PRP Records

Probable Primes Top 10000

(252675 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 ?
425142^57867-4193933Norbert Schneider08/2018
42522^311992-1620993919Enzo Doria04/2013
4253(85^48677+1)/8693917Paul Bourdelais08/2017
42542^311965-3993911Lelio R Paula11/2012
42552^311920-11168993898Enzo Doria05/2014
4256130^44414+12993889Norbert Schneider01/2019
42577*10^93887-4793888Robert Price02/2017
425812^86965-1393851Lelio R Paula06/2016
42592^311705+1609593833Lelio R Paula03/2016
42602^311665-8193821Lelio R Paula11/2012
4261730^32761+32761^73093806Norbert Schneider09/2017
426211^90073+9293802Lelio R Paula05/2016
42636*10^93792+4193793Robert Price01/2017
4264(2^311580+7)/59132993790Lelio R Paula06/2013
426512^86900-7793781Lelio R Paula06/2016
42662^311508-10976993774Enzo Doria04/2014
42672^311486-185962193767Enzo Doria03/2016
4268Phi(93811,10)/968129521/2109997013/3280113810431/63963778254583193765Kurt Beschorner04/2015
4269(10^93811-1)/(9*968129521*2109997013*3280113810431*639637782545831)93765Gord Palameta10/2018
42702^311471+31146993763Renaud Lifchitz01/2003
4271(88*10^93760-1)/393762Robert Price10/2017
42722^311426+7945993749Enzo Doria06/2016
42732^311294+577593709Lelio R Paula03/2016
42742^311252-101793697Lelio R Paula03/2016
42752^311247-11204193695Enzo Doria06/2014
42767*10^93692-8393693Robert Price09/2017
42772^311205-10964593683Enzo Doria04/2014
42785^134027-8493681Lelio R Paula04/2016
4279(2^311148-1017)/55793663Lelio R Paula06/2013
4280(2^311027-2^155514+1)/59362811/2006
42813^196192-2893608Robert Price12/2013
4282216091#+26143393606Makoto Morimoto12/2015
42835^133917+6893604Lelio R Paula04/2016
42842^310924-170993598Yves Minet03/2013
4285(266*10^93577-11)/393579Robert Price09/2016
4286(16*10^93577+161)/393578Robert Price05/2016
42873^196113-5693570Lelio R Paula04/2016
42882^310806-11034593562Enzo Doria05/2014
42893^196093+8693561Lelio R Paula04/2016
42902^310780-232793555Yves Minet10/2013
429130^63332+4193550Lelio R Paula08/2012
4292(21181*2^310707+1)/2193536Lelio R Paula06/2014
42938*5^133807+793528Lelio R Paula10/2014
42942^310686+819393526Lelio R Paula03/2016
42952^310646+6393514Lelio R Paula11/2012
4296(77*10^93508+31)/993509Robert Price10/2015
4297(1000907^15583+1)/100090893499Faysal YAtim04/2009
4298(2*10^93497+7)/993497Erik Branger03/2011
42993^195958-11285293496Enzo Doria07/2014
43002^310583+1638593495Lelio R Paula03/2016
4301(9913*2^310557-1)/3593490Lelio R Paula04/2015
43029*7^110614+293481Lelio R Paula11/2014
43032^310469-829593461Lelio R Paula03/2016
43042^310459-115993458Yves Minet11/2012
43056^120075-9593437Lelio R Paula05/2016
43062^310289+9832793407Yves Minet11/2010
43072^310217-11314393385Enzo Doria07/2014
43087^110494-6893379Lelio R Paula04/2016
43092^310184-11309393375Enzo Doria07/2014
43102^310180-11041793374Enzo Doria05/2014
4311gcd(V(1124905),5*F(224981)*(F(224981)-1)+1)93372Serge Batalov04/2015
43123^195669+6893358Lelio R Paula04/2016
431310^93356+9193357Robert Price04/2011
431410^93356-2831393356Patrick De Geest08/2013
4315(85*10^93346+23)/993347Robert Price11/2015
4316(3^195648-5)/315827693342Lelio R Paula04/2013
43173^195556+868093304Lelio R Paula04/2016
43182^309942-10999193302Enzo Doria04/2014
43192^309926-186730193298Enzo Doria03/2016
43202^309924+8595193297Yves Minet03/2011
43212^309896-422993288Yves Minet08/2018
4322(86*10^93263-77)/993264Robert Price05/2016
43236^119836-12593251Lelio R Paula05/2016
4324(77*10^93249-257)/993250Robert Price10/2017
43253^195430-293244Theodore Burton02/2007
4326(13*10^93236+47)/393237Robert Price01/2017
4327(67*10^93226-7)/393228Robert Price10/2017
4328(86*10^93217-221)/993218Robert Price06/2017
43292^309637-1632993211Enzo Doria04/2013
4330(41*10^93207+49)/993208Robert Price04/2016
433114^81312-5793194Lelio R Paula06/2016
