PRP Records

Probable Primes Top 10000

(288949 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 (> 50000) Who ? When ?
8251(7*10^89383+167)/389384Robert Kinser10/2017
8252(85*10^89375-31)/989376Robert Price11/2015
82539*2^296870+789368Lelio R Paula08/2014
8254100^44683-99^4468389366Robert Price07/2013
82552^296810+7651989349Enzo Doria05/2016
8256(2747^25981-1)/274689342Serge Batalov08/2020
82578^98928+7^(98928+1)89341Robert Price06/2016
8259(3^187247+4)/102789337Lelio R Paula01/2013
825821832^12359+12359^2183289337Hans Havermann08/2020
8260(3^187235-2)/204589331Lelio R Paula01/2013
82612^296736-43214989327Paul Bourdelais05/2013
82622^296737-11251989327Enzo Doria06/2014
82632^296718-364589322Lelio R Paula11/2013
8264(2^296702+2338)/289316Stefano Morozzi01/2020
82652^296681-1622189310Enzo Doria04/2013
82662^296669-1651389307Enzo Doria04/2013
8267(2^296626+1282)/289294Stefano Morozzi01/2020
82682^296619-1635789292Enzo Doria04/2013
82692^296614-11005189290Enzo Doria04/2014
8270(2^296601+1730)/289286Stefano Morozzi01/2020
8271(3^187138+8)/8314789283Lelio R Paula01/2013
8272(2*10^89279+457)/989279Robert Price01/2017
8273(2^296568+1222)/289276Stefano Morozzi01/2020
8274(133*10^89273+17)/389275Robert Price11/2021
827515^75907-2889274Lelio R Paula11/2015
82762^296547-3789270Yves Minet01/2012
82772^296485+19189251Lelio R Paula10/2012
82782^296467-7589246Lelio R Paula10/2012
8279(2^296462+1674)/289244Stefano Morozzi01/2020
82802^296416-10953589231Enzo Doria04/2014
8281(23*2^296406+1)/389228Lelio R Paula01/2013
828266^49037-6589225Norbert Schneider11/2014
82832^296377-1624589219Enzo Doria04/2013
82842^296372-6487589217Lelio R Paula11/2013
82855*6^114648-789215Lelio R Paula10/2014
8286(2^296361+1262)/289214Stefano Morozzi01/2020
82873*10^89206+1389207Robert Price08/2017
82887*3^186960-489204Lelio R Paula08/2014
8289(28*10^89203+47)/389204Robert Price02/2021
82902^296290-11213389193Enzo Doria06/2014
82916^114620-1700389192Enzo Doria02/2013
8292(4*10^89189+41)/989189Robert Price11/2014
82932^296261-16118189184Enzo Doria04/2013
8294(19*2^296269-1)/53062389182Lelio R Paula02/2014
82953^186903-1089176Robert Price09/2013
82967*10^89169-389170Dmitry Domanov11/2010
8297(2^296221-1017)/3589170Lelio R Paula01/2013
8298(43*10^89169+47)/989170Robert Price12/2017
8299(10^89160+29)/389160Serge Batalov12/2014
8300(28*10^89141-97)/389142Robert Price07/2016
83012^296116-73463989140Paul Bourdelais04/2013
8302(2^296101+1250)/289135Stefano Morozzi01/2020
830322574^8883+8883^2257489135Hans Havermann08/2020
83046^114544-13389133Lelio R Paula12/2015
83052^296076-11329789128Enzo Doria07/2014
8306(11*2^296060-1)/21589122Lelio R Paula02/2014
83075*10^89118+8189119Robert Price08/2017
83082^296037-141189117Yves Minet01/2013
83092^296020-260480989111Enzo Doria05/2015
83102^296016+8189110Henri Lifchitz02/2007
83112^296010-1189108Lelio R Paula10/2012
83122^295998-11191189105Enzo Doria05/2014
8313(2^296014+47)/9399114989102Lelio R Paula01/2013
