PRP Records

Probable Primes Top 10000

(224660 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 ?
40012^312562-11268594091Enzo Doria06/2014
4002137^44026-294072Lelio R Paula10/2017
40032^312404-86968810594043Lelio R Paula09/2016
40042^312387+279353394038Enzo Doria03/2016
400610^94016+9194017Robert Price04/2011
4005(15*2^312325-1)/720194017Lelio R Paula02/2014
400710^94016-18896394016Patrick De Geest08/2013
4008(17*2^312315-1)/4594016Lelio R Paula02/2014
40096^120802+766194003Mike Oakes04/2011
4010(67607*2^312254+1)/17794001Lelio R Paula06/2014
4011(11*2^312207+1)/1993984Lelio R Paula09/2013
40122^312201+5193982Lelio R Paula11/2012
4013(4*6^120749+1)/593961Serge Batalov10/2014
40143^196892+5893942Lelio R Paula05/2016
40152^312060+1891593940Lelio R Paula03/2016
401642^57867-4193933Norbert Schneider08/2018
40172^311992-1620993919Enzo Doria04/2013
4018(85^48677+1)/8693917Paul Bourdelais08/2017
40192^311965-3993911Lelio R Paula11/2012
40202^311920-11168993898Enzo Doria05/2014
40217*10^93887-4793888Robert Price02/2017
402212^86965-1393851Lelio R Paula06/2016
40232^311705+1609593833Lelio R Paula03/2016
40242^311665-8193821Lelio R Paula11/2012
4025730^32761+32761^73093806Norbert Schneider09/2017
402611^90073+9293802Lelio R Paula05/2016
40276*10^93792+4193793Robert Price01/2017
4028(2^311580+7)/59132993790Lelio R Paula06/2013
402912^86900-7793781Lelio R Paula06/2016
40302^311508-10976993774Enzo Doria04/2014
40312^311486-185962193767Enzo Doria03/2016
4032Phi(93811,10)/968129521/2109997013/3280113810431/63963778254583193765Kurt Beschorner04/2015
4033(10^93811-1)/(9*968129521*2109997013*3280113810431*639637782545831)93765Gord Palameta10/2018
40342^311471+31146993763Renaud Lifchitz01/2003
4035(88*10^93760-1)/393762Robert Price10/2017
40362^311426+7945993749Enzo Doria06/2016
40372^311294+577593709Lelio R Paula03/2016
40382^311252-101793697Lelio R Paula03/2016
40392^311247-11204193695Enzo Doria06/2014
40407*10^93692-8393693Robert Price09/2017
40412^311205-10964593683Enzo Doria04/2014
40425^134027-8493681Lelio R Paula04/2016
4043(2^311148-1017)/55793663Lelio R Paula06/2013
4044(2^311027-2^155514+1)/59362811/2006
40453^196192-2893608Robert Price12/2013
4046216091#+26143393606Makoto Morimoto12/2015
40475^133917+6893604Lelio R Paula04/2016
40482^310924-170993598Yves Minet03/2013
4049(266*10^93577-11)/393579Robert Price09/2016
4050(16*10^93577+161)/393578Robert Price05/2016
40513^196113-5693570Lelio R Paula04/2016
40522^310806-11034593562Enzo Doria05/2014
40533^196093+8693561Lelio R Paula04/2016
40542^310780-232793555Yves Minet10/2013
405530^63332+4193550Lelio R Paula08/2012
4056(21181*2^310707+1)/2193536Lelio R Paula06/2014
40578*5^133807+793528Lelio R Paula10/2014
40582^310686+819393526Lelio R Paula03/2016
40592^310646+6393514Lelio R Paula11/2012
4060(77*10^93508+31)/993509Robert Price10/2015
4061(1000907^15583+1)/100090893499Faysal YAtim04/2009
4062(2*10^93497+7)/993497Erik Branger03/2011
40633^195958-11285293496Enzo Doria07/2014
40642^310583+1638593495Lelio R Paula03/2016
4065(9913*2^310557-1)/3593490Lelio R Paula04/2015
40669*7^110614+293481Lelio R Paula11/2014
40672^310469-829593461Lelio R Paula03/2016
40682^310459-115993458Yves Minet11/2012
40696^120075-9593437Lelio R Paula05/2016
40702^310289+9832793407Yves Minet11/2010
40712^310217-11314393385Enzo Doria07/2014
40727^110494-6893379Lelio R Paula04/2016
40732^310184-11309393375Enzo Doria07/2014
40742^310180-11041793374Enzo Doria05/2014
4075gcd(V(1124905),5*F(224981)*(F(224981)-1)+1)93372Serge Batalov04/2015
40763^195669+6893358Lelio R Paula04/2016
407710^93356+9193357Robert Price04/2011
407810^93356-2831393356Patrick De Geest08/2013
4079(85*10^93346+23)/993347Robert Price11/2015
4080(3^195648-5)/315827693342Lelio R Paula04/2013
40813^195556+868093304Lelio R Paula04/2016
