682^282819+186941385138Enzo Doria05/2016
53693^178428+285132Ray Chandler07/2011
5370(22699*2^282742+1)/7385117Lelio R Paula06/2014
5371(16^70687+5^70687)/2185115Robert Price07/2013
5372(3^178352-2)/785095Lelio R Paula12/2012
537311^81699-279085081Enzo Doria12/2012
53742^282612-9585075Lelio R Paula08/2012
53752^282609-406985074Yves Minet02/2018
537675^45366-285065Lelio R Paula08/2013
53772^282511+6985045Lelio R Paula08/2012
537869^46249+285045Lelio R Paula06/2013
53793^178226+1085036Robert Price10/2013
5380(182*10^85017+43)/985019Robert Price11/2017
5381(14*10^85010+73)/385011Robert Price04/2016
53829*2^282338-784994Lelio R Paula08/2014
5383(9913*2^282330-1)/157800384988Lelio R Paula04/2015
53842^282203+584952Lelio R Paula08/2012
53852^282184+1384946Lelio R Paula08/2012
538611^81568-240084945Enzo Doria12/2012
538711^81562-234084939Enzo Doria12/2012
5388(41*10^84927+31)/984928Robert Price05/2015
5389(2*10^84904-17)/384904Robert Price08/2014
5390(4^141017+23)/384901Robert Price02/2017
53916^109100-1865384897Enzo Doria03/2013
53922^281973+102584883Lelio R Paula09/2013
53932^281951-10965184876Enzo Doria04/2014
539411^81491-543084865Enzo Doria01/2013
5395((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
53962^281825-186148384838Enzo Doria03/2016
53972^281809-9730584833Lelio R Paula09/2013
53982^281780-11489384825Enzo Doria05/2015
53993^177719+6484794Lelio R Paula12/2015
54012^281675-19984793Lelio R Paula08/2012
54002^281673-11122384793Enzo Doria05/2014
5402(4*10^84779+149)/984779Robert Price03/2017
5403129^40167-12884777Norbert Schneider01/2019
5404(72*10^84772-27)/984773Ray Chandler01/2011
540511^81398-63084768Enzo Doria11/2012
5406(25*2^281577-1)/2384764Lelio R Paula02/2014
54072^281500-45584740Yves Minet03/2012
540810^84725+114514191984726Marisa Kirisame03/2015
540910^84725+14204184726Patrick De Geest10/2015
541010^84725-13867784725Patrick De Geest02/2016
541176^45044+7584720Norbert Schneider02/2015
541254^48897-5384709Norbert Schneider08/2014
5413(9913*2^281377-1)/6584706Lelio R Paula04/2015
5414Phi(171124,10)/29946701/7761329021/5856034404184700Maksym Voznyy11/2015
54152^281337-11122384691Enzo Doria05/2014
54162^281308+5461584683Lelio R Paula09/2013
54177*5^121144-684677Lelio R Paula10/2014
5418(2^281252+47)/384665Lelio R Paula01/2013
541911^81297-315084663Enzo Doria12/2012
54202^281208-30384653Yves Minet02/2012
5421197^36892-284648Lelio R Paula10/2017
5422(21*2^281187+1)/248384644Lelio R Paula01/2013
542311^81247-8484611Lelio R Paula10/2015
542417^68747-6484590Lelio R Paula11/2015
54255^121018-1559684588Enzo Doria02/2013
54266^108702+784587Lelio R Paula11/2014
542710^84582+10067784583Patrick De Geest05/2016
542810^84582-800184582Robert Price03/2016
54293*5^121004-884579Lelio R Paula10/2014
54305^120996-8484573Lelio R Paula10/2015
5431(10223*2^280881+1)/6841984553Lelio R Paula06/2014
54322^280852+9768184545Yves Minet08/2004
54332^280848-120384544Lelio R Paula09/2013
54345^120946-2484538Lelio R Paula10/2015
54352^280810-211184533Yves Minet08/2013
543611^81161-516084521Enzo Doria01/2013