433241^57783-4093192Theodore Burton02/2007
43333*10^93179-9793180Robert Price08/2017
43345*7^110252-493175Lelio R Paula11/2014
43352^309380-2793133Lelio R Paula11/2012
433623*10^93116-793118Robert Price03/2016
4337(29*10^93082+1)/393083Robert Price11/2015
4338(58*10^93062-13)/993063Robert Price09/2015
43392^309131+186938393058Enzo Doria05/2016
43402^309066-9393039Lelio R Paula11/2012
43412^309063-11326993038Enzo Doria07/2014
43423^194965+1693022Robert Price10/2013
43432^308979+186914393012Enzo Doria05/2016
43445^133064+5493008Lelio R Paula04/2016
4345(2^308905-509203)/11992988Lelio R Paula06/2013
4346(94*10^92981-49)/9992981Ray Chandler07/2011
4347(2*10^92976-17)/392976Robert Price08/2014
43482^308809+3796792961Phil Moore03/2008
4349(3^194825+5)/1165692952Lelio R Paula04/2013
4350(2^308679+5)/157392919Lelio R Paula06/2013
43512^308650+51392913Lelio R Paula02/2016
43525*7^109936+692908Lelio R Paula10/2014
43532*10^92897+8992898Robert Price07/2016
435412^86073-2992889Lelio R Paula06/2016
43552^308566-11792888Lelio R Paula11/2012
4356(17*10^92869-11)/392870Robert Price07/2015
43572^308459+7543192856Enzo Doria04/2016
43582^308426-186637792846Enzo Doria03/2016
4359(96^46831-1)/9592830Paul Bourdelais09/2017
43602^308349-11211192823Enzo Doria06/2014
43619*10^92821+1992822Robert Price05/2016
43622^308337-7592819Lelio R Paula11/2012
43634*3^194508+792805Lelio R Paula08/2014
436422*25^66379-11392796Curtis Bright05/2015
436511^89101-108092790Enzo Doria12/2012
43662^308236-186785992789Enzo Doria04/2016
436712^85963+2592770Lelio R Paula06/2016
43687^109750-6692750Lelio R Paula04/2016
43699*10^92742+1192743Robert Kinser01/2017
4370(21*2^308046-1)/885792729Lelio R Paula02/2014
43712^307997-11065592717Enzo Doria05/2014
4372L(443609)92709Renaud Lifchitz11/2003
437310^92691+992692Robert Price03/2011
437410^92691-25229192691Patrick De Geest08/2013
43752^307879-252192681Yves Minet07/2014
4376(2^307780-7)/1995966992644Lelio R Paula06/2013
437714^80831+4792643Lelio R Paula06/2016
437815^78744+9292611Lelio R Paula07/2016
437965^51083-6492610Norbert Schneider11/2014
4380131^43737-13092604Norbert Schneider02/2019
43816^118996-1694392597Enzo Doria02/2013
4382(16*10^92591+41)/392592Robert Price10/2017
4383(3^194014-7)/292568Lelio R Paula04/2013
4384(63^51439+1)/6492555Paul Bourdelais08/2017
4385(26*10^92546-77)/392547Robert Price02/2017
43863^193954+34092540Lelio R Paula04/2016
43872^307407-307407^292539Henri Lifchitz05/2005
4388(17*10^92513-11)/392514Robert Price07/2015
43892^307318-421192512Yves Minet06/2011
43902^307280+19392501Lelio R Paula11/2012
439120^71075-3392471Lelio R Paula05/2016
43922^307126-7879592455Lelio R Paula02/2016
43932^307125-4978992454Henri Lifchitz08/2005
43942^307099+2392447Lelio R Paula11/2012
4395129^43798+12892440Norbert Schneider01/2019
43967*10^92414-6992415Robert Price01/2017
4397(9787*2^306975-1)/212915592407Lelio R Paula04/2015
43982^306915+187337392391Enzo Doria06/2016
43992^306908+1291592389Lelio R Paula02/2016
440019^72244-8092383Lelio R Paula06/2016
44012^306849+7592371Lelio R Paula11/2012
4402(397*10^92369+53)/992371Robert Price11/2017
44032^306813-86968810592360Lelio R Paula08/2016
44042^306672-10905992318Enzo Doria04/2014
44056^118604-1706392292Enzo Doria02/2013
4406(31*2^306487-1)/229192260Lelio R Paula02/2014
44072^306467-183561192256Enzo Doria04/2015
44082^306433+7642792246Enzo Doria05/2016
44092^306430-11331392245Enzo Doria07/2014
4410(23*10^92244-59)/992245Robert Price03/2017
4411(47*2^306398+1)/138480392231Lelio R Paula04/2015
4412(25*10^92186+59)/392187Robert Price05/2016
44132^306213-28618392180Enzo Doria06/2015
441410^92178+6192179Robert Price04/2011
441510^92178-17550992178Patrick De Geest07/2013
44162^306200+118592176Lelio R Paula02/2016
44172^306153+1192162Lelio R Paula11/2012
