PRP Records

Probable Primes Top 10000

(172213 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 ?
3501(26*10^92546-77)/392547Robert Price02/2017
35023^193954+34092540Lelio R Paula04/2016
35032^307407-307407^292539Henri Lifchitz05/2005
3504(17*10^92513-11)/392514Robert Price07/2015
35052^307318-421192512Yves Minet06/2011
35062^307280+19392501Lelio R Paula11/2012
350720^71075-3392471Lelio R Paula05/2016
35082^307126-7879592455Lelio R Paula02/2016
35092^307125-4978992454Henri Lifchitz08/2005
35102^307099+2392447Lelio R Paula11/2012
35117*10^92414-6992415Robert Price01/2017
3512(9787*2^306975-1)/212915592407Lelio R Paula04/2015
35132^306915+187337392391Enzo Doria06/2016
35142^306908+1291592389Lelio R Paula02/2016
351519^72244-8092383Lelio R Paula06/2016
35162^306849+7592371Lelio R Paula11/2012
35172^306813-86968810592360Lelio R Paula08/2016
35182^306672-10905992318Enzo Doria04/2014
35196^118604-1706392292Enzo Doria02/2013
3520(31*2^306487-1)/229192260Lelio R Paula02/2014
35212^306467-183561192256Enzo Doria04/2015
35222^306433+7642792246Enzo Doria05/2016
35242^306430-11331392245Enzo Doria07/2014
3523(23*10^92244-59)/992245Robert Price03/2017
3525(47*2^306398+1)/138480392231Lelio R Paula04/2015
3526(25*10^92186+59)/392187Robert Price05/2016
35272^306213-28618392180Enzo Doria06/2015
352810^92178+6192179Robert Price04/2011
352910^92178-17550992178Patrick De Geest07/2013
35302^306200+118592176Lelio R Paula02/2016
35312^306153+1192162Lelio R Paula11/2012
3532(2^306141-7)/592157Lelio R Paula06/2013
3533(26*10^92152-23)/392153Robert Price08/2016
35344*10^92099+3*7^9209992100Mike Oakes12/2010
3535(2^305867-2^152934+1)/59207511/2006
35362^305851-10949592071Enzo Doria04/2014
353712^85300+3592055Lelio R Paula06/2016
35383^192911+9292042Lelio R Paula04/2016
35392^305723-27627192032Enzo Doria07/2015
35402^305676+9392018Donovan Johnson06/2008
35413^192819+491999Lelio R Paula04/2013
3542(38*10^91997-83)/9991997Ray Chandler07/2011
35432^305539+7291191977Enzo Doria04/2016
3544(2^305427-5)/129799821391934Lelio R Paula06/2013
354585^47642+8491922Norbert Schneider10/2015
354610^91920+18765191921Patrick De Geest07/2013
354710^91920-3991920Robert Price05/2011
3548(22*10^91903+41)/991904Robert Price02/2015
35502^305275-2791897Lelio R Paula11/2012
35493^192607-772691897Enzo Doria05/2014
3551(7*10^91856-61)/991856Erik Branger12/2009
3552(89*10^91839-53)/991840Robert Price11/2015
35538*5^131351+791812Lelio R Paula10/2014
35543^192426-6891811Lelio R Paula04/2016
35552^304973+11791807Lelio R Paula11/2012
35562^304939-186372791796Enzo Doria03/2016
35572^304902+841591785Lelio R Paula02/2016
355818^73119+6191785Lelio R Paula06/2016
3559(78557*2^304740+1)/15991739Lelio R Paula06/2014
35602^304747+7135591738Lelio R Paula02/2016
35618*3^192251+591728Lelio R Paula08/2014
35622^304674-8791717Lelio R Paula11/2012
3563(2^304698+9)/136280995391715Lelio R Paula06/2013
3564(5*10^91707-119)/391708Robert Price04/2016
35652^304633-11277191704Enzo Doria06/2014
35662^304578-1671391688Enzo Doria05/2013
35676^117824-1871391685Enzo Doria03/2013
3568(17^74509-1)/1691679Paul Bourdelais03/2010
3569(2^304551-7)/891223191673Lelio R Paula06/2013
3570(2^304532-3)/301391670Lelio R Paula06/2013
35712^304507-1664591666Enzo Doria04/2013
3572(29*2^304489+1)/3191661Lelio R Paula09/2013
35732^304471-183612791655Enzo Doria04/2015
35742^304433+3276991644Lelio R Paula02/2016
35752^304410-1662591637Enzo Doria04/2013
35764*5^131052+791603Lelio R Paula10/2014
35772^304272-186637791595Enzo Doria03/2016
35782^304268+1968391594Lelio R Paula02/2016
35792^304162-16191562Lelio R Paula11/2012
35805*7^108331+691552Lelio R Paula10/2014
35812^304082-278782191538Enzo Doria03/2016
35822^304015+6413391518David Broadhurst06/2002
3583(7*2^303963+1)/391503Lelio R Paula09/2013
