PRP Records

Probable Primes Top 10000

(202622 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 ?
40012^301546-10903790775Enzo Doria04/2014
400214^79195-390768Lelio R Paula06/2016
40032^301517-186169390766Enzo Doria11/2015
40042^301460-17390749Lelio R Paula11/2012
4005(85*10^90745-103)/990746Robert Price10/2017
40062^301312-8990704Lelio R Paula11/2012
40072^301285-12990696Lelio R Paula11/2012
40082^301282-10999190695Enzo Doria04/2014
40092^301228-185426990679Enzo Doria09/2015
4010(151*10^90669-1)/390671Robert Price04/2017
4011(32*10^90669+13)/990670Robert Price04/2015
40123*5^129698+890656Lelio R Paula10/2014
4013F(433781)90655Henri Lifchitz09/2003
401419^70891+8290653Lelio R Paula06/2016
4015(29*2^301124-1)/1390648Lelio R Paula02/2014
40167*3^189953-890632Lelio R Paula08/2014
401711^87022-180090625Enzo Doria12/2012
4018(2^301042+47)/1203696990616Lelio R Paula06/2013
40192^301004-278693990612Enzo Doria03/2016
40202^300980-2790605Lelio R Paula11/2012
40212*10^90597-790598Dmitry Domanov11/2010
4022197^39485+290597Lelio R Paula06/2013
40237^107198+4890593Lelio R Paula04/2016
4024(86*10^90588+121)/990589Robert Price03/2017
40252^300923+5390587Lelio R Paula11/2012
40262^300874+790573Lelio R Paula10/2012
40275^129568-5690565Lelio R Paula04/2016
40282^300847-11283190564Enzo Doria06/2014
40292^300718+25525590526Lelio R Paula02/2016
40302^300637+9590501Lelio R Paula11/2012
40317^107087-2490500Lelio R Paula04/2016
4032(10^90499+3^90499)/1390498Robert Price01/2013
403313^81241+9090498Lelio R Paula06/2016
40346^116273-8590478Lelio R Paula05/2016
40356^116256-1757390465Enzo Doria02/2013
40362^300502+5461590461Lelio R Paula02/2016
4037(13*2^300487+1)/4590456Lelio R Paula09/2013
4038(3^189545-8)/590436Lelio R Paula01/2013
4039(7*2^300406-1)/390432Lelio R Paula02/2014
40404*5^129332+390400Lelio R Paula10/2014
40412^300249-1624590384Enzo Doria04/2013
4042(7*10^90371-313)/990371Robert Price11/2016
40432*6^116118+790358Lelio R Paula10/2014
4044(24737*2^300101+1)/2590343Lelio R Paula06/2014
40454*10^90334-2190335Robert Price04/2016
40462^300019-11033590315Enzo Doria05/2014
40472^299949-100590294Lelio R Paula11/2013
40482^299868-10961390270Enzo Doria04/2014
40495*2^299799-390250Lelio R Paula08/2014
405013^81008-290239Lelio R Paula09/2013
405164^49957-63^4995790232Robert Price07/2013
405210^90227+5628190228Patrick De Geest06/2016
40552^299725+31590227Lelio R Paula11/2013
405310^90227-100000000190227Robert Price05/2016
405410^90227-6876390227Patrick De Geest06/2016
40565^129082+4890225Lelio R Paula03/2016
40572^299699+19590219Lelio R Paula10/2012
4058(55*10^90211-1)/990212Ray Chandler02/2012
40593^189053+28090202Lelio R Paula04/2016
40602^299639-18790201Lelio R Paula10/2012
40612^299631+18390198Lelio R Paula10/2012
4062(21*2^299611-1)/2990192Lelio R Paula02/2014
40632^299567+11390179Lelio R Paula10/2012
40642^299550+18990174Lelio R Paula10/2012
4065(2^299535+3)/2990168Lelio R Paula01/2013
4066(97*10^90155-1)/390157Serge Batalov12/2014
40673^188938+868090147Lelio R Paula04/2016
40686^115840-5590142Lelio R Paula05/2016
4069(5*10^90142-473)/990142Robert Price12/2017
40708*7^106659+590139Lelio R Paula10/2014
40712^299406-1665390131Enzo Doria05/2013
4072208049#+(216091#)/(208049#)90128Makoto Morimoto04/2016
4073(F(5)^128941-F(4)^128941)/F(3)90126Wayne Halsdorf03/2012
40746^115819-5390125Lelio R Paula05/2016
40756^115816-1685390123Enzo Doria02/2013
40766^115813-2390121Lelio R Paula05/2016
4077(22*10^90110+161)/390111Robert Price02/2017
4078(2^299330-509203)/6990106Lelio R Paula01/2013
4079(29*10^90096-17)/390097Erik Branger09/2014
40802^299247+187052990083Enzo Doria05/2016
40812^299229-279778390077Enzo Doria04/2016
40822^299220-1631790075Enzo Doria04/2013
408311^86491-135090072Enzo Doria12/2012
