PRP Records

Probable Primes Top 10000

(218736 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 ?
40017^110494-6893379Lelio R Paula04/2016
40022^310184-11309393375Enzo Doria07/2014
40032^310180-11041793374Enzo Doria05/2014
4004gcd(V(1124905),5*F(224981)*(F(224981)-1)+1)93372Serge Batalov04/2015
40053^195669+6893358Lelio R Paula04/2016
400610^93356+9193357Robert Price04/2011
400710^93356-2831393356Patrick De Geest08/2013
4008(85*10^93346+23)/993347Robert Price11/2015
4009(3^195648-5)/315827693342Lelio R Paula04/2013
40103^195556+868093304Lelio R Paula04/2016
40112^309942-10999193302Enzo Doria04/2014
40122^309926-186730193298Enzo Doria03/2016
40132^309924+8595193297Yves Minet03/2011
40142^309896-422993288Yves Minet08/2018
4015(86*10^93263-77)/993264Robert Price05/2016
40166^119836-12593251Lelio R Paula05/2016
4017(77*10^93249-257)/993250Robert Price10/2017
40183^195430-293244Theodore Burton02/2007
4019(13*10^93236+47)/393237Robert Price01/2017
4020(67*10^93226-7)/393228Robert Price10/2017
4021(86*10^93217-221)/993218Robert Price06/2017
40222^309637-1632993211Enzo Doria04/2013
4023(41*10^93207+49)/993208Robert Price04/2016
402414^81312-5793194Lelio R Paula06/2016
402541^57783-4093192Theodore Burton02/2007
40263*10^93179-9793180Robert Price08/2017
40275*7^110252-493175Lelio R Paula11/2014
40282^309380-2793133Lelio R Paula11/2012
402923*10^93116-793118Robert Price03/2016
4030(29*10^93082+1)/393083Robert Price11/2015
4031(58*10^93062-13)/993063Robert Price09/2015
40322^309131+186938393058Enzo Doria05/2016
40332^309066-9393039Lelio R Paula11/2012
40342^309063-11326993038Enzo Doria07/2014
40353^194965+1693022Robert Price10/2013
40362^308979+186914393012Enzo Doria05/2016
40375^133064+5493008Lelio R Paula04/2016
4038(2^308905-509203)/11992988Lelio R Paula06/2013
4039(94*10^92981-49)/9992981Ray Chandler07/2011
4040(2*10^92976-17)/392976Robert Price08/2014
40412^308809+3796792961Phil Moore03/2008
4042(3^194825+5)/1165692952Lelio R Paula04/2013
4043(2^308679+5)/157392919Lelio R Paula06/2013
40442^308650+51392913Lelio R Paula02/2016
40455*7^109936+692908Lelio R Paula10/2014
40462*10^92897+8992898Robert Price07/2016
404712^86073-2992889Lelio R Paula06/2016
40482^308566-11792888Lelio R Paula11/2012
4049(17*10^92869-11)/392870Robert Price07/2015
40502^308459+7543192856Enzo Doria04/2016
40512^308426-186637792846Enzo Doria03/2016
4052(96^46831-1)/9592830Paul Bourdelais09/2017
40532^308349-11211192823Enzo Doria06/2014
40549*10^92821+1992822Robert Price05/2016
40552^308337-7592819Lelio R Paula11/2012
40564*3^194508+792805Lelio R Paula08/2014
405722*25^66379-11392796Curtis Bright05/2015
405811^89101-108092790Enzo Doria12/2012
40592^308236-186785992789Enzo Doria04/2016
406012^85963+2592770Lelio R Paula06/2016
40617^109750-6692750Lelio R Paula04/2016
40629*10^92742+1192743Robert Kinser01/2017
4063(21*2^308046-1)/885792729Lelio R Paula02/2014
40642^307997-11065592717Enzo Doria05/2014
4065L(443609)92709Renaud Lifchitz11/2003
406610^92691+992692Robert Price03/2011
406710^92691-25229192691Patrick De Geest08/2013
40682^307879-252192681Yves Minet07/2014
4069(2^307780-7)/1995966992644Lelio R Paula06/2013
407014^80831+4792643Lelio R Paula06/2016
407115^78744+9292611Lelio R Paula07/2016
407265^51083-6492610Norbert Schneider11/2014
40736^118996-1694392597Enzo Doria02/2013
4074(16*10^92591+41)/392592Robert Price10/2017
4075(3^194014-7)/292568Lelio R Paula04/2013
4076(63^51439+1)/6492555Paul Bourdelais08/2017
4077(26*10^92546-77)/392547Robert Price02/2017
40783^193954+34092540Lelio R Paula04/2016
40792^307407-307407^292539Henri Lifchitz05/2005
4080(17*10^92513-11)/392514Robert Price07/2015
40812^307318-421192512Yves Minet06/2011
40822^307280+19392501Lelio R Paula11/2012
408320^71075-3392471Lelio R Paula05/2016
