PRP Records

Probable Primes Top 10000

(212140 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 ?
82512^195833-1717358952Enzo Doria05/2013
8252(27*2^195833-1)/5358952Lelio R Paula01/2014
8253(13*2^195821-1)/12242558945Lelio R Paula01/2014
8254139^27504-13858942Norbert Schneider10/2015
8255(418*10^58923+23)/958925Robert Price08/2017
82563^123495+4458923Lelio R Paula10/2012
82572^195737-1856558923Enzo Doria05/2013
825814^51407+4758920Lelio R Paula03/2013
82592^195691-9958909Lelio R Paula04/2011
82602^195667-185982758902Enzo Doria04/2016
82622^195642+7549958895Enzo Doria04/2016
8261(299*10^58893+1)/358895Robert Price11/2017
82638*6^75678+558890Lelio R Paula09/2014
82652^195618+7318958887Enzo Doria04/2016
8264(3928^20480+1)/(3928^4096+1)58887Serge Batalov01/2017
8266t(197953)58881Robert Price12/2014
82672^195581-1610558876Enzo Doria04/2013
8268(8*10^58872+67)/358873Robert Price01/2017
82697*2^195542-558865Lelio R Paula03/2014
82702*10^58861+9^5886158862Mike Oakes04/2011
827111^56513-162058853Enzo Doria11/2012
82722^195496+16558851Lelio R Paula04/2011
82735^84187+6658845Lelio R Paula10/2012
8274(28*10^58843-43)/358844Robert Price04/2016
82752^195462-1756558840Enzo Doria05/2013
82762^195449-417158837Yves Minet02/2018
82772^195435+5927358832Yves Minet01/2011
82782^195424-1860558829Enzo Doria05/2013
82792^195385-11158817Lelio R Paula04/2011
82807*10^58815-8358816Robert Price09/2017
8281(47*2^195254+1)/26882158774Lelio R Paula03/2015
82822^195207-1810958764Enzo Doria05/2013
82832^195199-156758761Yves Minet08/2012
82842^195190+7375958759Enzo Doria04/2016
82859*7^69525-458757Lelio R Paula09/2014
82862^195170-1804558753Enzo Doria05/2013
82872^195166-16558751Lelio R Paula04/2011
8288(754*10^58748-7)/958750Robert Price11/2017
8289(22699*2^195140+1)/17558746Lelio R Paula05/2014
82907*3^123109-258739Lelio R Paula04/2014
8291(8*10^58738-611)/958738Robert Price11/2017
829218^46790+7758735Lelio R Paula03/2013
82942^195095-33729758730Gary Barnes09/2009
8293(14*10^58729+31)/958730Robert Price02/2015
829599^29424+9858720Norbert Schneider07/2013
8296(15185*2^195039-1)/21958715Lelio R Paula04/2015
82972^195001-6958702Lelio R Paula04/2011
82982^194978-48781158695Gary Barnes09/2009
8299163^26530+26530^16358690Serge Batalov05/2014
83002^194940-194940+158683Robert Price10/2014
8301(76*10^58669+41)/958670Robert Price10/2015
830214^51186+8758666Lelio R Paula03/2013
83032^194878-9730558665Lelio R Paula09/2011
83045^83927-1813658663Enzo Doria05/2014
8305(24737*2^194865+1)/108558662Lelio R Paula06/2014
83067^69411+4058660Lelio R Paula10/2012
83076^75382-7958659Lelio R Paula10/2012
83082^194854+2758657Lelio R Paula04/2011
83092^194801+2983558641Lelio R Paula10/2012
83102^194752+19558627Lelio R Paula04/2011
83117^69371-6^6937158626Predrag Minovic08/2004
83122^194747-11251958625Enzo Doria06/2014
8313(15*2^194737+1)/5958622Lelio R Paula07/2012
8314(23*2^194700+1)/358612Lelio R Paula02/2012
831510^58608+5527358609Patrick De Geest07/2017
831610^58608-80000158608Robert Price06/2017
831710^58608-6011958608Patrick De Geest07/2017
83185^83836+7658599Lelio R Paula10/2012
831918^46664+3158577Lelio R Paula03/2013
8320(34*10^58577-7)/9/19/46358574Makoto Morimoto04/2016
83212^194574+16558573Lelio R Paula04/2011
83222^194569-1221158572Enzo Doria06/2014
832310^58571+5^58571+2^5857158572Robert Price12/2016
832410^58571+20283758572Patrick De Geest02/2017
8325(10^58571+41)/358571Robert Price01/2017
832610^58571-34362958571Patrick De Geest02/2017
8327(43*10^58563-403)/958564Robert Price04/2017
832811^56235-795058563Enzo Doria02/2013
8329(14*10^58550+211)/958551Robert Price11/2017
83302^194479-11323958545Enzo Doria07/2014
83312^194455-11224958537Enzo Doria06/2014
83322^194405-11191958522Enzo Doria05/2014
8333(4*10^58521-19)/358522Robert Price06/2017
8335(7^69247-4^69247)/358521Robert Price06/2012
