PRP Records

Probable Primes Top 10000

(211563 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 ?
4001(63^51439+1)/6492555Paul Bourdelais08/2017
4002(26*10^92546-77)/392547Robert Price02/2017
40033^193954+34092540Lelio R Paula04/2016
40042^307407-307407^292539Henri Lifchitz05/2005
4005(17*10^92513-11)/392514Robert Price07/2015
40062^307318-421192512Yves Minet06/2011
40072^307280+19392501Lelio R Paula11/2012
400820^71075-3392471Lelio R Paula05/2016
40092^307126-7879592455Lelio R Paula02/2016
40102^307125-4978992454Henri Lifchitz08/2005
40112^307099+2392447Lelio R Paula11/2012
40127*10^92414-6992415Robert Price01/2017
4013(9787*2^306975-1)/212915592407Lelio R Paula04/2015
40142^306915+187337392391Enzo Doria06/2016
40152^306908+1291592389Lelio R Paula02/2016
401619^72244-8092383Lelio R Paula06/2016
40182^306849+7592371Lelio R Paula11/2012
4017(397*10^92369+53)/992371Robert Price11/2017
40192^306813-86968810592360Lelio R Paula08/2016
40202^306672-10905992318Enzo Doria04/2014
40216^118604-1706392292Enzo Doria02/2013
4022(31*2^306487-1)/229192260Lelio R Paula02/2014
40232^306467-183561192256Enzo Doria04/2015
40242^306433+7642792246Enzo Doria05/2016
40262^306430-11331392245Enzo Doria07/2014
4025(23*10^92244-59)/992245Robert Price03/2017
4027(47*2^306398+1)/138480392231Lelio R Paula04/2015
4028(25*10^92186+59)/392187Robert Price05/2016
40292^306213-28618392180Enzo Doria06/2015
403010^92178+6192179Robert Price04/2011
403110^92178-17550992178Patrick De Geest07/2013
40322^306200+118592176Lelio R Paula02/2016
40332^306153+1192162Lelio R Paula11/2012
4034(2^306141-7)/592157Lelio R Paula06/2013
4035(26*10^92152-23)/392153Robert Price08/2016
4036(2*10^92152+67)/392152Robert Price04/2017
40374*10^92099+3*7^9209992100Mike Oakes12/2010
4038(2^305867-2^152934+1)/59207511/2006
40392^305851-10949592071Enzo Doria04/2014
404012^85300+3592055Lelio R Paula06/2016
40413^192911+9292042Lelio R Paula04/2016
40422^305723-27627192032Enzo Doria07/2015
40432^305676+9392018Donovan Johnson06/2008
40443^192819+491999Lelio R Paula04/2013
4045(38*10^91997-83)/9991997Ray Chandler07/2011
40462^305539+7291191977Enzo Doria04/2016
4047(2^305427-5)/129799821391934Lelio R Paula06/2013
404885^47642+8491922Norbert Schneider10/2015
404910^91920+18765191921Patrick De Geest07/2013
405010^91920-3991920Robert Price05/2011
4051(22*10^91903+41)/991904Robert Price02/2015
40532^305275-2791897Lelio R Paula11/2012
40523^192607-772691897Enzo Doria05/2014
4054(7*10^91856-61)/991856Erik Branger12/2009
4055(89*10^91839-53)/991840Robert Price11/2015
40568*5^131351+791812Lelio R Paula10/2014
40573^192426-6891811Lelio R Paula04/2016
40582^304973+11791807Lelio R Paula11/2012
40592^304939-186372791796Enzo Doria03/2016
40602^304902+841591785Lelio R Paula02/2016
406118^73119+6191785Lelio R Paula06/2016
4062(78557*2^304740+1)/15991739Lelio R Paula06/2014
40632^304747+7135591738Lelio R Paula02/2016
40648*3^192251+591728Lelio R Paula08/2014
40652^304674-8791717Lelio R Paula11/2012
4066(28*10^91715+701)/991716Robert Price11/2017
4067(2^304698+9)/136280995391715Lelio R Paula06/2013
4068(5*10^91707-119)/391708Robert Price04/2016
40692^304633-11277191704Enzo Doria06/2014
40709*10^91693+2391694Robert Price11/2017
40712^304578-1671391688Enzo Doria05/2013
40726^117824-1871391685Enzo Doria03/2013
4073(17^74509-1)/1691679Paul Bourdelais03/2010
4074(2^304551-7)/891223191673Lelio R Paula06/2013
4075(2^304532-3)/301391670Lelio R Paula06/2013
40762^304507-1664591666Enzo Doria04/2013
4077(29*2^304489+1)/3191661Lelio R Paula09/2013
40782^304471-183612791655Enzo Doria04/2015
40792^304433+3276991644Lelio R Paula02/2016
40802^304410-1662591637Enzo Doria04/2013
4081183^40500-291630Lelio R Paula10/2017
4082(203*10^91613+1)/391615Robert Price09/2017