40842^307126-7879592455Lelio R Paula02/2016
40852^307125-4978992454Henri Lifchitz08/2005
40862^307099+2392447Lelio R Paula11/2012
40877*10^92414-6992415Robert Price01/2017
4088(9787*2^306975-1)/212915592407Lelio R Paula04/2015
40892^306915+187337392391Enzo Doria06/2016
40902^306908+1291592389Lelio R Paula02/2016
409119^72244-8092383Lelio R Paula06/2016
40922^306849+7592371Lelio R Paula11/2012
4093(397*10^92369+53)/992371Robert Price11/2017
40942^306813-86968810592360Lelio R Paula08/2016
40952^306672-10905992318Enzo Doria04/2014
40966^118604-1706392292Enzo Doria02/2013
4097(31*2^306487-1)/229192260Lelio R Paula02/2014
40982^306467-183561192256Enzo Doria04/2015
40992^306433+7642792246Enzo Doria05/2016
41012^306430-11331392245Enzo Doria07/2014
4100(23*10^92244-59)/992245Robert Price03/2017
4102(47*2^306398+1)/138480392231Lelio R Paula04/2015
4103(25*10^92186+59)/392187Robert Price05/2016
41042^306213-28618392180Enzo Doria06/2015
410510^92178+6192179Robert Price04/2011
410610^92178-17550992178Patrick De Geest07/2013
41072^306200+118592176Lelio R Paula02/2016
41082^306153+1192162Lelio R Paula11/2012
4109(2^306141-7)/592157Lelio R Paula06/2013
4110(26*10^92152-23)/392153Robert Price08/2016
4111(2*10^92152+67)/392152Robert Price04/2017
41124*10^92099+3*7^9209992100Mike Oakes12/2010
4113115^44684+11492081Norbert Schneider07/2018
4114(2^305867-2^152934+1)/59207511/2006
41152^305851-10949592071Enzo Doria04/2014
411612^85300+3592055Lelio R Paula06/2016
41173^192911+9292042Lelio R Paula04/2016
41182^305723-27627192032Enzo Doria07/2015
41192^305676+9392018Donovan Johnson06/2008
41203^192819+491999Lelio R Paula04/2013
4121(38*10^91997-83)/9991997Ray Chandler07/2011
41222^305539+7291191977Enzo Doria04/2016
4123(2^305427-5)/129799821391934Lelio R Paula06/2013
412485^47642+8491922Norbert Schneider10/2015
412510^91920+18765191921Patrick De Geest07/2013
412610^91920-3991920Robert Price05/2011
4127(22*10^91903+41)/991904Robert Price02/2015
41292^305275-2791897Lelio R Paula11/2012
41283^192607-772691897Enzo Doria05/2014
4130(7*10^91856-61)/991856Erik Branger12/2009
4131(89*10^91839-53)/991840Robert Price11/2015
41328*5^131351+791812Lelio R Paula10/2014
41333^192426-6891811Lelio R Paula04/2016
41342^304973+11791807Lelio R Paula11/2012
41352^304939-186372791796Enzo Doria03/2016
41362^304902+841591785Lelio R Paula02/2016
413718^73119+6191785Lelio R Paula06/2016
4138(78557*2^304740+1)/15991739Lelio R Paula06/2014
41392^304747+7135591738Lelio R Paula02/2016
41408*3^192251+591728Lelio R Paula08/2014
41412^304674-8791717Lelio R Paula11/2012
4142(28*10^91715+701)/991716Robert Price11/2017
4143(2^304698+9)/136280995391715Lelio R Paula06/2013
4144(5*10^91707-119)/391708Robert Price04/2016
41452^304633-11277191704Enzo Doria06/2014
41469*10^91693+2391694Robert Price11/2017
41472^304578-1671391688Enzo Doria05/2013
41486^117824-1871391685Enzo Doria03/2013
4149(17^74509-1)/1691679Paul Bourdelais03/2010
4150(2^304551-7)/891223191673Lelio R Paula06/2013
4151(2^304532-3)/301391670Lelio R Paula06/2013
41522^304507-1664591666Enzo Doria04/2013
4153(29*2^304489+1)/3191661Lelio R Paula09/2013
41542^304471-183612791655Enzo Doria04/2015
41552^304433+3276991644Lelio R Paula02/2016
41562^304410-1662591637Enzo Doria04/2013
4157183^40500-291630Lelio R Paula10/2017
4158(203*10^91613+1)/391615Robert Price09/2017
41594*5^131052+791603Lelio R Paula10/2014
41602^304278-400191597Yves Minet04/2017
41612^304272-186637791595Enzo Doria03/2016
41622^304268+1968391594Lelio R Paula02/2016
41632^304162-16191562Lelio R Paula11/2012
41645*7^108331+691552Lelio R Paula10/2014
41652^304082-278782191538Enzo Doria03/2016
41662^304015+6413391518David Broadhurst06/2002
4167(7*2^303963+1)/391503Lelio R Paula09/2013
4168(2^303945-9)/361791494Lelio R Paula06/2013