3584(2^303945-9)/361791494Lelio R Paula06/2013
35852^303930+188052791493Enzo Doria10/2016
35863^191684-6891457Lelio R Paula04/2016
3587(21*2^303813-1)/16991456Lelio R Paula02/2014
358811^87797-12091432Enzo Doria07/2012
35892^303698-184723191423Enzo Doria07/2015
3590(38^28933-1)^2-291416Norbert Schneider06/2016
35912^303554+7729991379Enzo Doria05/2016
35922^303542+1270591376Lelio R Paula02/2016
359331^61269-291375Lelio R Paula09/2013
35942^303516-6487591368Lelio R Paula02/2016
3595(24737*2^303428+1)/391345Lelio R Paula06/2014
3596(21181*2^303357+1)/3236191320Lelio R Paula06/2014
35972^303344-278696991316Enzo Doria03/2016
35986^117346+6591313Lelio R Paula05/2016
35992^303321+85591309Lelio R Paula02/2016
360012^84606+4791306Lelio R Paula06/2016
36012^303288+187431191299Enzo Doria06/2016
360211^87663-171091292Enzo Doria12/2012
36032^303224+253391280Henri Lifchitz05/2005
36046^117302+14391279Lelio R Paula05/2016
36053^191306-11288091277Enzo Doria07/2014
36062^303207+1291591275Lelio R Paula02/2016
36072^303191-11125991270Enzo Doria05/2014
360810^91230+9^(91230+1)91231Robert Price08/2016
360910^91230+792191231Patrick De Geest11/2016
361010^91230-91114191230Patrick De Geest11/2016
36116^117232-1742391225Enzo Doria02/2013
36127*10^91215+391216Erik Branger11/2009
361397*10^91205-391207Robert Price01/2017
36142^302979-16118191206Enzo Doria04/2013
36152^302949+8191197Henri Lifchitz02/2007
36164*6^117192-591194Lelio R Paula10/2014
36172^302918+9991188Lelio R Paula11/2012
36182^302797+186958791151Enzo Doria05/2016
3619265^37614+37614^26591148Norbert Schneider01/2015
36207^107852+8291146Lelio R Paula04/2016
3621(38*10^91144-11)/991145Robert Price05/2015
3622249^38030+38030^24991128Norbert Schneider01/2015
36236^117094-21104991117Mike Oakes05/2011
36242^302602-186718191093Enzo Doria03/2016
3625(1017*2^302592-1)/5391091Lelio R Paula04/2015
362615^77445-1691083Lelio R Paula07/2016
36272^302505+8191064Henri Lifchitz02/2007
36282^302496-11234991061Enzo Doria06/2014
362917^73999-7291052Lelio R Paula07/2016
36302^302332+57729457591012Lelio R Paula08/2016
36312^302274+7420990994Enzo Doria04/2016
3632(3^190668+2)/8990970Lelio R Paula04/2013
36332^302188+9019590968Lelio R Paula02/2016
3634(53*10^90965-71)/990966Robert Price09/2015
36352^302113+7410590946Enzo Doria04/2016
36362^302102-655590942Lelio R Paula02/2016
3637156*(10^(4*22731)-1)/101-190925Robert Price05/2014
36383^190568+3890925Lelio R Paula04/2016
36392^302009-1644990914Enzo Doria04/2013
3640(17*2^301951-1)/16590896Lelio R Paula02/2014
36413^190497+7490891Lelio R Paula04/2016
3642(24737*2^301896+1)/39990882Lelio R Paula06/2014
364318^72397+8990878Lelio R Paula06/2016
36446^116769-4790864Lelio R Paula05/2016
36452^301712-46590825Lelio R Paula02/2016
36462^301693-6990819Lelio R Paula11/2012
36472^301683-301683^290816Henri Lifchitz05/2005
364811^87187-171090796Enzo Doria12/2012
36495*10^90793+2190794Robert Price01/2017
3650(22*10^90792-13)/990793Robert Price03/2015
36512^301591-161590788Lelio R Paula02/2016
36522^301546-10903790775Enzo Doria04/2014
365314^79195-390768Lelio R Paula06/2016
36542^301517-186169390766Enzo Doria11/2015
36552^301460-17390749Lelio R Paula11/2012
36562^301312-8990704Lelio R Paula11/2012
36572^301285-12990696Lelio R Paula11/2012
36582^301282-10999190695Enzo Doria04/2014
36592^301228-185426990679Enzo Doria09/2015
3660(32*10^90669+13)/990670Robert Price04/2015
36613*5^129698+890656Lelio R Paula10/2014
3662F(433781)90655Henri Lifchitz09/2003
366319^70891+8290653Lelio R Paula06/2016
3664(29*2^301124-1)/1390648Lelio R Paula02/2014
36657*3^189953-890632Lelio R Paula08/2014
366611^87022-180090625Enzo Doria12/2012
3667(2^301042+47)/1203696990616Lelio R Paula06/2013
36682^301004-278693990612Enzo Doria03/2016