831429529^1040+1040^2952989090Hans Havermann08/2020
83152^295939-1662189087Enzo Doria04/2013
83162^295934-10969189086Enzo Doria04/2014
8317(2^295921+2246)/289081Stefano Morozzi01/2020
8318(185*10^89070-11)/389072Robert Price10/2020
8319(185*10^89063+7)/389065Robert Price02/2017
8320(8*10^89055-59)/389056Robert Price08/2021
83212^295831+14389055Lelio R Paula10/2012
832231^59713-3089054Theodore Burton02/2007
8323(7*2^295834-1)/2766389052Lelio R Paula02/2014
832479731!4-3289049Robert Price11/2019
8325123^42608+289047Lelio R Paula05/2013
83266^114433-114433^689047Norbert Schneider04/2017
83272^295800-45965989045Enzo Doria05/2015
8328(52*10^89037-1)/389039Robert Price02/2017
8329(2^295782+1870)/289039Stefano Morozzi01/2020
8330(6^114398-11)/589019Paul Bourdelais11/2011
833111^85470-585089008Enzo Doria02/2013
8332(2^295650+522)/289000Stefano Morozzi01/2020
8333(27*2^295634+1)/468788993Lelio R Paula01/2013
8334(p(18424)#-4)/288985Robert Price09/2017
83352^295564-18988974Lelio R Paula10/2012
83362^295557+7309788972Enzo Doria04/2016
833711^85433-576088970Enzo Doria01/2013
833823074^7165+7165^2307488956Hans Havermann08/2020
8339(2^295479+3050)/288948Stefano Morozzi01/2020
83406*10^88938-9188939Robert Price11/2017
834115^75619-8888935Lelio R Paula11/2015
8342(2^295433+2234)/288934Stefano Morozzi01/2020
8343(15589^21211-1)/1558888930Serge Batalov08/2020
834423776^5499+5499^2377688929Hans Havermann08/2020
834521112^16291+16291^2111288923Hans Havermann08/2020
83462^295385-8588920Lelio R Paula10/2012
83472^295385-1633388920Enzo Doria04/2013
8348(89*10^88916-377)/988917Robert Price07/2021
834979617!4+3288909Robert Price09/2019
835022077^10640+10640^2207788903Hans Havermann08/2020
83512^295309+5988897Lelio R Paula10/2012
83522^295288-10979988891Enzo Doria04/2014
835310^88888+17037388889Stefano Morozzi07/2018
835410^88888+27139988889Stefano Morozzi07/2018
835510^88888+37539788889Stefano Morozzi07/2018
835610^88888+54882388889Stefano Morozzi07/2018
835710^88888+82086188889Stefano Morozzi07/2018
835810^88888+120634988889Stefano Morozzi07/2018
835910^88888+129204788889Stefano Morozzi07/2018
836010^88888+145602988889Stefano Morozzi07/2018
836110^88888-49028788888Patrick De Geest09/2018
83622^295245+6588878Lelio R Paula10/2012
83635*10^88874-3788875Robert Price11/2021
8365Padovan(727734)88874Eric W. Weisstein04/2011
8364(2^295231+1554)/288874Stefano Morozzi01/2020
836679585!4-3288870Robert Price11/2019
836718^70793-1788865Lelio R Paula11/2015
83686^114196-1757388862Enzo Doria02/2013
8369302^35829+35829^30288857Norbert Schneider12/2014
83703^186223+1688851Robert Price10/2013
83713*2^295139+788847Lelio R Paula08/2014
83723^186212-11300888846Enzo Doria07/2014
83732*10^88844+2388845Robert Price12/2020
837423415^6224+6224^2341588839Hans Havermann08/2020
837587^45803-8688836Norbert Schneider11/2015
83762^295094-11027388833Enzo Doria05/2014
83772^295080+186915188828Enzo Doria05/2016