40834*5^131052+791603Lelio R Paula10/2014
40842^304278-400191597Yves Minet04/2017
40852^304272-186637791595Enzo Doria03/2016
40862^304268+1968391594Lelio R Paula02/2016
40872^304162-16191562Lelio R Paula11/2012
40885*7^108331+691552Lelio R Paula10/2014
40892^304082-278782191538Enzo Doria03/2016
40902^304015+6413391518David Broadhurst06/2002
4091(7*2^303963+1)/391503Lelio R Paula09/2013
4092(2^303945-9)/361791494Lelio R Paula06/2013
40932^303930+188052791493Enzo Doria10/2016
40943^191684-6891457Lelio R Paula04/2016
4095(21*2^303813-1)/16991456Lelio R Paula02/2014
409611^87797-12091432Enzo Doria07/2012
40972^303698-184723191423Enzo Doria07/2015
4098(38^28933-1)^2-291416Norbert Schneider06/2016
40992^303554+7729991379Enzo Doria05/2016
41002^303542+1270591376Lelio R Paula02/2016
410131^61269-291375Lelio R Paula09/2013
41022^303516-6487591368Lelio R Paula02/2016
4103(24737*2^303428+1)/391345Lelio R Paula06/2014
4104(21181*2^303357+1)/3236191320Lelio R Paula06/2014
41052^303344-278696991316Enzo Doria03/2016
41066^117346+6591313Lelio R Paula05/2016
41072^303321+85591309Lelio R Paula02/2016
410812^84606+4791306Lelio R Paula06/2016
41092^303288+187431191299Enzo Doria06/2016
4110197^39788-291293Lelio R Paula10/2017
411111^87663-171091292Enzo Doria12/2012
41122^303224+253391280Henri Lifchitz05/2005
41136^117302+14391279Lelio R Paula05/2016
41143^191306-11288091277Enzo Doria07/2014
41152^303207+1291591275Lelio R Paula02/2016
41162^303191-11125991270Enzo Doria05/2014
411710^91230+9^(91230+1)91231Robert Price08/2016
411810^91230+792191231Patrick De Geest11/2016
411910^91230-91114191230Patrick De Geest11/2016
41206^117232-1742391225Enzo Doria02/2013
41217*10^91215+391216Erik Branger11/2009
412297*10^91205-391207Robert Price01/2017
41232^302979-16118191206Enzo Doria04/2013
41242^302949+8191197Henri Lifchitz02/2007
41254*6^117192-591194Lelio R Paula10/2014
41262^302918+9991188Lelio R Paula11/2012
41272^302797+186958791151Enzo Doria05/2016
4128265^37614+37614^26591148Norbert Schneider01/2015
41297^107852+8291146Lelio R Paula04/2016
4130(38*10^91144-11)/991145Robert Price05/2015
4131(55*10^91142+377)/991143Robert Price10/2017
4132249^38030+38030^24991128Norbert Schneider01/2015
41336^117094-21104991117Mike Oakes05/2011
41342^302602-186718191093Enzo Doria03/2016
4135(1017*2^302592-1)/5391091Lelio R Paula04/2015
413615^77445-1691083Lelio R Paula07/2016
41372^302505+8191064Henri Lifchitz02/2007
41382^302496-11234991061Enzo Doria06/2014
413917^73999-7291052Lelio R Paula07/2016
4140(16*10^91032+41)/391033Robert Price10/2017
41412^302332+57729457591012Lelio R Paula08/2016
41422^302274+7420990994Enzo Doria04/2016
4143(311^36497-1)/31090976Eric Chen09/2017
4144(3^190668+2)/8990970Lelio R Paula04/2013
41452^302188+9019590968Lelio R Paula02/2016
4146(53*10^90965-71)/990966Robert Price09/2015
41472^302113+7410590946Enzo Doria04/2016
41482^302102-655590942Lelio R Paula02/2016
4149156*(10^(4*22731)-1)/101-190925Robert Price05/2014
41503^190568+3890925Lelio R Paula04/2016
41512^302009-1644990914Enzo Doria04/2013
4152(17*2^301951-1)/16590896Lelio R Paula02/2014
41533^190497+7490891Lelio R Paula04/2016
4154(24737*2^301896+1)/39990882Lelio R Paula06/2014
415518^72397+8990878Lelio R Paula06/2016
41566^116769-4790864Lelio R Paula05/2016
41572^301712-46590825Lelio R Paula02/2016
41582^301693-6990819Lelio R Paula11/2012
41592^301683-301683^290816Henri Lifchitz05/2005
416011^87187-171090796Enzo Doria12/2012
41615*10^90793+2190794Robert Price01/2017
4162(22*10^90792-13)/990793Robert Price03/2015
41632^301591-161590788Lelio R Paula02/2016
4164(52^52901+1)/5390777Paul Bourdelais08/2017
41652^301546-10903790775Enzo Doria04/2014
416614^79195-390768Lelio R Paula06/2016
41672^301517-186169390766Enzo Doria11/2015
41682^301460-17390749Lelio R Paula11/2012
