PRP Records

Probable Primes Top 10000

(205869 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 ?
40016^117824-1871391685Enzo Doria03/2013
4002(17^74509-1)/1691679Paul Bourdelais03/2010
4003(2^304551-7)/891223191673Lelio R Paula06/2013
4004(2^304532-3)/301391670Lelio R Paula06/2013
40052^304507-1664591666Enzo Doria04/2013
4006(29*2^304489+1)/3191661Lelio R Paula09/2013
40072^304471-183612791655Enzo Doria04/2015
40082^304433+3276991644Lelio R Paula02/2016
40092^304410-1662591637Enzo Doria04/2013
4010183^40500-291630Lelio R Paula10/2017
4011(203*10^91613+1)/391615Robert Price09/2017
40124*5^131052+791603Lelio R Paula10/2014
40132^304278-400191597Yves Minet04/2017
40142^304272-186637791595Enzo Doria03/2016
40152^304268+1968391594Lelio R Paula02/2016
40162^304162-16191562Lelio R Paula11/2012
40175*7^108331+691552Lelio R Paula10/2014
40182^304082-278782191538Enzo Doria03/2016
40192^304015+6413391518David Broadhurst06/2002
4020(7*2^303963+1)/391503Lelio R Paula09/2013
4021(2^303945-9)/361791494Lelio R Paula06/2013
40222^303930+188052791493Enzo Doria10/2016
40233^191684-6891457Lelio R Paula04/2016
4024(21*2^303813-1)/16991456Lelio R Paula02/2014
402511^87797-12091432Enzo Doria07/2012
40262^303698-184723191423Enzo Doria07/2015
4027(38^28933-1)^2-291416Norbert Schneider06/2016
40282^303554+7729991379Enzo Doria05/2016
40292^303542+1270591376Lelio R Paula02/2016
403031^61269-291375Lelio R Paula09/2013
40312^303516-6487591368Lelio R Paula02/2016
4032(24737*2^303428+1)/391345Lelio R Paula06/2014
4033(21181*2^303357+1)/3236191320Lelio R Paula06/2014
40342^303344-278696991316Enzo Doria03/2016
40356^117346+6591313Lelio R Paula05/2016
40362^303321+85591309Lelio R Paula02/2016
403712^84606+4791306Lelio R Paula06/2016
40382^303288+187431191299Enzo Doria06/2016
4039197^39788-291293Lelio R Paula10/2017
404011^87663-171091292Enzo Doria12/2012
40412^303224+253391280Henri Lifchitz05/2005
40426^117302+14391279Lelio R Paula05/2016
40433^191306-11288091277Enzo Doria07/2014
40442^303207+1291591275Lelio R Paula02/2016
40452^303191-11125991270Enzo Doria05/2014
404610^91230+9^(91230+1)91231Robert Price08/2016
404710^91230+792191231Patrick De Geest11/2016
404810^91230-91114191230Patrick De Geest11/2016
40496^117232-1742391225Enzo Doria02/2013
40507*10^91215+391216Erik Branger11/2009
405197*10^91205-391207Robert Price01/2017
40522^302979-16118191206Enzo Doria04/2013
40532^302949+8191197Henri Lifchitz02/2007
40544*6^117192-591194Lelio R Paula10/2014
40552^302918+9991188Lelio R Paula11/2012
40562^302797+186958791151Enzo Doria05/2016
4057265^37614+37614^26591148Norbert Schneider01/2015
40587^107852+8291146Lelio R Paula04/2016
4059(38*10^91144-11)/991145Robert Price05/2015
4060(55*10^91142+377)/991143Robert Price10/2017
4061249^38030+38030^24991128Norbert Schneider01/2015
40626^117094-21104991117Mike Oakes05/2011
40632^302602-186718191093Enzo Doria03/2016
4064(1017*2^302592-1)/5391091Lelio R Paula04/2015
406515^77445-1691083Lelio R Paula07/2016
40662^302505+8191064Henri Lifchitz02/2007
40672^302496-11234991061Enzo Doria06/2014
406817^73999-7291052Lelio R Paula07/2016
4069(16*10^91032+41)/391033Robert Price10/2017
40702^302332+57729457591012Lelio R Paula08/2016
40712^302274+7420990994Enzo Doria04/2016
4072(311^36497-1)/31090976Eric Chen09/2017
4073(3^190668+2)/8990970Lelio R Paula04/2013
40742^302188+9019590968Lelio R Paula02/2016
4075(53*10^90965-71)/990966Robert Price09/2015
40762^302113+7410590946Enzo Doria04/2016
40772^302102-655590942Lelio R Paula02/2016
4078156*(10^(4*22731)-1)/101-190925Robert Price05/2014
40793^190568+3890925Lelio R Paula04/2016
40802^302009-1644990914Enzo Doria04/2013
4081(17*2^301951-1)/16590896Lelio R Paula02/2014
40823^190497+7490891Lelio R Paula04/2016
4083(24737*2^301896+1)/39990882Lelio R Paula06/2014
