PRP Records

Probable Primes Top 10000

(293510 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 ?
7512^983620+60451296100Phil Moore03/2008
7522^982721-2683295829Yves Minet02/2016
753(23*10^295581+7)/3295582Robert Price05/2023
7542^981298-2788421295401Enzo Doria12/2015
7552^981163-2790967295360Enzo Doria12/2015
7562^981016-15295316Stefano Morozzi07/2022
7578*10^295160-13295161Robert Price08/2023
7582^979594+1865839294888Enzo Doria02/2016
7592*10^294527-91294528Robert Price02/2023
76010^294475+49294476Robert Price02/2023
761(11*10^294308+91)/3294309Robert Price03/2023
7622^976760+1885021294035Enzo Doria02/2017
7633*2^976518+5293962Jon Grantham07/2023
7642^974441+1878407293336Enzo Doria08/2016
7652^974180+1876831293258Enzo Doria07/2016
7662^974170+453319293255Enzo Doria01/2017
7672^972744-114419292826Enzo Doria03/2015
76811^281143+6292781Paul Bourdelais03/2021
769(4*10^292619-91)/3292620Robert Price12/2022
770CopelandErdos(292447)292447Mark Rodenkirch12/2015
7713*10^292344-97292345Robert Price01/2023
7722^970911+1873373292274Enzo Doria07/2016
7732^970670+383059292201Enzo Doria12/2016
7742^970141-100363292042Enzo Doria02/2014
7752^969945+1874717291983Enzo Doria06/2016
7762^969384+1880701291814Enzo Doria10/2016
777(13*10^291721-43)/3291722Robert Price08/2023
778(3^611333-2^611333)/(99035947*87109884549431)291659Mike Oakes02/2017
7793*2^963892+5290161Jon Grantham07/2023
780(151*10^289877-1)/3289879Robert Price07/2023
7812^962194+60139289650Enzo Doria02/2016
7822^959307-1861507288781Enzo Doria11/2015
783(17*10^288692+31)/3288693Robert Price04/2023
78414^251797-3288592Paul Bourdelais12/2020
785(2*10^288371-23)/3288371Robert Price10/2022
786(31*10^288238-1)/3288240Robert Price02/2023
787(7^341063-2^341063)/5288231Jon Grantham08/2023
7882^957372+283531288198Enzo Doria02/2017
7892^957192-1864049288144Enzo Doria01/2016
7902^956446+1875199287919Enzo Doria06/2016
7917*10^287854+39287855Robert Price01/2023
792(17^233689+1)/18287542Paul Bourdelais09/2013
7932^955178+1883587287538Enzo Doria12/2016
7942^954127-954127^2287221Henri Lifchitz01/2021
7952^954001+1875257287183Enzo Doria07/2016
7962*10^287175-49287176Robert Price05/2023
797(22*10^287085-19)/3287086Robert Price07/2023
7982^953488+22411287029Enzo Doria09/2023
799(23891^65536+1)/2286932Serge Batalov03/2018
8005*3^601336-2^601336286911Jon Grantham08/2023
8012^952268+1878601286662Enzo Doria09/2016
8022^950801+81557286220Enzo Doria08/2016
80322845^65536+22844^65536285658Kellen Shenton03/2021
804(11*2^948635-13)/15285568Renaud Lifchitz11/2011
805(54^164839+1)/55285565Paul Bourdelais07/2019
8062^948510+782569285530Enzo Doria10/2016
8072^948374-114137285490Enzo Doria01/2015
8082^947739+1872923285298Enzo Doria06/2016
8097*10^284751+9284752Robert Price04/2023
8102^944561-21284342Stefano Morozzi07/2022
811(4*10^284330-31)/9284330Serge Batalov11/2022
812(32*10^283826-23)/9283827Serge Batalov01/2023
8132^942533+82067283731Enzo Doria09/2016
8142^941469+39283411Jon Grantham08/2023
815(10^283342-31)/3283342Robert Price03/2023
8162^940950+1874989283255Enzo Doria06/2016
8172^940426-2786141283097Enzo Doria11/2015
818(2*10^282948-11)/9282948Serge Batalov11/2022
8192^939881-114115282933Enzo Doria12/2014
820(14*10^282673-143)/3282674Robert Price05/2023
82110^282493+632551282494Patrick De Geest02/2017
82310^282493-9^282493282493Jean-Louis Charton03/2007
82210^282493-132327282493Patrick De Geest02/2017
8243^591827-2^591827282374Mike Oakes08/2009
825Tau(509^18946)282048Nik Lygeros / Olivier Rozier05/2015
8262^936716-1835519281980Enzo Doria04/2015
8272^936588+79411281942Enzo Doria06/2016
8282^936047+1877423281779Enzo Doria08/2016
8292^935713+1869377281678Enzo Doria05/2016
8302^933082+1877059280886Enzo Doria08/2016
831(5*10^280710+1)/3280711Serge Batalov10/2014
8322^931976+25280553Stefano Morozzi05/2021
833(42^172663+1)/43280274Paul Bourdelais07/2019