8378(2^295061+2174)/288822Stefano Morozzi01/2020
83792^295027-11340788812Enzo Doria07/2014
8380(2*10^88808-71)/388808Robert Price01/2017
8381(2^295009+2102)/288807Stefano Morozzi01/2020
838213^79722-8088806Lelio R Paula11/2015
838321112^16077+16077^2111288802Hans Havermann08/2020
83843^186103+10488794Lelio R Paula12/2015
8385(3*2^294971+1)/2556588792Lelio R Paula01/2013
8386(4025^24631-1)/402488786Serge Batalov08/2020
83872^294937-11500388785Enzo Doria06/2015
8388(2^294923+3134)/288781Stefano Morozzi01/2020
8389(15326^21211-1)/1532588773Serge Batalov08/2020
83902551^26056+26056^255188766Norbert Schneider01/2020
83912^294868-10970988765Enzo Doria04/2014
83922^294864-298588763Yves Minet09/2014
8393(17*10^88761-41)/388762Robert Price09/2017
8394(2^294834+2854)/288754Stefano Morozzi01/2020
8395(2^294823+2466)/288751Stefano Morozzi01/2020
8396(2^294764+642)/288733Stefano Morozzi01/2020
83972^294754+1501588730Lelio R Paula10/2013
8398(3^185951-7)/2088720Lelio R Paula01/2013
8399(2^294688+3186)/288710Stefano Morozzi01/2020
8400(2^294673+3906)/288706Stefano Morozzi01/2020
8401(2^294661+5)/44369338388694Lelio R Paula01/2013
8402(2^294631+2514)/288693Stefano Morozzi01/2020
8403(10^88680+11)/388680Robert Price11/2014
84042*7^104928-988675Lelio R Paula10/2014
840511^85150+1288675Lelio R Paula11/2015
84068*6^113951+588673Lelio R Paula10/2014
8407(2^294549+3110)/288668Stefano Morozzi01/2020
84086^113940-1856388663Enzo Doria03/2013
840938^56123-56123^3888663Norbert Schneider02/2017
84102^294492-6588651Lelio R Paula10/2012
8411(2^294481+2822)/288648Stefano Morozzi01/2020
841223874^5165+5165^2387488646Hans Havermann08/2020
8413(2^294469+1466)/288644Stefano Morozzi01/2020
84147*10^88634-2788635Dylan Delgado08/2019
841520^68120-5388627Lelio R Paula01/2016
8416122^42477-12188623Norbert Schneider10/2018
84172^294391-11325788621Enzo Doria07/2014
84185^126784-1547688619Enzo Doria02/2013
8419(2^294335+554)/288604Stefano Morozzi01/2020
84202^294327+988602Lelio R Paula10/2012
84212^294320+1891588600Lelio R Paula10/2013
8422(98*10^88595-89)/9988595Ray Chandler07/2011
842320723^18834+18834^2072388590Hans Havermann08/2020
8424(68*10^88586-329)/988587Robert Price03/2021
8425(2^294268+1402)/288584Stefano Morozzi01/2020
8426(17*2^294262-1)/1388582Lelio R Paula02/2014
84276*10^88571+7788572Robert Price06/2020
84282^294224-93307588571Paul Bourdelais04/2021
8429(2^294145+1346)/288547Stefano Morozzi01/2020
8430(2*10^88545+7)/988545Erik Branger03/2011
84312^294137-13388545Lelio R Paula10/2012
8432(2^294109+3494)/288536Stefano Morozzi01/2020
843323515^5818+5818^2351588529Hans Havermann08/2020
8434(2^294092-1017)/117188528Lelio R Paula01/2013
84354^147036+147036^4+188525Robert Price04/2014
843622541^8458+8458^2254188525Hans Havermann08/2020
8437(14^77213-5^77213)/988496Robert Price04/2013
84382^293965+279337788493Enzo Doria03/2016
8439(2^293956+3306)/288490Stefano Morozzi01/2020
844011^84971-15088489Enzo Doria08/2012