4084(31*10^90064-1)/390066Robert Price03/2017
4085L(430949)/861899/144038756153990045Serge Batalov07/2017
40862^299112+7395190042Enzo Doria04/2016
40878^99702+7^(99702-1)90040Robert Price02/2016
40885*10^90033+390034Dmitry Domanov11/2010
4089243^37738+37738^24390029Norbert Schneider01/2015
40902^299048-11329790023Enzo Doria07/2014
40913^188648+9290008Lelio R Paula12/2015
40925*2^298991+790006Lelio R Paula08/2014
4093(25*2^298997+1)/326790005Lelio R Paula01/2013
409410^90000+886990001Patrick De Geest12/2009
409610^89999+8293990000Dirk Augustin04/2007
409510^90000-14034390000Patrick De Geest12/2009
409710^89999-19489189999Patrick De Geest11/2009
409819^70365-7889980Lelio R Paula12/2015
4099NaturalLogarithmOf2(89973)89973Eric W. Weisstein10/2015
41002^298852-6487589964Lelio R Paula11/2013
410118^71659+3789952Lelio R Paula12/2015
4102(2908*29^61501-3)/789942Curtis Bright05/2015
410317^73067+2089906Lelio R Paula11/2015
41042^298637-9989899Lelio R Paula10/2012
41059^94188+3*8^94188-2*4^94188-3*2^9418889879Mike Oakes01/2011
41069*10^89858+1989859Robert Price05/2016
41072^298501+187006789858Enzo Doria05/2016
410811^86280-9889852Lelio R Paula11/2015
41092^298473-11005989850Enzo Doria04/2014
411019^70263-3289850Lelio R Paula12/2015
4111(299*10^89836-17)/389838Robert Price01/2017
41123^188286+1489836Robert Price09/2013
4113gcd(V(1091095),5*F(218219)*(F(218219)+1)+1)89822Serge Batalov04/2015
41142^298367+5890589818Lelio R Paula11/2013
41152^298319-10965789803Enzo Doria04/2014
41168*10^89800+8189801Robert Price05/2017
411718^71505-9189759Lelio R Paula12/2015
4118(7^106187+1)/889738Paul Bourdelais04/2008
41192^298079-10953189731Enzo Doria04/2014
4120(22699*2^298016+1)/38589714Lelio R Paula06/2014
4121156*(10^(4*22427)-1)/101-189709Robert Price05/2014
41222^298003-6694589708Lelio R Paula11/2013
4123(23*10^89705-83)/389706Robert Price09/2017
412417^72900-5489700Lelio R Paula11/2015
41253*2^297956+589695Lelio R Paula08/2014
412620^68938-1189691Lelio R Paula01/2016
412789*10^89687-789689Robert Price03/2017
41282^297923+7778389684Enzo Doria05/2016
412911^86107-2457600089672Enzo Doria02/2013
41302^297878-11191189671Enzo Doria05/2014
41317^106084+4089652Lelio R Paula10/2015
4132(86*10^89640-311)/989641Robert Price10/2017
41333*10^89608-5989609Robert Price10/2017
41343^187780-1103889594Enzo Doria05/2014
4135(13*2^297560-1)/4915178789568Lelio R Paula02/2014
41365^128141-3689567Lelio R Paula10/2015
41374*7^105951+989540Lelio R Paula10/2014
4138(7*10^89539-439)/989539Robert Price09/2017
41392^297397+17725789526Enzo Doria05/2016
41402^297346-1624189511Enzo Doria04/2013
4141(5*10^89510+79)/389511Robert Price11/2017
41434^148663-3^14866389505Jean-Louis Charton11/2005
41422^297328-86968810589505Lelio R Paula07/2016
41442^297325-45904389504Enzo Doria05/2015
41452^297310-11239189500Enzo Doria06/2014
41462^297296-11215789496Enzo Doria06/2014
414757^50966-289490Lelio R Paula08/2013
4148(266*10^89482+1)/389484Robert Price02/2016
4149(14*10^89480-101)/389481Robert Price04/2017
41502^297122+9989443Lelio R Paula10/2012
4151(3^187435-5)/128689427Lelio R Paula01/2013
4152(25*10^89413+161)/389414Robert Price01/2017
41532^296990+187069989403Enzo Doria05/2016
41542^296972-101789398Lelio R Paula11/2013
4155(7*10^89383+167)/389384Robert Kinser10/2017
4156(85*10^89375-31)/989376Robert Price11/2015
41579*2^296870+789368Lelio R Paula08/2014
4158100^44683-99^4468389366Robert Price07/2013
41592^296810+7651989349Enzo Doria05/2016
41608^98928+7^(98928+1)89341Robert Price06/2016
4161(3^187247+4)/102789337Lelio R Paula01/2013
4162(3^187235-2)/204589331Lelio R Paula01/2013
41642^296736-43214989327Paul Bourdelais05/2013
41632^296737-11251989327Enzo Doria06/2014
41652^296718-364589322Lelio R Paula11/2013
41662^296681-1622189310Enzo Doria04/2013
41672^296669-1651389307Enzo Doria04/2013