41692^303930+188052791493Enzo Doria10/2016
41703^191684-6891457Lelio R Paula04/2016
4171(21*2^303813-1)/16991456Lelio R Paula02/2014
417211^87797-12091432Enzo Doria07/2012
41732^303698-184723191423Enzo Doria07/2015
4174(38^28933-1)^2-291416Norbert Schneider06/2016
41752^303554+7729991379Enzo Doria05/2016
41762^303542+1270591376Lelio R Paula02/2016
417731^61269-291375Lelio R Paula09/2013
41782^303516-6487591368Lelio R Paula02/2016
4179(24737*2^303428+1)/391345Lelio R Paula06/2014
4180(21181*2^303357+1)/3236191320Lelio R Paula06/2014
41812^303344-278696991316Enzo Doria03/2016
41826^117346+6591313Lelio R Paula05/2016
41832^303321+85591309Lelio R Paula02/2016
418412^84606+4791306Lelio R Paula06/2016
41852^303288+187431191299Enzo Doria06/2016
4186197^39788-291293Lelio R Paula10/2017
418711^87663-171091292Enzo Doria12/2012
41882^303224+253391280Henri Lifchitz05/2005
41896^117302+14391279Lelio R Paula05/2016
41903^191306-11288091277Enzo Doria07/2014
41912^303207+1291591275Lelio R Paula02/2016
41922^303191-11125991270Enzo Doria05/2014
419310^91230+9^(91230+1)91231Robert Price08/2016
419410^91230+792191231Patrick De Geest11/2016
419510^91230-91114191230Patrick De Geest11/2016
41966^117232-1742391225Enzo Doria02/2013
41977*10^91215+391216Erik Branger11/2009
419897*10^91205-391207Robert Price01/2017
41992^302979-16118191206Enzo Doria04/2013
42002^302949+8191197Henri Lifchitz02/2007
42014*6^117192-591194Lelio R Paula10/2014
42022^302918+9991188Lelio R Paula11/2012
42032^302797+186958791151Enzo Doria05/2016
4204265^37614+37614^26591148Norbert Schneider01/2015
42057^107852+8291146Lelio R Paula04/2016
4206(38*10^91144-11)/991145Robert Price05/2015
4207(55*10^91142+377)/991143Robert Price10/2017
4208249^38030+38030^24991128Norbert Schneider01/2015
42096^117094-21104991117Mike Oakes05/2011
42102^302602-186718191093Enzo Doria03/2016
4211(1017*2^302592-1)/5391091Lelio R Paula04/2015
421215^77445-1691083Lelio R Paula07/2016
42132^302505+8191064Henri Lifchitz02/2007
42142^302496-11234991061Enzo Doria06/2014
421517^73999-7291052Lelio R Paula07/2016
4216(16*10^91032+41)/391033Robert Price10/2017
42172^302332+57729457591012Lelio R Paula08/2016
42182^302274+7420990994Enzo Doria04/2016
4219(311^36497-1)/31090976Eric Chen09/2017
4220(3^190668+2)/8990970Lelio R Paula04/2013
42212^302188+9019590968Lelio R Paula02/2016
4222(53*10^90965-71)/990966Robert Price09/2015
42232^302113+7410590946Enzo Doria04/2016
42242^302102-655590942Lelio R Paula02/2016
4225156*(10^(4*22731)-1)/101-190925Robert Price05/2014
42263^190568+3890925Lelio R Paula04/2016
42272^302009-1644990914Enzo Doria04/2013
4228(17*2^301951-1)/16590896Lelio R Paula02/2014
42293^190497+7490891Lelio R Paula04/2016
4230(24737*2^301896+1)/39990882Lelio R Paula06/2014
423118^72397+8990878Lelio R Paula06/2016
42326^116769-4790864Lelio R Paula05/2016
42332^301712-46590825Lelio R Paula02/2016
42342^301693-6990819Lelio R Paula11/2012
42352^301683-301683^290816Henri Lifchitz05/2005
423611^87187-171090796Enzo Doria12/2012
42375*10^90793+2190794Robert Price01/2017
4238(22*10^90792-13)/990793Robert Price03/2015
42392^301591-161590788Lelio R Paula02/2016
4240(52^52901+1)/5390777Paul Bourdelais08/2017
42412^301546-10903790775Enzo Doria04/2014
424214^79195-390768Lelio R Paula06/2016
42432^301517-186169390766Enzo Doria11/2015
42442^301460-17390749Lelio R Paula11/2012
4245(85*10^90745-103)/990746Robert Price10/2017
42462^301312-8990704Lelio R Paula11/2012
42472^301285-12990696Lelio R Paula11/2012
42482^301282-10999190695Enzo Doria04/2014
42492^301228-185426990679Enzo Doria09/2015
4250(151*10^90669-1)/390671Robert Price04/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 14 2018 21:45 (Time in France)

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