54372^280737-9384511Lelio R Paula08/2012
54382^280698+31584499Lelio R Paula09/2013
54393^177099-34084498Lelio R Paula12/2015
5440(5*10^84469-107)/384470Robert Price01/2017
5441(3^177002+7)/669602227216174484436Lelio R Paula12/2012
5442(2^280500-1017)/82384436Lelio R Paula01/2013
544314^73660-584424Lelio R Paula11/2015
5444(19*10^84409-61)/384410Robert Price04/2017
54452^280388+11784406Lelio R Paula08/2012
54462^280389-56653384406Paul Bourdelais03/2013
5447(141584^16384+1)/6553784390Syoichiro Yamada06/2008
5448119^40652+11884376Norbert Schneider09/2018
54492^280240-17384361Lelio R Paula08/2012
5450(184*10^84348-1)/384350Robert Price02/2017
54514*10^84346+9384347Robert Price01/2017
54527*2^280156-584337Lelio R Paula08/2014
54538*7^99782-384327Lelio R Paula10/2014
54542^280116+13384324Lelio R Paula08/2012
54552^280118+5461584324Lelio R Paula09/2013
5456(509203*2^280090-1)/384321Lelio R Paula04/2015
54576^108354+4784316Lelio R Paula12/2015
545810^84305+14196384306Patrick De Geest07/2013
545910^84305-5784305Robert Price05/2011
54609^88339+3*8^88339-2*4^88339-3*2^8833984297Mike Oakes01/2011
54613^176648-11280484283Enzo Doria06/2014
54626^108310+11584282Lelio R Paula12/2015
5463(11*2^279968-1)/584280Lelio R Paula02/2014
54646^108288-1664384265Enzo Doria02/2013
54652^279917-5869584264Lelio R Paula08/2013
546665^46477+3684259Lelio R Paula01/2016
54672^279866-190784249Yves Minet05/2013
5468(3^176580-5)/2807684246Lelio R Paula12/2012
5469(p(17530)#+4)/284246Robert Price09/2017
5470(2*10^84239+1)/384239Serge Batalov07/2009
547218^67103-4184233Lelio R Paula11/2015
547120^64743-4384233Lelio R Paula01/2016
5473143^39070+39070^14384209Serge Batalov05/2014
547411^80857-540084204Enzo Doria01/2013
5475(13*10^84179+161)/384180Robert Price04/2017
54762^279634-11040584179Enzo Doria05/2014
5477(74*10^84170+313)/984171Robert Price11/2017
54782^279582-101784163Lelio R Paula08/2013
5479(22*10^84159-19)/384160Robert Price02/2017
5480p(17513)#/2+51284156Robert Price05/2017
5481(19*10^84144-43)/384145Robert Price10/2017
5482(9*2^279507-1)/13784139Lelio R Paula02/2014
548311^80792-81084137Enzo Doria11/2012
5484(97*10^84134-1)/384136Serge Batalov12/2014
5485p(17507)#/2+3284125Robert Price12/2016
548621485^8224+8224^2148584116Hans Havermann04/2017
54873^176294-34084114Lelio R Paula12/2015
5488(3^176287+4)/219184107Lelio R Paula12/2012
54892^279388-71984105Yves Minet05/2012
5490(22699*2^279378+1)/22184104Lelio R Paula06/2014
54912^279332-11044784088Enzo Doria05/2014
54922^279320+784084Lelio R Paula06/2012
5493127^39966-284081Lelio R Paula10/2017
5494(11*2^279240-1)/9584059Lelio R Paula02/2014
54952^279218-11134784053Enzo Doria05/2014
549635^54435+284052Lelio R Paula05/2013
5497(31*2^279191-1)/1251152384040Lelio R Paula02/2014
549820996^10059+10059^2099684038Hans Havermann05/2017
549997*10^84033-384035Robert Price01/2017
550021234^9067+9067^2123484033Hans Havermann05/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2019 07:14 (Time in France)

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