4169(85*10^90745-103)/990746Robert Price10/2017
41702^301312-8990704Lelio R Paula11/2012
41712^301285-12990696Lelio R Paula11/2012
41722^301282-10999190695Enzo Doria04/2014
41732^301228-185426990679Enzo Doria09/2015
4174(151*10^90669-1)/390671Robert Price04/2017
4175(32*10^90669+13)/990670Robert Price04/2015
41763*5^129698+890656Lelio R Paula10/2014
4177F(433781)90655Henri Lifchitz09/2003
417819^70891+8290653Lelio R Paula06/2016
4179(29*2^301124-1)/1390648Lelio R Paula02/2014
41807*3^189953-890632Lelio R Paula08/2014
418111^87022-180090625Enzo Doria12/2012
4182(2^301042+47)/1203696990616Lelio R Paula06/2013
41832^301004-278693990612Enzo Doria03/2016
41842^300980-2790605Lelio R Paula11/2012
41852*10^90597-790598Dmitry Domanov11/2010
4186197^39485+290597Lelio R Paula06/2013
41877^107198+4890593Lelio R Paula04/2016
4188(86*10^90588+121)/990589Robert Price03/2017
41892^300923+5390587Lelio R Paula11/2012
41902^300874+790573Lelio R Paula10/2012
41915^129568-5690565Lelio R Paula04/2016
41922^300847-11283190564Enzo Doria06/2014
41932^300718+25525590526Lelio R Paula02/2016
41942^300637+9590501Lelio R Paula11/2012
41957^107087-2490500Lelio R Paula04/2016
4197(10^90499+3^90499)/1390498Robert Price01/2013
419613^81241+9090498Lelio R Paula06/2016
41986^116273-8590478Lelio R Paula05/2016
41996^116256-1757390465Enzo Doria02/2013
42002^300502+5461590461Lelio R Paula02/2016
4201(13*2^300487+1)/4590456Lelio R Paula09/2013
4202(3^189545-8)/590436Lelio R Paula01/2013
4203(7*2^300406-1)/390432Lelio R Paula02/2014
42044*5^129332+390400Lelio R Paula10/2014
42052^300249-1624590384Enzo Doria04/2013
4206(7*10^90371-313)/990371Robert Price11/2016
42072*6^116118+790358Lelio R Paula10/2014
4208(24737*2^300101+1)/2590343Lelio R Paula06/2014
42094*10^90334-2190335Robert Price04/2016
42102^300019-11033590315Enzo Doria05/2014
42112^299949-100590294Lelio R Paula11/2013
42122^299868-10961390270Enzo Doria04/2014
42135*2^299799-390250Lelio R Paula08/2014
421413^81008-290239Lelio R Paula09/2013
421564^49957-63^4995790232Robert Price07/2013
421610^90227+5628190228Patrick De Geest06/2016
42192^299725+31590227Lelio R Paula11/2013
421710^90227-100000000190227Robert Price05/2016
421810^90227-6876390227Patrick De Geest06/2016
42205^129082+4890225Lelio R Paula03/2016
42212^299699+19590219Lelio R Paula10/2012
4222(55*10^90211-1)/990212Ray Chandler02/2012
42233^189053+28090202Lelio R Paula04/2016
42242^299639-18790201Lelio R Paula10/2012
42252^299631+18390198Lelio R Paula10/2012
4226(21*2^299611-1)/2990192Lelio R Paula02/2014
42272^299567+11390179Lelio R Paula10/2012
42282^299550+18990174Lelio R Paula10/2012
4229(2^299535+3)/2990168Lelio R Paula01/2013
4230(97*10^90155-1)/390157Serge Batalov12/2014
42313^188938+868090147Lelio R Paula04/2016
42326^115840-5590142Lelio R Paula05/2016
4233(5*10^90142-473)/990142Robert Price12/2017
42348*7^106659+590139Lelio R Paula10/2014
42352^299406-1665390131Enzo Doria05/2013
4236208049#+(216091#)/(208049#)90128Makoto Morimoto04/2016
4237(F(5)^128941-F(4)^128941)/F(3)90126Wayne Halsdorf03/2012
42386^115819-5390125Lelio R Paula05/2016
42396^115816-1685390123Enzo Doria02/2013
42406^115813-2390121Lelio R Paula05/2016
4241(22*10^90110+161)/390111Robert Price02/2017
4242(2^299330-509203)/6990106Lelio R Paula01/2013
4243(29*10^90096-17)/390097Erik Branger09/2014
42442^299247+187052990083Enzo Doria05/2016
42452^299229-279778390077Enzo Doria04/2016
42462^299220-1631790075Enzo Doria04/2013
424711^86491-135090072Enzo Doria12/2012
4248(31*10^90064-1)/390066Robert Price03/2017
4249L(430949)/861899/144038756153990045Serge Batalov07/2017
42502^299112+7395190042Enzo Doria04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2018 23:06 (Time in France)

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