408418^72397+8990878Lelio R Paula06/2016
40856^116769-4790864Lelio R Paula05/2016
40862^301712-46590825Lelio R Paula02/2016
40872^301693-6990819Lelio R Paula11/2012
40882^301683-301683^290816Henri Lifchitz05/2005
408911^87187-171090796Enzo Doria12/2012
40905*10^90793+2190794Robert Price01/2017
4091(22*10^90792-13)/990793Robert Price03/2015
40922^301591-161590788Lelio R Paula02/2016
4093(52^52901+1)/5390777Paul Bourdelais08/2017
40942^301546-10903790775Enzo Doria04/2014
409514^79195-390768Lelio R Paula06/2016
40962^301517-186169390766Enzo Doria11/2015
40972^301460-17390749Lelio R Paula11/2012
4098(85*10^90745-103)/990746Robert Price10/2017
40992^301312-8990704Lelio R Paula11/2012
41002^301285-12990696Lelio R Paula11/2012
41012^301282-10999190695Enzo Doria04/2014
41022^301228-185426990679Enzo Doria09/2015
4103(151*10^90669-1)/390671Robert Price04/2017
4104(32*10^90669+13)/990670Robert Price04/2015
41053*5^129698+890656Lelio R Paula10/2014
4106F(433781)90655Henri Lifchitz09/2003
410719^70891+8290653Lelio R Paula06/2016
4108(29*2^301124-1)/1390648Lelio R Paula02/2014
41097*3^189953-890632Lelio R Paula08/2014
411011^87022-180090625Enzo Doria12/2012
4111(2^301042+47)/1203696990616Lelio R Paula06/2013
41122^301004-278693990612Enzo Doria03/2016
41132^300980-2790605Lelio R Paula11/2012
41142*10^90597-790598Dmitry Domanov11/2010
4115197^39485+290597Lelio R Paula06/2013
41167^107198+4890593Lelio R Paula04/2016
4117(86*10^90588+121)/990589Robert Price03/2017
41182^300923+5390587Lelio R Paula11/2012
41192^300874+790573Lelio R Paula10/2012
41205^129568-5690565Lelio R Paula04/2016
41212^300847-11283190564Enzo Doria06/2014
41222^300718+25525590526Lelio R Paula02/2016
41232^300637+9590501Lelio R Paula11/2012
41247^107087-2490500Lelio R Paula04/2016
4125(10^90499+3^90499)/1390498Robert Price01/2013
412613^81241+9090498Lelio R Paula06/2016
41276^116273-8590478Lelio R Paula05/2016
41286^116256-1757390465Enzo Doria02/2013
41292^300502+5461590461Lelio R Paula02/2016
4130(13*2^300487+1)/4590456Lelio R Paula09/2013
4131(3^189545-8)/590436Lelio R Paula01/2013
4132(7*2^300406-1)/390432Lelio R Paula02/2014
41334*5^129332+390400Lelio R Paula10/2014
41342^300249-1624590384Enzo Doria04/2013
4135(7*10^90371-313)/990371Robert Price11/2016
41362*6^116118+790358Lelio R Paula10/2014
4137(24737*2^300101+1)/2590343Lelio R Paula06/2014
41384*10^90334-2190335Robert Price04/2016
41392^300019-11033590315Enzo Doria05/2014
41402^299949-100590294Lelio R Paula11/2013
41412^299868-10961390270Enzo Doria04/2014
41425*2^299799-390250Lelio R Paula08/2014
414313^81008-290239Lelio R Paula09/2013
414464^49957-63^4995790232Robert Price07/2013
414510^90227+5628190228Patrick De Geest06/2016
41482^299725+31590227Lelio R Paula11/2013
414610^90227-100000000190227Robert Price05/2016
414710^90227-6876390227Patrick De Geest06/2016
41495^129082+4890225Lelio R Paula03/2016
41502^299699+19590219Lelio R Paula10/2012
4151(55*10^90211-1)/990212Ray Chandler02/2012
41523^189053+28090202Lelio R Paula04/2016
41532^299639-18790201Lelio R Paula10/2012
41542^299631+18390198Lelio R Paula10/2012
4155(21*2^299611-1)/2990192Lelio R Paula02/2014
41562^299567+11390179Lelio R Paula10/2012
41572^299550+18990174Lelio R Paula10/2012
4158(2^299535+3)/2990168Lelio R Paula01/2013
4159(97*10^90155-1)/390157Serge Batalov12/2014
41603^188938+868090147Lelio R Paula04/2016
41616^115840-5590142Lelio R Paula05/2016
4162(5*10^90142-473)/990142Robert Price12/2017
41638*7^106659+590139Lelio R Paula10/2014
41642^299406-1665390131Enzo Doria05/2013
4165208049#+(216091#)/(208049#)90128Makoto Morimoto04/2016
4166(F(5)^128941-F(4)^128941)/F(3)90126Wayne Halsdorf03/2012
41676^115819-5390125Lelio R Paula05/2016
41686^115816-1685390123Enzo Doria02/2013
41696^115813-2390121Lelio R Paula05/2016
4170(22*10^90110+161)/390111Robert Price02/2017