83345*7^69246+858521Lelio R Paula09/2014
83362^194358-116758508Lelio R Paula05/2011
8337(2^194366+7)/137358507Lelio R Paula02/2012
8338(493*10^58486-7)/958488Robert Price07/2016
83393^122579-34058486Lelio R Paula10/2012
8340(11*10^58458-149)/358459Robert Price01/2017
8341(47*10^58456+133)/958457Robert Price04/2017
83422^194186+8558456Lelio R Paula04/2011
83433^122506-2^(122506-1)58451Robert Price01/2016
8344(74^31267-1)/7358444Paul Bourdelais08/2017
8345177^25998-258443Lelio R Paula10/2017
834615^49690-2658440Lelio R Paula03/2013
834710^58437+11072158438Patrick De Geest12/2012
834810^58437-1158437Robert Price05/2011
83492^194095+6958429Lelio R Paula04/2011
8350(29*10^58417-77)/358418Robert Price01/2017
83512^194034+17758411Lelio R Paula04/2011
8352789^20158+20158^78958400Norbert Schneider06/2016
835314^50949+7558395Lelio R Paula03/2013
83542^193974-11476158392Enzo Doria05/2015
83552^193965+558390Henri Lifchitz12/2002
8356(5*10^58384-29)/358385Robert Price02/2017
83573^122360+8058381Lelio R Paula10/2012
835810103^14577-11458373Enzo Doria07/2012
8359(22699*2^193883+1)/2158368Lelio R Paula06/2014
8360(31*2^193886+1)/14076558362Lelio R Paula07/2012
836111^56041-156058361Enzo Doria11/2012
8362(2^193881+9)/1769958360Lelio R Paula02/2012
83633^122313+5858359Lelio R Paula10/2012
83646^74996-11958359Lelio R Paula10/2012
8365(11*2^193859+1)/1358358Lelio R Paula07/2012
83662^193861-11225558358Enzo Doria06/2014
8367(22699*2^193854+1)/492758357Lelio R Paula06/2014
836818^46487+3758354Lelio R Paula03/2013
836917^47419+5458347Lelio R Paula03/2013
8370(31*2^193791+1)/358338Lelio R Paula02/2012
8371(27*2^193805-1)/98224958337Lelio R Paula01/2014
83723^122219-2^12221958314Mike Oakes09/2003
8373(199*10^58306+11)/358308Robert Price05/2017
83742^193674-1882558302Lelio R Paula05/2011
83755*10^58275+358276Dmitry Domanov11/2010
83762^193578-11291358273Enzo Doria06/2014
83772^193541+129958262Lelio R Paula05/2011
837810^58250+9358251Robert Price01/2011
837910^58250-17560758250Patrick De Geest12/2012
8380(107^28703+1)/10858248Richard Fischer05/2018
83812^193492+841558247Lelio R Paula10/2012
83822^193444+15758233Lelio R Paula04/2011
8383Phi(28754,28754)58231Henri Lifchitz08/2013
83842^193430-11188158229Enzo Doria05/2014
838510^58225+12457958226Patrick De Geest12/2012
838610^58225-9358225Robert Price05/2011
83872^193375-29558212Yves Minet05/2013
83882^193345+7726758203Enzo Doria05/2016
838921^44017-20^4401758201Robert Price05/2012
8390(17*2^193329-1)/958199Lelio R Paula01/2014
839117^47291+2058190Lelio R Paula03/2013
8392p(12528)#/2-12858170Robert Price05/2017
83932^193214-13558164Lelio R Paula04/2011
839419^45483-8058162Lelio R Paula03/2013
8395(4*10^58155+83)/358156Robert Price01/2017
839614^50739-1358154Lelio R Paula03/2013
8397(1017*2^193184-1)/482358154Lelio R Paula04/2015
8398(2*10^58151+457)/958151Robert Price01/2017
8399(9179*2^193183-1)/399926787958149Lelio R Paula04/2015
8400(19*2^193114-1)/118675558129Lelio R Paula01/2014
84022^193091-123758127Yves Minet08/2012
84019*7^68780-258127Lelio R Paula09/2014
84032^193083-86968810558124Lelio R Paula10/2012
84042^193058-4558117Lelio R Paula04/2011
8405(14016^14016+14017^14017)/(23*7103*19913)58115David Broadhurst09/2009
840611^55795-4258105Lelio R Paula03/2013
84073^121779-1658104Lelio R Paula10/2012
8408(13*10^58103+191)/358104Robert Price08/2017
84092^192986+19558095Lelio R Paula04/2011
84107^68740+2*3^6874058093Mike Oakes07/2010
8411(85*10^58091-1)/358093Robert Price07/2017
8412(404*10^58087-53)/958089Robert Price11/2017
841312^53821+1158083Lelio R Paula02/2013
8414119^27979-11858072Norbert Schneider10/2013
8415(10223*2^192828+1)/24358049Lelio R Paula05/2014
84162^192808-112758041Yves Minet05/2013
8417(27*2^192803+1)/982758037Lelio R Paula07/2012
8419(2^192781+lucasV(1,2,192781)+1)/458033Mike Oakes11/2016