4418(2^306141-7)/592157Lelio R Paula06/2013
4419(26*10^92152-23)/392153Robert Price08/2016
4420(2*10^92152+67)/392152Robert Price04/2017
44214*10^92099+3*7^9209992100Mike Oakes12/2010
4422115^44684+11492081Norbert Schneider07/2018
4423(2^305867-2^152934+1)/59207511/2006
44242^305851-10949592071Enzo Doria04/2014
442512^85300+3592055Lelio R Paula06/2016
44263^192911+9292042Lelio R Paula04/2016
44272^305723-27627192032Enzo Doria07/2015
44282^305676+9392018Donovan Johnson06/2008
44293^192819+491999Lelio R Paula04/2013
4430(38*10^91997-83)/9991997Ray Chandler07/2011
44312^305539+7291191977Enzo Doria04/2016
4432(2^305427-5)/129799821391934Lelio R Paula06/2013
443385^47642+8491922Norbert Schneider10/2015
443410^91920+18765191921Patrick De Geest07/2013
443510^91920-3991920Robert Price05/2011
4436(22*10^91903+41)/991904Robert Price02/2015
44382^305275-2791897Lelio R Paula11/2012
44373^192607-772691897Enzo Doria05/2014
4439(7*10^91856-61)/991856Erik Branger12/2009
4440(89*10^91839-53)/991840Robert Price11/2015
44418*5^131351+791812Lelio R Paula10/2014
44423^192426-6891811Lelio R Paula04/2016
44432^304973+11791807Lelio R Paula11/2012
44442^304939-186372791796Enzo Doria03/2016
44452^304902+841591785Lelio R Paula02/2016
444618^73119+6191785Lelio R Paula06/2016
4447(78557*2^304740+1)/15991739Lelio R Paula06/2014
44482^304747+7135591738Lelio R Paula02/2016
44498*3^192251+591728Lelio R Paula08/2014
44502^304674-8791717Lelio R Paula11/2012
4451(28*10^91715+701)/991716Robert Price11/2017
4452(2^304698+9)/136280995391715Lelio R Paula06/2013
4453(5*10^91707-119)/391708Robert Price04/2016
44542^304633-11277191704Enzo Doria06/2014
44559*10^91693+2391694Robert Price11/2017
44562^304578-1671391688Enzo Doria05/2013
44576^117824-1871391685Enzo Doria03/2013
4458(17^74509-1)/1691679Paul Bourdelais03/2010
4459(2^304551-7)/891223191673Lelio R Paula06/2013
4460(2^304532-3)/301391670Lelio R Paula06/2013
44612^304507-1664591666Enzo Doria04/2013
4462(29*2^304489+1)/3191661Lelio R Paula09/2013
44632^304471-183612791655Enzo Doria04/2015
44642^304433+3276991644Lelio R Paula02/2016
44652^304410-1662591637Enzo Doria04/2013
4466183^40500-291630Lelio R Paula10/2017
4467(203*10^91613+1)/391615Robert Price09/2017
44684*5^131052+791603Lelio R Paula10/2014
44692^304278-400191597Yves Minet04/2017
44702^304272-186637791595Enzo Doria03/2016
44712^304268+1968391594Lelio R Paula02/2016
44722^304162-16191562Lelio R Paula11/2012
44735*7^108331+691552Lelio R Paula10/2014
44742^304082-278782191538Enzo Doria03/2016
44752^304015+6413391518David Broadhurst06/2002
4476(7*2^303963+1)/391503Lelio R Paula09/2013
4477(2^303945-9)/361791494Lelio R Paula06/2013
44782^303930+188052791493Enzo Doria10/2016
44793^191684-6891457Lelio R Paula04/2016
4480(21*2^303813-1)/16991456Lelio R Paula02/2014
448111^87797-12091432Enzo Doria07/2012
44822^303698-184723191423Enzo Doria07/2015
4483(38^28933-1)^2-291416Norbert Schneider06/2016
44842^303554+7729991379Enzo Doria05/2016
44852^303542+1270591376Lelio R Paula02/2016
448631^61269-291375Lelio R Paula09/2013
44872^303516-6487591368Lelio R Paula02/2016
4488(24737*2^303428+1)/391345Lelio R Paula06/2014
4489(21181*2^303357+1)/3236191320Lelio R Paula06/2014
44902^303344-278696991316Enzo Doria03/2016
44916^117346+6591313Lelio R Paula05/2016
44922^303321+85591309Lelio R Paula02/2016
449312^84606+4791306Lelio R Paula06/2016
44942^303288+187431191299Enzo Doria06/2016
4495197^39788-291293Lelio R Paula10/2017
449611^87663-171091292Enzo Doria12/2012
44972^303224+253391280Henri Lifchitz05/2005
44986^117302+14391279Lelio R Paula05/2016
44993^191306-11288091277Enzo Doria07/2014
45002^303207+1291591275Lelio R Paula02/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 20 2019 09:21 (Time in France)

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