834(10^279978+11)/3279978Serge Batalov07/2015
8352^929524-1864829279815Enzo Doria01/2016
8362^929329+22697279756Enzo Doria09/2023
8372^929152+60181279703Enzo Doria02/2016
8382^928621-2787883279543Enzo Doria11/2015
839(2^927763+lucasV(-1,2,927763)+1)/2279285Mike Oakes04/2017
8402^927429+1882277279184Enzo Doria12/2016
8412^926766-11278985Stefano Morozzi07/2022
842(71^150697-1)/70278978Paul Bourdelais07/2019
843(33^183661-1)/32278891Paul Bourdelais12/2018
844(166*10^278633-7)/3278635Robert Price02/2023
845(2^925391+lucasV(-1,2,925391)+1)/2278571Mike Oakes03/2017
8462^925330-1301278553Yves Minet06/2015
847(299*10^278546+1)/3278548Robert Price01/2023
848(21^210599+1)/22278457Paul Bourdelais08/2013
849(266*10^278325+1)/3278327Robert Price01/2023
8502^923261-69175277930Enzo Doria11/2015
851757^96487-756^96487277796Jean-Louis Charton12/2012
8522^922301+57277641Stefano Morozzi05/2021
8537*10^277478-39277479Robert Price07/2023
854((((((((((((((291487327^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2277369Serge Batalov07/2016
855(5^396413-1)/4277081Paul Bourdelais06/2010
8562^920318+2792299277044Enzo Doria02/2016
857(16*10^276537-31)/3276538Robert Price03/2023
8582^918596-2786939276525Enzo Doria11/2015
8592^916639+60563275936Enzo Doria04/2016
860(2*10^275922+1)/3275922Serge Batalov11/2022
8612^916385-2786383275860Enzo Doria11/2015
8622^915928+82081275722Enzo Doria09/2016
863(4*10^275671+11)/3275672Tyler Busby02/2023
8642^915576-114137275616Enzo Doria01/2015
8652^914828+1876741275391Enzo Doria07/2016
8662^914757-2203275370Yves Minet12/2015
8677*10^275157-27275158Robert Price11/2022
8682^912744+20011274764Enzo Doria06/2023
8692^911900+1871245274510Enzo Doria05/2016
870(16*10^274251-91)/3274252Robert Price11/2022
8712^910999+9274239Stefano Morozzi05/2021
872(2^910869-7)/5274199Stefano Morozzi08/2022
8732^910490+283429274085Enzo Doria01/2017
8747*10^273983+39273984Robert Price01/2023
8752^909988-1862249273934Enzo Doria12/2015
8762^909297+1879157273726Enzo Doria08/2016
8772^909257-1864423273714Enzo Doria01/2016
8782^908739-7273558Stefano Morozzi07/2022
8792^908579-1861747273510Enzo Doria12/2015
8803*2^908005-5273338Jon Grantham07/2023
8812^907635-2791597273226Enzo Doria01/2016
8822^907059+211193273052Enzo Doria08/2023
883(53^158341+1)/54273022Paul Bourdelais07/2019
8842^906594-113201272912Enzo Doria08/2014
8859*10^272800+91272801Robert Price05/2023
8862*10^272710-49272711Robert Price05/2023
8872*10^272403-91272404Robert Price02/2023
8882^904773+1872167272364Enzo Doria06/2016
8896^349903+5272278Paul Bourdelais02/2021
8902^904149-1862473272176Enzo Doria12/2015
891(7*10^271757-61)/9271757Erik Branger03/2012
8922^902497+1880117271679Enzo Doria09/2016
8932^901858+77689271487Enzo Doria06/2016
8942^901372+1875301271341Enzo Doria06/2016
895(8*10^271039-77)/3271040Robert Price04/2023
8962^899999+1144031270927Norman Luhn09/2023
8972*10^270802-91270803Robert Price02/2023
89823*10^270799-7270801Robert Price10/2022
8992^899121-115033270663Enzo Doria07/2015
9002^898900+883021270596Enzo Doria12/2016
9012^898762-251511270555Enzo Doria12/2013
9022^898589+47270503Lelio R Paula03/2016
903187322*10^270343-187321270349Danilo Nitsche09/2013
90448358*10^270343-48357270348Danilo Nitsche09/2013
905(10^270343-1)/9270343Maksym Voznyy07/2007
9062^897867-3217270285Yves Minet12/2016
9072^897849-115273270280Enzo Doria07/2015
9082^896616-114179269909Enzo Doria12/2014
909(22*10^269517-19)/3269518Robert Price07/2023
91010^(2*134739+1)-7*10^134739-1269479Robert Price07/2023
9112^894928+583561269401Enzo Doria04/2017
9122^894673-39343269324Enzo Doria08/2015
913F(1285607)268676Henri Lifchitz11/2008
9142^892234+22189268590Enzo Doria09/2023
9152^892112+187663268553Enzo Doria08/2016
916(266*10^268407-17)/3268409Robert Price02/2023
917(10^268207+1)/11268206Paul Bourdelais02/2010
9182^890957-69583268205Enzo Doria12/2015