40822^309942-10999193302Enzo Doria04/2014
40832^309926-186730193298Enzo Doria03/2016
40842^309924+8595193297Yves Minet03/2011
40852^309896-422993288Yves Minet08/2018
4086(86*10^93263-77)/993264Robert Price05/2016
40876^119836-12593251Lelio R Paula05/2016
4088(77*10^93249-257)/993250Robert Price10/2017
40893^195430-293244Theodore Burton02/2007
4090(13*10^93236+47)/393237Robert Price01/2017
4091(67*10^93226-7)/393228Robert Price10/2017
4092(86*10^93217-221)/993218Robert Price06/2017
40932^309637-1632993211Enzo Doria04/2013
4094(41*10^93207+49)/993208Robert Price04/2016
409514^81312-5793194Lelio R Paula06/2016
409641^57783-4093192Theodore Burton02/2007
40973*10^93179-9793180Robert Price08/2017
40985*7^110252-493175Lelio R Paula11/2014
40992^309380-2793133Lelio R Paula11/2012
410023*10^93116-793118Robert Price03/2016
4101(29*10^93082+1)/393083Robert Price11/2015
4102(58*10^93062-13)/993063Robert Price09/2015
41032^309131+186938393058Enzo Doria05/2016
41042^309066-9393039Lelio R Paula11/2012
41052^309063-11326993038Enzo Doria07/2014
41063^194965+1693022Robert Price10/2013
41072^308979+186914393012Enzo Doria05/2016
41085^133064+5493008Lelio R Paula04/2016
4109(2^308905-509203)/11992988Lelio R Paula06/2013
4110(94*10^92981-49)/9992981Ray Chandler07/2011
4111(2*10^92976-17)/392976Robert Price08/2014
41122^308809+3796792961Phil Moore03/2008
4113(3^194825+5)/1165692952Lelio R Paula04/2013
4114(2^308679+5)/157392919Lelio R Paula06/2013
41152^308650+51392913Lelio R Paula02/2016
41165*7^109936+692908Lelio R Paula10/2014
41172*10^92897+8992898Robert Price07/2016
411812^86073-2992889Lelio R Paula06/2016
41192^308566-11792888Lelio R Paula11/2012
4120(17*10^92869-11)/392870Robert Price07/2015
41212^308459+7543192856Enzo Doria04/2016
41222^308426-186637792846Enzo Doria03/2016
4123(96^46831-1)/9592830Paul Bourdelais09/2017
41242^308349-11211192823Enzo Doria06/2014
41259*10^92821+1992822Robert Price05/2016
41262^308337-7592819Lelio R Paula11/2012
41274*3^194508+792805Lelio R Paula08/2014
412822*25^66379-11392796Curtis Bright05/2015
412911^89101-108092790Enzo Doria12/2012
41302^308236-186785992789Enzo Doria04/2016
413112^85963+2592770Lelio R Paula06/2016
41327^109750-6692750Lelio R Paula04/2016
41339*10^92742+1192743Robert Kinser01/2017
4134(21*2^308046-1)/885792729Lelio R Paula02/2014
41352^307997-11065592717Enzo Doria05/2014
4136L(443609)92709Renaud Lifchitz11/2003
413710^92691+992692Robert Price03/2011
413810^92691-25229192691Patrick De Geest08/2013
41392^307879-252192681Yves Minet07/2014
4140(2^307780-7)/1995966992644Lelio R Paula06/2013
414114^80831+4792643Lelio R Paula06/2016
414215^78744+9292611Lelio R Paula07/2016
414365^51083-6492610Norbert Schneider11/2014
41446^118996-1694392597Enzo Doria02/2013
4145(16*10^92591+41)/392592Robert Price10/2017
4146(3^194014-7)/292568Lelio R Paula04/2013
4147(63^51439+1)/6492555Paul Bourdelais08/2017
4148(26*10^92546-77)/392547Robert Price02/2017
41493^193954+34092540Lelio R Paula04/2016
41502^307407-307407^292539Henri Lifchitz05/2005
4151(17*10^92513-11)/392514Robert Price07/2015
41522^307318-421192512Yves Minet06/2011
41532^307280+19392501Lelio R Paula11/2012
415420^71075-3392471Lelio R Paula05/2016
41552^307126-7879592455Lelio R Paula02/2016
41562^307125-4978992454Henri Lifchitz08/2005
41572^307099+2392447Lelio R Paula11/2012
41587*10^92414-6992415Robert Price01/2017
4159(9787*2^306975-1)/212915592407Lelio R Paula04/2015
41602^306915+187337392391Enzo Doria06/2016
41612^306908+1291592389Lelio R Paula02/2016
416219^72244-8092383Lelio R Paula06/2016
41642^306849+7592371Lelio R Paula11/2012
4163(397*10^92369+53)/992371Robert Price11/2017
41652^306813-86968810592360Lelio R Paula08/2016
41662^306672-10905992318Enzo Doria04/2014
41676^118604-1706392292Enzo Doria02/2013
