PRP Records

Probable Primes Top 10000

(173061 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 ?
7501(2^196744-3)*6-759227Gilbert Mozzo05/2016
7502(67607*2^196696+1)/359216Lelio R Paula05/2014
75032^196696-11296759212Enzo Doria06/2014
750420^45508-422359208Enzo Doria03/2013
7505gcd(Phi(325820,10),(10^16291+1)^3*(10^16291+1-10^8146)+(10^32582+10^16291)*(10^8146+1)+10^48873)59201Serge Batalov04/2015
750614^51651-8159199Lelio R Paula03/2013
75072^196650-145159198Yves Minet08/2012
75082^196636-279779959194Enzo Doria04/2016
75091111*2^196610-55559189Henri Lifchitz04/2005
75103^124041+65859183Lelio R Paula10/2012
75112^196590-11179759180Enzo Doria05/2014
7512(10^59174-13)/359174Robert Price02/2017
7513(9179*2^196533-1)/78359164Lelio R Paula04/2015
7514379*10^59152+959155Arkadiusz Wesolowski10/2011
751513^53095+4059145Lelio R Paula03/2013
75172*F(282999)-159144Henri Lifchitz12/2009
75164*7^69984+359144Lelio R Paula09/2014
7518(5*10^59142+1)/359143Erik Branger12/2013
75192^196463+571159142Lelio R Paula10/2011
75202^196453-9730559139Lelio R Paula09/2011
7521(28*10^59135+53)/959136Serge Batalov11/2008
7522(28*10^59133+113)/359134Robert Price03/2016
75232^196434+759133Lelio R Paula04/2011
7524(8*10^59127-29)/359128Robert Price05/2016
75252^196414+25559127Lelio R Paula05/2011
75265^84586-9259124Lelio R Paula10/2012
75272^196388-1717759119Enzo Doria05/2013
75283^123890+2059111Lelio R Paula10/2012
75292^196355-102177759109Paul Bourdelais11/2012
753011^56754-141059104Enzo Doria11/2012
7531(7*2^196297-1)/120040759087Lelio R Paula01/2014
7532(16*10^59062-19)/359063Robert Price03/2016
753335^38249-122859060Enzo Doria03/2013
75345^84475-1859046Lelio R Paula10/2012
75352^196123-1770159039Enzo Doria05/2013
753612^54702-3159034Lelio R Paula03/2013
75372^196101-17559033Lelio R Paula04/2011
75382^196085+577559028Lelio R Paula05/2011
75392^196034+1171559013Lelio R Paula05/2011
75402^196018-1848559008Enzo Doria05/2013
75412^195984-216358998Yves Minet08/2013
75423^123645-1658994Lelio R Paula10/2012
754339^37078-3858994Norbert Schneider05/2014
75442^195958-1685358990Enzo Doria05/2013
75452^195930-307158981Yves Minet10/2014
75462^195924+51358980Lelio R Paula05/2011
75472^195863+15558961Lelio R Paula04/2011
7548(28*10^58956+113)/358957Robert Price03/2016
754911^56612-930058956Enzo Doria02/2013
75502^195833-1717358952Enzo Doria05/2013
7551(27*2^195833-1)/5358952Lelio R Paula01/2014
7552(13*2^195821-1)/12242558945Lelio R Paula01/2014
7553139^27504-13858942Norbert Schneider10/2015
75543^123495+4458923Lelio R Paula10/2012
75552^195737-1856558923Enzo Doria05/2013
755614^51407+4758920Lelio R Paula03/2013
75572^195691-9958909Lelio R Paula04/2011
75582^195667-185982758902Enzo Doria04/2016
75592^195642+7549958895Enzo Doria04/2016
75608*6^75678+558890Lelio R Paula09/2014
75622^195618+7318958887Enzo Doria04/2016
7561(3928^20480+1)/(3928^4096+1)58887Serge Batalov01/2017
7563t(197953)58881Robert Price12/2014
75642^195581-1610558876Enzo Doria04/2013
7565(8*10^58872+67)/358873Robert Price01/2017
75667*2^195542-558865Lelio R Paula03/2014
75672*10^58861+9^5886158862Mike Oakes04/2011
756811^56513-162058853Enzo Doria11/2012
75692^195496+16558851Lelio R Paula04/2011
75705^84187+6658845Lelio R Paula10/2012
7571(28*10^58843-43)/358844Robert Price04/2016
75722^195462-1756558840Enzo Doria05/2013
75732^195435+5927358832Yves Minet01/2011
75742^195424-1860558829Enzo Doria05/2013
75752^195385-11158817Lelio R Paula04/2011
7576(47*2^195254+1)/26882158774Lelio R Paula03/2015
75772^195207-1810958764Enzo Doria05/2013
75782^195199-156758761Yves Minet08/2012
75792^195190+7375958759Enzo Doria04/2016
75809*7^69525-458757Lelio R Paula09/2014
75812^195170-1804558753Enzo Doria05/2013
75822^195166-16558751Lelio R Paula04/2011
7583(22699*2^195140+1)/17558746Lelio R Paula05/2014
75847*3^123109-258739Lelio R Paula04/2014