91932841!^2+32840!^2+...+2!^2+1!^2268128Serge Batalov07/2017
9202^890122-351401267954Enzo Doria07/2015
921(19^209359-1)/18267718Paul Bourdelais08/2010
922(85^138647+1)/86267507Paul Bourdelais07/2019
923(485^99523-1)/484267291Michael Stocker05/2020
9242^886324+77791266811Enzo Doria06/2016
9257*10^266731+87266732Robert Price11/2022
9262^884714+1880527266326Enzo Doria10/2016
9277*10^266024-47266025Robert Price08/2023
92811^255426+255426^11265999Serge Batalov05/2014
9292^883462-343421265949Enzo Doria07/2015
9302^883442+1875019265943Enzo Doria06/2016
9312^883333-291583265910Enzo Doria07/2015
93210^265566+3593037265567Paul Bourdelais08/2023
933(2*10^265321-17)/3265321Serge Batalov11/2022
934(16*10^265052-91)/3265053Robert Price11/2022
9352^880411+1882673265031Enzo Doria12/2016
936(14*10^264791-11)/3264792Robert Price08/2022
9372^879530-2788031264765Enzo Doria12/2015
938(2*10^264539+61)/9264539Serge Batalov11/2022
9392^878118+2793079264340Enzo Doria02/2016
940(2^878073-7)/5264326Stefano Morozzi08/2022
941(37^168527-1)/36264283Paul Bourdelais08/2019
9425^377865+3^377865-1264117Jon Grantham08/2023
943(19*10^263971+131)/3263972Robert Price08/2023
9442^876202-17263764Stefano Morozzi07/2022
945(14*10^263720-11)/3263721Robert Price08/2022
9462^875748-461129263627Enzo Doria07/2015
9472^875518-15263558Stefano Morozzi07/2022
948(29*10^263523-17)/3263524Robert Price01/2023
9492^875181-2789923263456Enzo Doria12/2015
9502^875101-350083263432Enzo Doria08/2015
9512^874684+1883587263307Enzo Doria01/2017
9522^874616+1872211263286Enzo Doria05/2016
9533^551491+16263129Robert Price04/2020
9542^874073+2792957263123Enzo Doria02/2016
9552^873628+1878751262989Enzo Doria08/2016
9562^873497+20837262949Enzo Doria08/2023
9572^873288-269262886Yves Minet01/2015
958(2*10^262874+7)/9262874Rytis Slatkevicius01/2023
959(28*10^262655-43)/3262656Robert Price04/2023
960(2*10^262603-11)/9262603Serge Batalov11/2022
9612^871991-4207262496Yves Minet03/2021
962(23*10^262324+7)/3262325Robert Price05/2023
9632^871146-3173262242Yves Minet07/2016
9642^869601-163261776Yves Minet01/2015
965(2*10^261704+61)/9261704Serge Batalov11/2022
9662^869326+282859261694Enzo Doria11/2016
9672^869035-114181261606Enzo Doria12/2014
9684*10^261248+91261249Robert Price11/2022
9692^865715+80303260607Enzo Doria07/2016
9702^865048+1882411260406Enzo Doria12/2016
9712^864899-113871260361Enzo Doria10/2014
972(16*10^260256-91)/3260257Robert Price11/2022
973(7*10^260198-61)/9260198Erik Branger11/2011
9742^864298-2788421260180Enzo Doria12/2015
9752^864039-2791357260102Enzo Doria01/2016
9762^863621-113833259976Enzo Doria10/2014
97710^259945-11259945Mischa Rodermond04/2023
978(28*10^259897+113)/3259898Robert Price06/2023
9792^862837+75767259740Enzo Doria05/2016
9802^862637-31259680Jorge Menendez05/2019
9812^862088+1874941259515Enzo Doria06/2016
9822^861987-134557259484Hans Havermann10/2018
983(14*10^259431-143)/3259432Robert Price05/2023
9842^861516-1854029259343Enzo Doria09/2015
9852^860975-1853977259180Enzo Doria09/2015
9863^543128+16259138Robert Price04/2020
9872^860625-1858843259074Enzo Doria10/2015
9882^860110+77689258919Enzo Doria05/2016
9892^859600+1880371258766Enzo Doria10/2016
9902^859433+494711258716Makoto Morimoto10/2013
991(2^859433-44)/(2^2*3)258715Makoto Morimoto08/2019
992(2^859431-11)/3258715Stefano Morozzi08/2022
993(13*10^258710-43)/3258711Robert Price08/2023
994(2^859433+39899)/(73*3907*46301)258705Makoto Morimoto10/2016
9952^859240+1875271258658Enzo Doria06/2016
996Tau(971^15738)258571Nik Lygeros / Olivier Rozier05/2015
997(23*10^258494-47)/3258495Robert Price09/2023
998(144^119671+1)/145258292Paul Bourdelais08/2019
9992^857608+105258166Stefano Morozzi05/2021
1000(11*2^857159-13)/15258031Renaud Lifchitz08/2011


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2023 15:19 (Time in France)

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