84183*10^58032-2358033Robert Price11/2017
84202^192678+7294358002Enzo Doria04/2016
8421(13*10^57997-37)/357998Robert Price08/2017
84222^192657-318957996Yves Minet10/2014
84236^74525-14957992Lelio R Paula10/2012
842442^35723-4157988Norbert Schneider06/2014
8425(29*2^192625-1)/18357986Lelio R Paula01/2014
8426(3^121520-8)/384757977Lelio R Paula03/2012
8427(2^192596-5)/13957976Lelio R Paula02/2012
842810^57975+6783357976Patrick De Geest09/2013
842910^57975-4769357975Patrick De Geest09/2013
8430(F(7707)^37-F(7706)^37)/F(7705)57972Wayne Halsdorf03/2012
8431(29*10^57967+673)/957968Robert Price10/2017
8432(3^121492-5)/457966Lelio R Paula03/2012
84332^192549+3557964Lelio R Paula04/2011
843428799!2+257962Robert Price10/2012
8435(7*2^192534-1)/134757957Lelio R Paula01/2014
84367001^15069-10057943Enzo Doria07/2012
8437L(277273)/1109092157940Donovan Johnson11/2005
8438(2^192469-1017)/3557938Lelio R Paula02/2012
84392^192457-1155*19245757936Henri Lifchitz02/2005
84402^192443+138557932Lelio R Paula05/2011
8441132^27317-13157928Norbert Schneider03/2015
844241522!3-5904957912Robert Price12/2015
8443(3*2^192380-1)/16957911Lelio R Paula01/2014
84442^192339-251557900Yves Minet07/2014
84452^192303+769557889Lelio R Paula10/2012
84462^192273-595557880Lelio R Paula05/2011
84472^192257+1609557876Lelio R Paula05/2011
8448109^28401-257865Lelio R Paula10/2017
84492^192218-11186157864Enzo Doria05/2014
84502^192214-394157863Yves Minet04/2017
8451(2^192212+3)/25957860Lelio R Paula02/2012
8452(3^121270+8)/15593975357853Lelio R Paula03/2012
845380^30393-7957841Norbert Schneider03/2015
845420^44455-312357838Enzo Doria03/2013
84552^192122-19557835Lelio R Paula04/2011
8456(29*10^57834+91)/357835Robert Price03/2016
84578*6^74306+557823Lelio R Paula09/2014
8458(39^36341-1)/3857820Robert Price04/2012
84592^192037-11180557809Enzo Doria05/2014
84602^192023-192023^257805Henri Lifchitz05/2005
846121^43717+257804Ray Chandler08/2011
84628*5^82687+757797Lelio R Paula09/2014
84635^82680-2457791Lelio R Paula10/2012
8464(2^191915+47)/9557771Lelio R Paula02/2012
8465(74*10^57763+133)/957764Robert Price10/2017
84666^74227-9557760Lelio R Paula10/2012
84672^191861+2983557756Lelio R Paula10/2012
84691908^17605+17605^190857755Serge Batalov05/2014
84685*10^57754+5957755Robert Price09/2016
8470(5*2^191821-1)/892406757738Lelio R Paula01/2014
84713*8^63917+5^63917-3*4^63917+3*2^6391757724Mike Oakes11/2010
847241399!3-656157723Robert Price11/2015
8473(44*10^57721-233)/957722Robert Price10/2017
84742^191745+1757721Lelio R Paula04/2011
84752^191730-76157717Yves Minet01/2012
8476(2^191733-3)/225157715Lelio R Paula02/2012
84772^191698-11157707Lelio R Paula04/2011
8478(13*10^57691+23)/957692Robert Price02/2015
847920^44340-542357688Enzo Doria03/2013
8480(27*2^191629+1)/12557686Lelio R Paula07/2012
84814*10^57684+3*7^5768457685Mike Oakes11/2010
84822*3^120898+557684Lelio R Paula04/2014
8483(6883*2^191610-1)/734757681Lelio R Paula04/2015
84846^74117-4957675Lelio R Paula10/2012
84852^191586-11320157674Enzo Doria07/2014
84862^191580+19357672Lelio R Paula04/2011
8487(103*29^39433+10401)/457669Curtis Bright05/2015
84882^191560+25525557666Lelio R Paula05/2011
84892^191515-8557652Lelio R Paula04/2011
84902^191502-112757648Yves Minet05/2013
84912*5^82473-3^8247357647Mike Oakes08/2010
8492(13*10^57634-61)/357635Robert Price08/2017
849385^29868-29868^8557628Norbert Schneider11/2017
84942^191430+10357627Lelio R Paula04/2011
84953*2^191408+557621Lelio R Paula03/2014
84962^191382-185893157612Enzo Doria04/2016
84976*7^68163+557606Lelio R Paula09/2014
849891^29403-257602Lelio R Paula08/2013
849911^55308-795057598Enzo Doria02/2013
85002^191329+6557596Lelio R Paula04/2011


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 20 2018 08:38 (Time in France)

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