758518^46790+7758735Lelio R Paula03/2013
75872^195095-33729758730Gary Barnes09/2009
7586(14*10^58729+31)/958730Robert Price02/2015
758899^29424+9858720Norbert Schneider07/2013
7589(15185*2^195039-1)/21958715Lelio R Paula04/2015
75902^195001-6958702Lelio R Paula04/2011
75912^194978-48781158695Gary Barnes09/2009
7592163^26530+26530^16358690Serge Batalov05/2014
75932^194940-194940+158683Robert Price10/2014
7594(76*10^58669+41)/958670Robert Price10/2015
759514^51186+8758666Lelio R Paula03/2013
75962^194878-9730558665Lelio R Paula09/2011
75975^83927-1813658663Enzo Doria05/2014
7598(24737*2^194865+1)/108558662Lelio R Paula06/2014
75997^69411+4058660Lelio R Paula10/2012
76006^75382-7958659Lelio R Paula10/2012
76012^194854+2758657Lelio R Paula04/2011
76022^194801+2983558641Lelio R Paula10/2012
76032^194752+19558627Lelio R Paula04/2011
76047^69371-6^6937158626Predrag Minovic08/2004
76052^194747-11251958625Enzo Doria06/2014
7606(15*2^194737+1)/5958622Lelio R Paula07/2012
7607(23*2^194700+1)/358612Lelio R Paula02/2012
76085^83836+7658599Lelio R Paula10/2012
760918^46664+3158577Lelio R Paula03/2013
7610(34*10^58577-7)/9/19/46358574Makoto Morimoto04/2016
76112^194574+16558573Lelio R Paula04/2011
76142^194569-1221158572Enzo Doria06/2014
761210^58571+5^58571+2^5857158572Robert Price12/2016
761310^58571+20283758572Patrick De Geest02/2017
7615(10^58571+41)/358571Robert Price01/2017
761610^58571-34362958571Patrick De Geest02/2017
7617(43*10^58563-403)/958564Robert Price04/2017
761811^56235-795058563Enzo Doria02/2013
76192^194479-11323958545Enzo Doria07/2014
76202^194455-11224958537Enzo Doria06/2014
76212^194405-11191958522Enzo Doria05/2014
7623(7^69247-4^69247)/358521Robert Price06/2012
76225*7^69246+858521Lelio R Paula09/2014
76242^194358-116758508Lelio R Paula05/2011
7625(2^194366+7)/137358507Lelio R Paula02/2012
7626(493*10^58486-7)/958488Robert Price07/2016
76273^122579-34058486Lelio R Paula10/2012
7628(11*10^58458-149)/358459Robert Price01/2017
7629(47*10^58456+133)/958457Robert Price04/2017
76302^194186+8558456Lelio R Paula04/2011
76313^122506-2^(122506-1)58451Robert Price01/2016
763215^49690-2658440Lelio R Paula03/2013
763310^58437+11072158438Patrick De Geest12/2012
763410^58437-1158437Robert Price05/2011
76352^194095+6958429Lelio R Paula04/2011
7636(29*10^58417-77)/358418Robert Price01/2017
76372^194034+17758411Lelio R Paula04/2011
7638789^20158+20158^78958400Norbert Schneider06/2016
763914^50949+7558395Lelio R Paula03/2013
76402^193974-11476158392Enzo Doria05/2015
76412^193965+558390Henri Lifchitz12/2002
7642(5*10^58384-29)/358385Robert Price02/2017
76433^122360+8058381Lelio R Paula10/2012
764410103^14577-11458373Enzo Doria07/2012
7645(22699*2^193883+1)/2158368Lelio R Paula06/2014
7646(31*2^193886+1)/14076558362Lelio R Paula07/2012
764711^56041-156058361Enzo Doria11/2012
7648(2^193881+9)/1769958360Lelio R Paula02/2012
76493^122313+5858359Lelio R Paula10/2012
76506^74996-11958359Lelio R Paula10/2012
7651(11*2^193859+1)/1358358Lelio R Paula07/2012
76522^193861-11225558358Enzo Doria06/2014
7653(22699*2^193854+1)/492758357Lelio R Paula06/2014
765418^46487+3758354Lelio R Paula03/2013
765517^47419+5458347Lelio R Paula03/2013
7656(31*2^193791+1)/358338Lelio R Paula02/2012
7657(27*2^193805-1)/98224958337Lelio R Paula01/2014
76583^122219-2^12221958314Mike Oakes09/2003
7659(199*10^58306+11)/358308Robert Price05/2017
76602^193674-1882558302Lelio R Paula05/2011
76615*10^58275+358276Dmitry Domanov11/2010
76622^193578-11291358273Enzo Doria06/2014
76632^193541+129958262Lelio R Paula05/2011
766410^58250+9358251Robert Price01/2011
766510^58250-17560758250Patrick De Geest12/2012
76662^193492+841558247Lelio R Paula10/2012
76672^193444+15758233Lelio R Paula04/2011
7668Phi(28754,28754)58231Henri Lifchitz08/2013
76692^193430-11188158229Enzo Doria05/2014