41682^296619-1635789292Enzo Doria04/2013
41692^296614-11005189290Enzo Doria04/2014
4170(3^187138+8)/8314789283Lelio R Paula01/2013
4171(2*10^89279+457)/989279Robert Price01/2017
417215^75907-2889274Lelio R Paula11/2015
41732^296547-3789270Yves Minet01/2012
41742^296485+19189251Lelio R Paula10/2012
41752^296467-7589246Lelio R Paula10/2012
41762^296416-10953589231Enzo Doria04/2014
4177(23*2^296406+1)/389228Lelio R Paula01/2013
417866^49037-6589225Norbert Schneider11/2014
41792^296377-1624589219Enzo Doria04/2013
41802^296372-6487589217Lelio R Paula11/2013
41815*6^114648-789215Lelio R Paula10/2014
41823*10^89206+1389207Robert Price08/2017
41837*3^186960-489204Lelio R Paula08/2014
41842^296290-11213389193Enzo Doria06/2014
41856^114620-1700389192Enzo Doria02/2013
4186(4*10^89189+41)/989189Robert Price11/2014
41872^296261-16118189184Enzo Doria04/2013
4188(19*2^296269-1)/53062389182Lelio R Paula02/2014
41893^186903-1089176Robert Price09/2013
41927*10^89169-389170Dmitry Domanov11/2010
4190(2^296221-1017)/3589170Lelio R Paula01/2013
4191(43*10^89169+47)/989170Robert Price12/2017
4193(10^89160+29)/389160Serge Batalov12/2014
4194(28*10^89141-97)/389142Robert Price07/2016
41952^296116-73463989140Paul Bourdelais04/2013
41966^114544-13389133Lelio R Paula12/2015
41972^296076-11329789128Enzo Doria07/2014
4198(11*2^296060-1)/21589122Lelio R Paula02/2014
41995*10^89118+8189119Robert Price08/2017
42002^296037-141189117Yves Minet01/2013
42012^296020-260480989111Enzo Doria05/2015
42022^296016+8189110Henri Lifchitz02/2007
42032^296010-1189108Lelio R Paula10/2012
42042^295998-11191189105Enzo Doria05/2014
4205(2^296014+47)/9399114989102Lelio R Paula01/2013
42062^295939-1662189087Enzo Doria04/2013
42072^295934-10969189086Enzo Doria04/2014
4208(185*10^89063+7)/389065Robert Price02/2017
42092^295831+14389055Lelio R Paula10/2012
421031^59713-3089054Theodore Burton02/2007
4211(7*2^295834-1)/2766389052Lelio R Paula02/2014
4212123^42608+289047Lelio R Paula05/2013
42136^114433-114433^689047Norbert Schneider04/2017
42142^295800-45965989045Enzo Doria05/2015
4215(52*10^89037-1)/389039Robert Price02/2017
4216(6^114398-11)/589019Paul Bourdelais11/2011
421711^85470-585089008Enzo Doria02/2013
4218(27*2^295634+1)/468788993Lelio R Paula01/2013
4219(p(18424)#-4)/288985Robert Price09/2017
42202^295564-18988974Lelio R Paula10/2012
42212^295557+7309788972Enzo Doria04/2016
422211^85433-576088970Enzo Doria01/2013
42236*10^88938-9188939Robert Price11/2017
422415^75619-8888935Lelio R Paula11/2015
42252^295385-8588920Lelio R Paula10/2012
42262^295385-1633388920Enzo Doria04/2013
42272^295309+5988897Lelio R Paula10/2012
42282^295288-10979988891Enzo Doria04/2014
42292^295245+6588878Lelio R Paula10/2012
4230Padovan(727734)88874Eric W. Weisstein04/2011
423118^70793-1788865Lelio R Paula11/2015
42326^114196-1757388862Enzo Doria02/2013
4233302^35829+35829^30288857Norbert Schneider12/2014
42343^186223+1688851Robert Price10/2013
42353*2^295139+788847Lelio R Paula08/2014
42363^186212-11300888846Enzo Doria07/2014
423787^45803-8688836Norbert Schneider11/2015
42382^295094-11027388833Enzo Doria05/2014
42392^295080+186915188828Enzo Doria05/2016
42402^295027-11340788812Enzo Doria07/2014
4241(2*10^88808-71)/388808Robert Price01/2017
424213^79722-8088806Lelio R Paula11/2015
42433^186103+10488794Lelio R Paula12/2015
4244(3*2^294971+1)/2556588792Lelio R Paula01/2013
42452^294937-11500388785Enzo Doria06/2015
42462^294868-10970988765Enzo Doria04/2014
42472^294864-298588763Yves Minet09/2014
4248(17*10^88761-41)/388762Robert Price09/2017
42492^294754+1501588730Lelio R Paula10/2013
4250(3^185951-7)/2088720Lelio R Paula01/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 19 2018 09:17 (Time in France)

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