4171(2^299330-509203)/6990106Lelio R Paula01/2013
4172(29*10^90096-17)/390097Erik Branger09/2014
41732^299247+187052990083Enzo Doria05/2016
41742^299229-279778390077Enzo Doria04/2016
41752^299220-1631790075Enzo Doria04/2013
417611^86491-135090072Enzo Doria12/2012
4177(31*10^90064-1)/390066Robert Price03/2017
4178L(430949)/861899/144038756153990045Serge Batalov07/2017
41792^299112+7395190042Enzo Doria04/2016
41808^99702+7^(99702-1)90040Robert Price02/2016
41815*10^90033+390034Dmitry Domanov11/2010
4182243^37738+37738^24390029Norbert Schneider01/2015
41832^299048-11329790023Enzo Doria07/2014
41843^188648+9290008Lelio R Paula12/2015
41855*2^298991+790006Lelio R Paula08/2014
4186(25*2^298997+1)/326790005Lelio R Paula01/2013
418710^90000+886990001Patrick De Geest12/2009
418910^89999+8293990000Dirk Augustin04/2007
418810^90000-14034390000Patrick De Geest12/2009
419010^89999-19489189999Patrick De Geest11/2009
419119^70365-7889980Lelio R Paula12/2015
4192NaturalLogarithmOf2(89973)89973Eric W. Weisstein10/2015
41932^298852-6487589964Lelio R Paula11/2013
419418^71659+3789952Lelio R Paula12/2015
4195(2908*29^61501-3)/789942Curtis Bright05/2015
419617^73067+2089906Lelio R Paula11/2015
41972^298637-9989899Lelio R Paula10/2012
41989^94188+3*8^94188-2*4^94188-3*2^9418889879Mike Oakes01/2011
41999*10^89858+1989859Robert Price05/2016
42002^298501+187006789858Enzo Doria05/2016
420111^86280-9889852Lelio R Paula11/2015
42022^298473-11005989850Enzo Doria04/2014
420319^70263-3289850Lelio R Paula12/2015
4204(299*10^89836-17)/389838Robert Price01/2017
42053^188286+1489836Robert Price09/2013
4206gcd(V(1091095),5*F(218219)*(F(218219)+1)+1)89822Serge Batalov04/2015
42072^298367+5890589818Lelio R Paula11/2013
42082^298319-10965789803Enzo Doria04/2014
42098*10^89800+8189801Robert Price05/2017
421018^71505-9189759Lelio R Paula12/2015
4211(7^106187+1)/889738Paul Bourdelais04/2008
42122^298079-10953189731Enzo Doria04/2014
4213(22699*2^298016+1)/38589714Lelio R Paula06/2014
4214156*(10^(4*22427)-1)/101-189709Robert Price05/2014
42152^298003-6694589708Lelio R Paula11/2013
4216(23*10^89705-83)/389706Robert Price09/2017
421717^72900-5489700Lelio R Paula11/2015
42183*2^297956+589695Lelio R Paula08/2014
421920^68938-1189691Lelio R Paula01/2016
422089*10^89687-789689Robert Price03/2017
42212^297923+7778389684Enzo Doria05/2016
422211^86107-2457600089672Enzo Doria02/2013
42232^297878-11191189671Enzo Doria05/2014
42247^106084+4089652Lelio R Paula10/2015
4225(86*10^89640-311)/989641Robert Price10/2017
42263*10^89608-5989609Robert Price10/2017
42273^187780-1103889594Enzo Doria05/2014
4228(13*2^297560-1)/4915178789568Lelio R Paula02/2014
42295^128141-3689567Lelio R Paula10/2015
42304*7^105951+989540Lelio R Paula10/2014
4231(7*10^89539-439)/989539Robert Price09/2017
42322^297397+17725789526Enzo Doria05/2016
42342^297346-1624189511Enzo Doria04/2013
4233(5*10^89510+79)/389511Robert Price11/2017
42364^148663-3^14866389505Jean-Louis Charton11/2005
42352^297328-86968810589505Lelio R Paula07/2016
42372^297325-45904389504Enzo Doria05/2015
42382^297310-11239189500Enzo Doria06/2014
42392^297296-11215789496Enzo Doria06/2014
424057^50966-289490Lelio R Paula08/2013
4241(266*10^89482+1)/389484Robert Price02/2016
4242(14*10^89480-101)/389481Robert Price04/2017
42432^297122+9989443Lelio R Paula10/2012
4244(3^187435-5)/128689427Lelio R Paula01/2013
4245(25*10^89413+161)/389414Robert Price01/2017
42462^296990+187069989403Enzo Doria05/2016
42472^296972-101789398Lelio R Paula11/2013
4248(7*10^89383+167)/389384Robert Kinser10/2017
4249(85*10^89375-31)/989376Robert Price11/2015
42509*2^296870+789368Lelio R Paula08/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 22 2018 09:48 (Time in France)

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