PRP Records

Probable Primes Top 10000

(271023 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 ?
8501(2^253660+490)/276359Stefano Morozzi01/2020
850219227^9352+9352^1922776349Hans Havermann01/2020
8503(2^253617+2874)/276347Stefano Morozzi01/2020
85042^253561-11053376330Enzo Doria05/2014
8505(2^253546+954)/276325Stefano Morozzi01/2020
8506gcd(V(917285),5*F(183457)*(F(183457)+1)+1)76321Serge Batalov04/2015
85079*5^109182+276316Lelio R Paula10/2014
850811^73279-369076313Enzo Doria12/2012
8509(598*10^76309-31)/976311Robert Price02/2017
851011^73274-2400076308Enzo Doria12/2012
85117^90291-676305Theodore Burton11/2005
8512(2^253479+3650)/276305Stefano Morozzi01/2020
8513(2^253460+2902)/276299Stefano Morozzi01/2020
85146*10^76295-2976296Robert Price08/2020
8515(21181*2^253432+1)/2143776291Lelio R Paula06/2014
8516(2^253399+3254)/276281Stefano Morozzi01/2020
851769247!4+476280Robert Price09/2019
85186^98025+14576279Lelio R Paula01/2015
8519(2^253382+1978)/276276Stefano Morozzi01/2020
85202^253355+115576268Lelio R Paula05/2013
8521(73*10^76262+413)/976263Robert Price10/2017
85222^253292-7121976249Enzo Doria04/2016
85237^90221-3676246Lelio R Paula02/2015
8524(2^253273+3486)/276243Stefano Morozzi01/2020
8525(2^253238+894)/276232Stefano Morozzi01/2020
852618^60727-347376229Enzo Doria03/2013
8527(2^253210+1170)/276224Stefano Morozzi01/2020
8528(78557*2^253184+1)/376221Lelio R Paula06/2014
8529(8*10^76220-83)/376221Robert Price10/2017
853018568^12717+12717^1856876211Hans Havermann01/2020
8531(44791^20480+1)/(44791^4096+1)76206Serge Batalov01/2017
8532(5168^20521-1)/516776198Serge Batalov08/2020
853319443^8294+8294^1944376193Hans Havermann12/2019
853411^73163-201076192Enzo Doria12/2012
853519006^10201+10201^1900676189Hans Havermann12/2019
85362^253060+5461576179Lelio R Paula05/2013
8537(2^253049+3966)/276176Stefano Morozzi01/2020
85382^253029+186976176170Enzo Doria05/2016
8539(2^253028+1906)/276169Stefano Morozzi01/2020
8540(1078^25111-1)/107776150Serge Batalov08/2020
85412^252955-11100776148Enzo Doria05/2014
85422*5^108931+776140Lelio R Paula10/2014
8543(86*10^76128+121)/976129Robert Price03/2017
854422154*29^52050+976123Curtis Bright05/2015
854518915^10574+10574^1891576119Hans Havermann01/2020
85463^159530-11235876116Enzo Doria06/2014
854711^73089-4876115Lelio R Paula02/2015
854886^39337-8576098Norbert Schneider10/2015
8549(3^159505-7)/31329731676095Lelio R Paula06/2012
85506^97783+7776090Lelio R Paula01/2015
8551(2^252716+1842)/276075Stefano Morozzi01/2020
85522^252712-10576074Lelio R Paula03/2012
8553(10^76069-19)/976069Robert Price10/2017
8556131^35927+276068Lelio R Paula05/2013
8554(41*10^76067+373)/976068Robert Price04/2017
8555(10807^18859-1)/1080676068Serge Batalov08/2020
85572^252683-13976066Lelio R Paula03/2012
8558137^35597-13676061Norbert Schneider05/2015
85593^159413+10676060Lelio R Paula01/2015
8560(2^252593+1682)/276038Stefano Morozzi01/2020
85619^79677+3*8^79677-2*4^79677-3*2^7967776032Mike Oakes12/2010