767010^58225+12457958226Patrick De Geest12/2012
767110^58225-9358225Robert Price05/2011
76722^193375-29558212Yves Minet05/2013
76732^193345+7726758203Enzo Doria05/2016
767421^44017-20^4401758201Robert Price05/2012
7675(17*2^193329-1)/958199Lelio R Paula01/2014
767617^47291+2058190Lelio R Paula03/2013
7677p(12528)#/2-12858170Robert Price05/2017
76782^193214-13558164Lelio R Paula04/2011
767919^45483-8058162Lelio R Paula03/2013
7680(4*10^58155+83)/358156Robert Price01/2017
768114^50739-1358154Lelio R Paula03/2013
7682(1017*2^193184-1)/482358154Lelio R Paula04/2015
7683(2*10^58151+457)/958151Robert Price01/2017
7684(9179*2^193183-1)/399926787958149Lelio R Paula04/2015
7685(19*2^193114-1)/118675558129Lelio R Paula01/2014
76872^193091-123758127Yves Minet08/2012
76869*7^68780-258127Lelio R Paula09/2014
76882^193083-86968810558124Lelio R Paula10/2012
76892^193058-4558117Lelio R Paula04/2011
7690(14016^14016+14017^14017)/(23*7103*19913)58115David Broadhurst09/2009
769111^55795-4258105Lelio R Paula03/2013
76923^121779-1658104Lelio R Paula10/2012
76932^192986+19558095Lelio R Paula04/2011
76947^68740+2*3^6874058093Mike Oakes07/2010
769512^53821+1158083Lelio R Paula02/2013
7696119^27979-11858072Norbert Schneider10/2013
7697(10223*2^192828+1)/24358049Lelio R Paula05/2014
76982^192808-112758041Yves Minet05/2013
7699(27*2^192803+1)/982758037Lelio R Paula07/2012
7700(2^192781+lucasV(1,2,192781)+1)/458033Mike Oakes11/2016
77012^192678+7294358002Enzo Doria04/2016
77022^192657-318957996Yves Minet10/2014
77036^74525-14957992Lelio R Paula10/2012
770442^35723-4157988Norbert Schneider06/2014
7705(29*2^192625-1)/18357986Lelio R Paula01/2014
7706(3^121520-8)/384757977Lelio R Paula03/2012
7707(2^192596-5)/13957976Lelio R Paula02/2012
770810^57975+6783357976Patrick De Geest09/2013
770910^57975-4769357975Patrick De Geest09/2013
7710(F(7707)^37-F(7706)^37)/F(7705)57972Wayne Halsdorf03/2012
7711(3^121492-5)/457966Lelio R Paula03/2012
77122^192549+3557964Lelio R Paula04/2011
771328799!2+257962Robert Price10/2012
7714(7*2^192534-1)/134757957Lelio R Paula01/2014
77157001^15069-10057943Enzo Doria07/2012
7716L(277273)/1109092157940Donovan Johnson11/2005
7717(2^192469-1017)/3557938Lelio R Paula02/2012
77182^192457-1155*19245757936Henri Lifchitz02/2005
77192^192443+138557932Lelio R Paula05/2011
7720132^27317-13157928Norbert Schneider03/2015
772141522!3-5904957912Robert Price12/2015
7722(3*2^192380-1)/16957911Lelio R Paula01/2014
77232^192339-251557900Yves Minet07/2014
77242^192303+769557889Lelio R Paula10/2012
77252^192273-595557880Lelio R Paula05/2011
77262^192257+1609557876Lelio R Paula05/2011
77272^192218-11186157864Enzo Doria05/2014
77282^192214-394157863Yves Minet04/2017
7729(2^192212+3)/25957860Lelio R Paula02/2012
7730(3^121270+8)/15593975357853Lelio R Paula03/2012
773180^30393-7957841Norbert Schneider03/2015
773220^44455-312357838Enzo Doria03/2013
77332^192122-19557835Lelio R Paula04/2011
7734(29*10^57834+91)/357835Robert Price03/2016
77358*6^74306+557823Lelio R Paula09/2014
7736(39^36341-1)/3857820Robert Price04/2012
77372^192037-11180557809Enzo Doria05/2014
77382^192023-192023^257805Henri Lifchitz05/2005
773921^43717+257804Ray Chandler08/2011
77408*5^82687+757797Lelio R Paula09/2014
77415^82680-2457791Lelio R Paula10/2012
7742(2^191915+47)/9557771Lelio R Paula02/2012
77436^74227-9557760Lelio R Paula10/2012
77442^191861+2983557756Lelio R Paula10/2012
77451908^17605+17605^190857755Serge Batalov05/2014
77465*10^57754+5957755Robert Price09/2016
7747(5*2^191821-1)/892406757738Lelio R Paula01/2014
77483*8^63917+5^63917-3*4^63917+3*2^6391757724Mike Oakes11/2010
774941399!3-656157723Robert Price11/2015
77502^191745+1757721Lelio R Paula04/2011


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 27 2017 18:33 (Time in France)

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