8441(2^293944+1066)/288486Stefano Morozzi01/2020
84429*10^88485+9188486Robert Price10/2020
844348^52626-4788478Norbert Schneider08/2018
8444(2^293956-1017)/3985137669667788476Lelio R Paula01/2013
844511^84958-219088475Enzo Doria12/2012
8446(2^293902+3070)/288474Stefano Morozzi01/2020
84472^293880-11134788467Enzo Doria05/2014
8448(106*10^88459-1)/388461Serge Batalov12/2014
844910^88457+27873388458Patrick De Geest07/2017
845010^88457-40188457Robert Price06/2017
8451(2^293834+3018)/288453Stefano Morozzi01/2020
8452(2^293747+1626)/288427Stefano Morozzi01/2020
845322080^10109+10109^2208088424Hans Havermann08/2020
845411^84908-168088423Enzo Doria12/2012
8455(2^293703+3486)/288414Stefano Morozzi01/2020
84562^293679-11207588407Enzo Doria06/2014
84576^113608-6588405Lelio R Paula12/2015
84582^293624+8287588390Lelio R Paula10/2013
8459(2^293618+918)/288388Stefano Morozzi01/2020
84602^293612-11233788387Enzo Doria06/2014
8461758^30693+30693^75888386Norbert Schneider05/2017
8462gcd(V(1062695),5*F(212539)*(F(212539)-1)+1)88383Serge Batalov04/2015
84635*10^88377+7788378Robert Price06/2016
8464(2^293584+1558)/288378Stefano Morozzi01/2020
8465(5*2^293526+1)/30388359Lelio R Paula01/2013
846620918^16743+16743^2091888355Hans Havermann08/2020
8467(2^293499+2390)/288352Stefano Morozzi01/2020
846820727^18292+18292^2072788344Hans Havermann08/2020
84702^293461-278584388341Enzo Doria03/2016
8469(31*10^88340+257)/988341Robert Price12/2021
84722^293416-103788328Yves Minet11/2012
84716*10^88327+4388328Robert Price07/2020
847325109^3292+3292^2510988320Hans Havermann08/2020
8474(2^293384-7)/388317Lelio R Paula01/2013
8475(3^185092-5)/488311Lelio R Paula01/2013
8476(5*10^88303-173)/388304Robert Price11/2017
847714^77039-5788297Lelio R Paula11/2015
84783*10^88293-5988294Robert Price10/2017
84795^126303+4288283Lelio R Paula10/2015
848019^69025-1888266Theodore Burton01/2006
8481140^41128+13988266Norbert Schneider04/2019
84825*10^88261-388262Dmitry Domanov11/2010
8483(2^293195+2238)/288261Stefano Morozzi01/2020
84848^97731-7^(97731-1)88260Robert Price04/2016
84855*10^88254+5988255Robert Price09/2016
84864*3^184968-788253Lelio R Paula08/2014
848734*10^88251-988253Robert Price06/2020
84887^104426+8888251Lelio R Paula10/2015
84892^293142+9988245Lelio R Paula10/2012
849011^84736-213088244Enzo Doria12/2012
849123884^4945+4945^2388488232Hans Havermann08/2020
849222080^9907+9907^2208088231Hans Havermann08/2020
8493(10^110315+1)/(10^22063+1)/582481268216764857846028164188225Makoto Kamada04/2019
84942^293068-8988223Lelio R Paula10/2012
84952126^26511+26511^212688218Norbert Schneider02/2020
84962^293014-10965588207Enzo Doria04/2014
84978*7^104371-388205Lelio R Paula10/2014
84982^292995-214588201Lelio R Paula10/2013
849928534^1233+1233^2853488198Hans Havermann08/2020
85005*10^88182+7788183Robert Price06/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 19 2022 17:15 (Time in France)

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