8562(6716^19867-1)/671576030Serge Batalov08/2020
856322235^2626+2626^2223576029Hans Havermann12/2019
8564(2^252557-9)/7176026Lelio R Paula07/2012
8566(85*10^76021-103)/976022Robert Price10/2017
8565(2^252539+2690)/276022Stefano Morozzi01/2020
856711^72989+8076011Lelio R Paula02/2015
856899877!6-3675996Robert Price11/2018
85692^252449-45952375995Enzo Doria05/2015
857020^58408+7375991Lelio R Paula01/2015
85712^252418-142175986Yves Minet01/2013
8572(11*2^252396-1)/575980Lelio R Paula02/2014
857320871^4366+4366^2087175973Hans Havermann01/2020
85742^252365-11068975970Enzo Doria05/2014
857511^72949-102075969Enzo Doria11/2012
8576(2^252335+2394)/275961Stefano Morozzi01/2020
8577(2^252294+47)/654975945Lelio R Paula07/2012
85782^252261-11059575939Enzo Doria05/2014
85797^89853+7675935Lelio R Paula01/2015
8580(3043^21799-1)/304275930Serge Batalov08/2020
85813^159132+5675926Lelio R Paula01/2015
8582730^26513+26513^73075916Norbert Schneider11/2016
85837*10^75911-5775912Robert Price06/2020
8584(27*2^252163-1)/194575907Lelio R Paula01/2014
85855^108596-1484675906Enzo Doria02/2013
8586(1377^24179-1)/137675894Serge Batalov07/2020
8587(2^252082+2734)/275884Stefano Morozzi01/2020
85885^108560-1484675881Enzo Doria02/2013
85892^252051-11035975875Enzo Doria05/2014
85902^251971-11050975851Enzo Doria05/2014
8591(42457^16384+1)/32768275819Lelio R Paula11/2011
85922^251842-471575812Yves Minet05/2019
859399655!6-275811Robert Price07/2017
8594(2^251823+3290)/275806Stefano Morozzi01/2020
859514*10^75798+108975800Jens K. Andersen11/2007
85962^251784-45575795Yves Minet03/2012
85972^251780-128975794Yves Minet01/2013
85982^251760-21560975788Paul Bourdelais03/2013
859921947^2838+2838^2194775784Hans Havermann01/2020
860099^37973+275781Lelio R Paula05/2013
8601(185*10^75777+7)/375779Robert Price02/2017
86025*2^251690+375767Lelio R Paula06/2014
86036^97366+9575766Lelio R Paula01/2015
8604(4742^20611-1)/474175762Serge Batalov08/2020
8605s(23010)75760Hans Havermann11/2017
8606(2^251666+1882)/275759Stefano Morozzi01/2020
86078*6^97337-775744Lelio R Paula10/2014
860824045^1412+1412^2404575738Hans Havermann01/2020
86092^251588-11167775736Enzo Doria05/2014
8610(2^251580+2086)/275733Stefano Morozzi01/2020
86115^108346-1325675731Enzo Doria02/2013
8612(2^251570+1182)/275730Stefano Morozzi01/2020
8613(31^50777+1)/3275726Robert Price07/2013
8614(10^75707+77)/375707Robert Price01/2017
8615(174907#+1673)/(7*239*15467899)75700Makoto Morimoto10/2017
86162^251466+19375699Lelio R Paula03/2012
8617(2^251463+1338)/275698Stefano Morozzi01/2020
8618(5*2^251464+1)/942375695Lelio R Paula07/2012
86192^251422-10999175686Enzo Doria04/2014
862091*(10^23+1)*(10^1721+1)*(10^118749+1)/(10^69+1)/(10^5163+1)/(10^39583+1)75680Makoto Kamada03/2019
8621(2^251355+3806)/275666Stefano Morozzi01/2020
8622(2^251347+1278)/275663Stefano Morozzi01/2020
86234*5^108245-375661Lelio R Paula10/2014
8624(25*10^75653+143)/375654Robert Price08/2020
8625(2^251261+846)/275637Stefano Morozzi01/2020