4168(31*2^306487-1)/229192260Lelio R Paula02/2014
41692^306467-183561192256Enzo Doria04/2015
41702^306433+7642792246Enzo Doria05/2016
41722^306430-11331392245Enzo Doria07/2014
4171(23*10^92244-59)/992245Robert Price03/2017
4173(47*2^306398+1)/138480392231Lelio R Paula04/2015
4174(25*10^92186+59)/392187Robert Price05/2016
41752^306213-28618392180Enzo Doria06/2015
417610^92178+6192179Robert Price04/2011
417710^92178-17550992178Patrick De Geest07/2013
41782^306200+118592176Lelio R Paula02/2016
41792^306153+1192162Lelio R Paula11/2012
4180(2^306141-7)/592157Lelio R Paula06/2013
4181(26*10^92152-23)/392153Robert Price08/2016
4182(2*10^92152+67)/392152Robert Price04/2017
41834*10^92099+3*7^9209992100Mike Oakes12/2010
4184115^44684+11492081Norbert Schneider07/2018
4185(2^305867-2^152934+1)/59207511/2006
41862^305851-10949592071Enzo Doria04/2014
418712^85300+3592055Lelio R Paula06/2016
41883^192911+9292042Lelio R Paula04/2016
41892^305723-27627192032Enzo Doria07/2015
41902^305676+9392018Donovan Johnson06/2008
41913^192819+491999Lelio R Paula04/2013
4192(38*10^91997-83)/9991997Ray Chandler07/2011
41932^305539+7291191977Enzo Doria04/2016
4194(2^305427-5)/129799821391934Lelio R Paula06/2013
419585^47642+8491922Norbert Schneider10/2015
419610^91920+18765191921Patrick De Geest07/2013
419710^91920-3991920Robert Price05/2011
4198(22*10^91903+41)/991904Robert Price02/2015
42002^305275-2791897Lelio R Paula11/2012
41993^192607-772691897Enzo Doria05/2014
4201(7*10^91856-61)/991856Erik Branger12/2009
4202(89*10^91839-53)/991840Robert Price11/2015
42038*5^131351+791812Lelio R Paula10/2014
42043^192426-6891811Lelio R Paula04/2016
42052^304973+11791807Lelio R Paula11/2012
42062^304939-186372791796Enzo Doria03/2016
42072^304902+841591785Lelio R Paula02/2016
420818^73119+6191785Lelio R Paula06/2016
4209(78557*2^304740+1)/15991739Lelio R Paula06/2014
42102^304747+7135591738Lelio R Paula02/2016
42118*3^192251+591728Lelio R Paula08/2014
42122^304674-8791717Lelio R Paula11/2012
4213(28*10^91715+701)/991716Robert Price11/2017
4214(2^304698+9)/136280995391715Lelio R Paula06/2013
4215(5*10^91707-119)/391708Robert Price04/2016
42162^304633-11277191704Enzo Doria06/2014
42179*10^91693+2391694Robert Price11/2017
42182^304578-1671391688Enzo Doria05/2013
42196^117824-1871391685Enzo Doria03/2013
4220(17^74509-1)/1691679Paul Bourdelais03/2010
4221(2^304551-7)/891223191673Lelio R Paula06/2013
4222(2^304532-3)/301391670Lelio R Paula06/2013
42232^304507-1664591666Enzo Doria04/2013
4224(29*2^304489+1)/3191661Lelio R Paula09/2013
42252^304471-183612791655Enzo Doria04/2015
42262^304433+3276991644Lelio R Paula02/2016
42272^304410-1662591637Enzo Doria04/2013
4228183^40500-291630Lelio R Paula10/2017
4229(203*10^91613+1)/391615Robert Price09/2017
42304*5^131052+791603Lelio R Paula10/2014
42312^304278-400191597Yves Minet04/2017
42322^304272-186637791595Enzo Doria03/2016
42332^304268+1968391594Lelio R Paula02/2016
42342^304162-16191562Lelio R Paula11/2012
42355*7^108331+691552Lelio R Paula10/2014
42362^304082-278782191538Enzo Doria03/2016
42372^304015+6413391518David Broadhurst06/2002
4238(7*2^303963+1)/391503Lelio R Paula09/2013
4239(2^303945-9)/361791494Lelio R Paula06/2013
42402^303930+188052791493Enzo Doria10/2016
42413^191684-6891457Lelio R Paula04/2016
4242(21*2^303813-1)/16991456Lelio R Paula02/2014
424311^87797-12091432Enzo Doria07/2012
42442^303698-184723191423Enzo Doria07/2015
4245(38^28933-1)^2-291416Norbert Schneider06/2016
42462^303554+7729991379Enzo Doria05/2016
42472^303542+1270591376Lelio R Paula02/2016
424831^61269-291375Lelio R Paula09/2013
42492^303516-6487591368Lelio R Paula02/2016
4250(24737*2^303428+1)/391345Lelio R Paula06/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 15 2018 21:33 (Time in France)

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