36692^300980-2790605Lelio R Paula11/2012
36702*10^90597-790598Dmitry Domanov11/2010
3671197^39485+290597Lelio R Paula06/2013
36727^107198+4890593Lelio R Paula04/2016
3673(86*10^90588+121)/990589Robert Price03/2017
36742^300923+5390587Lelio R Paula11/2012
36752^300874+790573Lelio R Paula10/2012
36765^129568-5690565Lelio R Paula04/2016
36772^300847-11283190564Enzo Doria06/2014
36782^300718+25525590526Lelio R Paula02/2016
36792^300637+9590501Lelio R Paula11/2012
36807^107087-2490500Lelio R Paula04/2016
3682(10^90499+3^90499)/1390498Robert Price01/2013
368113^81241+9090498Lelio R Paula06/2016
36836^116273-8590478Lelio R Paula05/2016
36846^116256-1757390465Enzo Doria02/2013
36852^300502+5461590461Lelio R Paula02/2016
3686(13*2^300487+1)/4590456Lelio R Paula09/2013
3687(3^189545-8)/590436Lelio R Paula01/2013
3688(7*2^300406-1)/390432Lelio R Paula02/2014
36894*5^129332+390400Lelio R Paula10/2014
36902^300249-1624590384Enzo Doria04/2013
3691(7*10^90371-313)/990371Robert Price11/2016
36922*6^116118+790358Lelio R Paula10/2014
3693(24737*2^300101+1)/2590343Lelio R Paula06/2014
36944*10^90334-2190335Robert Price04/2016
36952^300019-11033590315Enzo Doria05/2014
36962^299949-100590294Lelio R Paula11/2013
36972^299868-10961390270Enzo Doria04/2014
36985*2^299799-390250Lelio R Paula08/2014
369913^81008-290239Lelio R Paula09/2013
370064^49957-63^4995790232Robert Price07/2013
370110^90227+5628190228Patrick De Geest06/2016
37042^299725+31590227Lelio R Paula11/2013
370210^90227-100000000190227Robert Price05/2016
370310^90227-6876390227Patrick De Geest06/2016
37055^129082+4890225Lelio R Paula03/2016
37062^299699+19590219Lelio R Paula10/2012
3707(55*10^90211-1)/990212Ray Chandler02/2012
37083^189053+28090202Lelio R Paula04/2016
37092^299639-18790201Lelio R Paula10/2012
37102^299631+18390198Lelio R Paula10/2012
3711(21*2^299611-1)/2990192Lelio R Paula02/2014
37122^299567+11390179Lelio R Paula10/2012
37132^299550+18990174Lelio R Paula10/2012
3714(2^299535+3)/2990168Lelio R Paula01/2013
3715(97*10^90155-1)/390157Serge Batalov12/2014
37163^188938+868090147Lelio R Paula04/2016
37176^115840-5590142Lelio R Paula05/2016
37188*7^106659+590139Lelio R Paula10/2014
37192^299406-1665390131Enzo Doria05/2013
3720208049#+(216091#)/(208049#)90128Makoto Morimoto04/2016
3721(F(5)^128941-F(4)^128941)/F(3)90126Wayne Halsdorf03/2012
37226^115819-5390125Lelio R Paula05/2016
37236^115816-1685390123Enzo Doria02/2013
37246^115813-2390121Lelio R Paula05/2016
3725(22*10^90110+161)/390111Robert Price02/2017
3726(2^299330-509203)/6990106Lelio R Paula01/2013
3727(29*10^90096-17)/390097Erik Branger09/2014
37282^299247+187052990083Enzo Doria05/2016
37292^299229-279778390077Enzo Doria04/2016
37302^299220-1631790075Enzo Doria04/2013
373111^86491-135090072Enzo Doria12/2012
3732(31*10^90064-1)/390066Robert Price03/2017
37332^299112+7395190042Enzo Doria04/2016
37348^99702+7^(99702-1)90040Robert Price02/2016
37355*10^90033+390034Dmitry Domanov11/2010
3736243^37738+37738^24390029Norbert Schneider01/2015
37372^299048-11329790023Enzo Doria07/2014
37383^188648+9290008Lelio R Paula12/2015
37395*2^298991+790006Lelio R Paula08/2014
3740(25*2^298997+1)/326790005Lelio R Paula01/2013
374110^90000+886990001Patrick De Geest12/2009
374310^89999+8293990000Dirk Augustin04/2007
374210^90000-14034390000Patrick De Geest12/2009
374410^89999-19489189999Patrick De Geest11/2009
374519^70365-7889980Lelio R Paula12/2015
3746NaturalLogarithmOf2(89973)89973Eric W. Weisstein10/2015
37472^298852-6487589964Lelio R Paula11/2013
374818^71659+3789952Lelio R Paula12/2015
3749(2908*29^61501-3)/789942Curtis Bright05/2015
375017^73067+2089906Lelio R Paula11/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 26 2017 17:51 (Time in France)

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