8626(2^251195+3770)/275617Stefano Morozzi01/2020
862712^70067-11^7006775615Jean-Louis Charton11/2006
862812^70066+9575614Lelio R Paula02/2015
8629(2^251181+1130)/275613Stefano Morozzi01/2020
8630-E20534/206375607Thomas Ritschel02/2017
863119^59120-5075600Lelio R Paula01/2015
863218^60222-469775596Enzo Doria03/2013
863318^60211-435575582Enzo Doria03/2013
86347*2^251014-975564Lelio R Paula06/2014
86356^97101-2575560Lelio R Paula01/2015
86368^83663-7^8366375556Jean-Louis Charton01/2004
8637(2^250974+3838)/275551Stefano Morozzi01/2020
86383^158331-14075544Lelio R Paula01/2015
8639(12235^18481-1)/1223475539Serge Batalov08/2020
8640(29*10^75532-107)/375533Robert Price08/2020
8643(37^48157-1)/3675519Robert Price03/2012
8641(19*10^75518-43)/375519Robert Price10/2017
86422^250868-422975519Yves Minet08/2018
864410^75516+3146775517Patrick De Geest03/2016
864610^75516-10^2256-175516Serge Batalov01/2011
864510^75516-6659175516Patrick De Geest03/2016
86472^250851-18775514Lelio R Paula03/2012
8648(2^250836+466)/275509Stefano Morozzi01/2020
864922273^2454+2454^2227375503Hans Havermann01/2020
8650(43*10^75498-7)/975499Robert Price12/2014
8651(3^158244-5)/24791675497Lelio R Paula06/2012
86524*5^107971-375470Lelio R Paula10/2014
8653(25*10^75465+71)/375466Robert Price01/2017
8654(2^250690+1222)/275465Stefano Morozzi01/2020
8656(5*2^250681-1)/99975461Lelio R Paula01/2014
8655(2^250674+1354)/275461Stefano Morozzi01/2020
8657(2^250670+1878)/275459Stefano Morozzi01/2020
8658(182*10^75456+1)/375458Robert Price02/2017
8659(2^250669-9)/9889772975451Lelio R Paula07/2012
8660(14583^18121-1)/1458275449Serge Batalov08/2020
866110^75441+1375442Robert Price01/2011
866210^75441-992375441Patrick De Geest05/2013
8663(27*2^250546-1)/645775420Lelio R Paula01/2014
86645*7^89231-675410Lelio R Paula10/2014
86662^250503-1699575409Lelio R Paula05/2013
866511^72411-2875409Lelio R Paula02/2015
86673*5^107860-875392Lelio R Paula10/2014
8668(34*10^75387-403)/975388Robert Price10/2017
86712^250426+2983575386Lelio R Paula05/2013
86698*3^157999-775386Lelio R Paula05/2014
8670(15671^17971-1)/1567075386Serge Batalov08/2020
8672(2^250417+2642)/275383Stefano Morozzi01/2020
8673(88*10^75381-43)/975382Robert Price11/2015
8674(2^250394+2902)/275376Stefano Morozzi01/2020
86752^250382-11175575373Enzo Doria05/2014
86762^250374-279805175371Eric Chen03/2016
8677(22*10^75368-1)/375369Robert Price12/2014
86782^250369-454375369Yves Minet03/2019
867920078^5667+5667^2007875360Hans Havermann02/2020
8680(2^250318+2242)/275353Stefano Morozzi01/2020
8681(21398^17401-1)/2139775349Serge Batalov08/2020
8683(19*10^75338+119)/375339Robert Price02/2017
868221517^3172+3172^2151775339Hans Havermann01/2020
86842^250223-185916775325Enzo Doria03/2016
8685(3^157854-7)/6602528275308Lelio R Paula06/2012
8686(2^250164+1578)/275307Stefano Morozzi01/2020
86873^157831-9875305Lelio R Paula01/2015
8688(46^45281+11^45281)/5775290Serge Batalov12/2016
868992^38335-9175282Norbert Schneider01/2016
8690(2^250026+2398)/275266Stefano Morozzi01/2020
86912^250020+1891575264Lelio R Paula05/2013
86922^250002+819375259Lelio R Paula05/2013
8693(2^249996+1678)/275256Stefano Morozzi01/2020
8694(11*2^249977-7)/1575251Renaud Lifchitz02/2011
8695(2^249968+78557)/6375247Lelio R Paula07/2012
8696(5*10^75244+91)/375245Robert Price11/2016
8697(10489!)^2+Prime(10489)75242Robert Price08/2014
869814^65644+6775237Lelio R Paula01/2015
869968383!4+3275236Robert Price09/2019
8700(2^249928-5)/1185905975229Lelio R Paula06/2012
8701129^35638+275218Lelio R Paula05/2013
87022^249853-11047575214Enzo Doria05/2014
8703(5704^20021-1)/570375199Serge Batalov08/2020
870420574^4517+4517^2057475195Hans Havermann01/2020
8705(11720^18481-1)/1171975194Serge Batalov08/2020
87062^249762+7540975186Enzo Doria04/2016
8707565^27318+27318^56575181Norbert Schneider12/2016
8708(2^249741-7)/68575177Lelio R Paula06/2012
87092^249726-11218175176Enzo Doria06/2014
87102^249721+1171575174Lelio R Paula05/2013
8711(2^249705+654)/275169Stefano Morozzi01/2020
8713(38661^16384+1)/275158Lelio R Paula11/2011
8712(15220^17971-1)/1521975158Serge Batalov08/2020
87142^249658-4735575155Lelio R Paula05/2013
8715155^34311+275153Lelio R Paula05/2013
8716(10^87682+1)/(10^12526+1)/99009900990175145Maksym Voznyy06/2015
8717(23*2^249602+1)/9375138Lelio R Paula08/2012
87182^249522+841575114Lelio R Paula05/2013
87192^249489-11091175104Enzo Doria05/2014
8720(28*10^75078+131)/375079Robert Price02/2017
8721(206*10^75073-17)/975075Robert Price03/2017
8722(2^249384+3330)/275072Stefano Morozzi01/2020
8723(5947^19891-1)/594675071Serge Batalov08/2020
87242^249368-11057375068Enzo Doria05/2014
8725NaturalLogarithmOf10(75067)75067Eric W. Weisstein10/2015
872619167^8248+8248^1916775065Hans Havermann02/2020
8727(2^249375+78557)/4505612575062Lelio R Paula07/2012
8728(26*10^75055-173)/375056Robert Price10/2017
87302^249272+19375039Lelio R Paula03/2012
872917433^17692-17692^1743375039Norbert Schneider11/2019
873114^65468+4375035Lelio R Paula01/2015
873237^47844+3675030Norbert Schneider05/2014
8733(52*10^75027-7)/975028Robert Price12/2014
873417943^15178+15178^1794375024Hans Havermann02/2020
8735(2^249219+494)/275023Stefano Morozzi01/2020
873620^57653+8975009Lelio R Paula01/2015
8737(2^249084+2682)/274982Stefano Morozzi01/2020
87382^249061-186835374975Enzo Doria04/2016
8739(2^249056+1006)/274974Stefano Morozzi01/2020
87407^88713+2*3^8871374972Mike Oakes07/2010
874118325^12334+12334^1832574970Hans Havermann02/2020
87422*6^96313+574947Lelio R Paula10/2014
8744(8*10^74944+49)/374945Robert Price03/2016
8743(1258^24179-1)/125774945Serge Batalov07/2020
8745300^30247+30247^30074926Norbert Schneider11/2014
87462^248866-17174917Lelio R Paula03/2012
8747(714^26251-1)/71374910Serge Batalov08/2020
87486*5^107168-774908Lelio R Paula10/2014
874911^71926+7874904Lelio R Paula02/2015
87502^248824+186939174904Enzo Doria05/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 30 2020 00:02 (Time in France)

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