PRP Records

Probable Primes Top 10000

(277054 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 ?
67512^296377-1624589219Enzo Doria04/2013
67522^296372-6487589217Lelio R Paula11/2013
67535*6^114648-789215Lelio R Paula10/2014
6754(2^296361+1262)/289214Stefano Morozzi01/2020
67553*10^89206+1389207Robert Price08/2017
67567*3^186960-489204Lelio R Paula08/2014
67572^296290-11213389193Enzo Doria06/2014
67586^114620-1700389192Enzo Doria02/2013
6759(4*10^89189+41)/989189Robert Price11/2014
67602^296261-16118189184Enzo Doria04/2013
6761(19*2^296269-1)/53062389182Lelio R Paula02/2014
67623^186903-1089176Robert Price09/2013
67637*10^89169-389170Dmitry Domanov11/2010
6764(2^296221-1017)/3589170Lelio R Paula01/2013
6765(43*10^89169+47)/989170Robert Price12/2017
6766(10^89160+29)/389160Serge Batalov12/2014
6767(28*10^89141-97)/389142Robert Price07/2016
67682^296116-73463989140Paul Bourdelais04/2013
6769(2^296101+1250)/289135Stefano Morozzi01/2020
677022574^8883+8883^2257489135Hans Havermann08/2020
67716^114544-13389133Lelio R Paula12/2015
67722^296076-11329789128Enzo Doria07/2014
6773(11*2^296060-1)/21589122Lelio R Paula02/2014
67745*10^89118+8189119Robert Price08/2017
67752^296037-141189117Yves Minet01/2013
67762^296020-260480989111Enzo Doria05/2015
67772^296016+8189110Henri Lifchitz02/2007
67782^296010-1189108Lelio R Paula10/2012
67792^295998-11191189105Enzo Doria05/2014
6780(2^296014+47)/9399114989102Lelio R Paula01/2013
678129529^1040+1040^2952989090Hans Havermann08/2020
67822^295939-1662189087Enzo Doria04/2013
67832^295934-10969189086Enzo Doria04/2014
6784(2^295921+2246)/289081Stefano Morozzi01/2020
6785(185*10^89070-11)/389072Robert Price10/2020
6786(185*10^89063+7)/389065Robert Price02/2017
67872^295831+14389055Lelio R Paula10/2012
678831^59713-3089054Theodore Burton02/2007
6789(7*2^295834-1)/2766389052Lelio R Paula02/2014
679079731!4-3289049Robert Price11/2019
6792123^42608+289047Lelio R Paula05/2013
67916^114433-114433^689047Norbert Schneider04/2017
67932^295800-45965989045Enzo Doria05/2015
6795(52*10^89037-1)/389039Robert Price02/2017
6794(2^295782+1870)/289039Stefano Morozzi01/2020
6796(6^114398-11)/589019Paul Bourdelais11/2011
679711^85470-585089008Enzo Doria02/2013
6798(2^295650+522)/289000Stefano Morozzi01/2020
6799(27*2^295634+1)/468788993Lelio R Paula01/2013
6800(p(18424)#-4)/288985Robert Price09/2017
68012^295564-18988974Lelio R Paula10/2012
68022^295557+7309788972Enzo Doria04/2016
680311^85433-576088970Enzo Doria01/2013
680423074^7165+7165^2307488956Hans Havermann08/2020
6805(2^295479+3050)/288948Stefano Morozzi01/2020
68066*10^88938-9188939Robert Price11/2017
680715^75619-8888935Lelio R Paula11/2015
6808(2^295433+2234)/288934Stefano Morozzi01/2020
6809(15589^21211-1)/1558888930Serge Batalov08/2020
681023776^5499+5499^2377688929Hans Havermann08/2020
681121112^16291+16291^2111288923Hans Havermann08/2020
68122^295385-8588920Lelio R Paula10/2012
68132^295385-1633388920Enzo Doria04/2013
681479617!4+3288909Robert Price09/2019
681522077^10640+10640^2207788903Hans Havermann08/2020
68162^295309+5988897Lelio R Paula10/2012
68172^295288-10979988891Enzo Doria04/2014
681810^88888+17037388889Stefano Morozzi07/2018
681910^88888+27139988889Stefano Morozzi07/2018
682010^88888+37539788889Stefano Morozzi07/2018
682110^88888+54882388889Stefano Morozzi07/2018
682210^88888+82086188889Stefano Morozzi07/2018
682310^88888+120634988889Stefano Morozzi07/2018
682410^88888+129204788889Stefano Morozzi07/2018
682510^88888+145602988889Stefano Morozzi07/2018
682610^88888-49028788888Patrick De Geest09/2018
68272^295245+6588878Lelio R Paula10/2012
6828Padovan(727734)88874Eric W. Weisstein04/2011
6829(2^295231+1554)/288874Stefano Morozzi01/2020
683079585!4-3288870Robert Price11/2019
683118^70793-1788865Lelio R Paula11/2015
68326^114196-1757388862Enzo Doria02/2013
6833302^35829+35829^30288857Norbert Schneider12/2014
68343^186223+1688851Robert Price10/2013
68353*2^295139+788847Lelio R Paula08/2014
68363^186212-11300888846Enzo Doria07/2014
68372*10^88844+2388845Robert Price12/2020
683823415^6224+6224^2341588839Hans Havermann08/2020
683987^45803-8688836Norbert Schneider11/2015
68402^295094-11027388833Enzo Doria05/2014
68412^295080+186915188828Enzo Doria05/2016
6842(2^295061+2174)/288822Stefano Morozzi01/2020
68432^295027-11340788812Enzo Doria07/2014
6844(2*10^88808-71)/388808Robert Price01/2017
6845(2^295009+2102)/288807Stefano Morozzi01/2020
684613^79722-8088806Lelio R Paula11/2015
684721112^16077+16077^2111288802Hans Havermann08/2020
68483^186103+10488794Lelio R Paula12/2015
6849(3*2^294971+1)/2556588792Lelio R Paula01/2013
6850(4025^24631-1)/402488786Serge Batalov08/2020
68512^294937-11500388785Enzo Doria06/2015
6852(2^294923+3134)/288781Stefano Morozzi01/2020
6853(15326^21211-1)/1532588773Serge Batalov08/2020
68542551^26056+26056^255188766Norbert Schneider01/2020
68552^294868-10970988765Enzo Doria04/2014
68562^294864-298588763Yves Minet09/2014
6857(17*10^88761-41)/388762Robert Price09/2017
6858(2^294834+2854)/288754Stefano Morozzi01/2020
6859(2^294823+2466)/288751Stefano Morozzi01/2020
6860(2^294764+642)/288733Stefano Morozzi01/2020
68612^294754+1501588730Lelio R Paula10/2013
6862(3^185951-7)/2088720Lelio R Paula01/2013
6863(2^294688+3186)/288710Stefano Morozzi01/2020
6864(2^294673+3906)/288706Stefano Morozzi01/2020
6865(2^294661+5)/44369338388694Lelio R Paula01/2013
6866(2^294631+2514)/288693Stefano Morozzi01/2020
6867(10^88680+11)/388680Robert Price11/2014
68682*7^104928-988675Lelio R Paula10/2014
686911^85150+1288675Lelio R Paula11/2015
68708*6^113951+588673Lelio R Paula10/2014
6871(2^294549+3110)/288668Stefano Morozzi01/2020
68736^113940-1856388663Enzo Doria03/2013
687238^56123-56123^3888663Norbert Schneider02/2017
68742^294492-6588651Lelio R Paula10/2012
6875(2^294481+2822)/288648Stefano Morozzi01/2020
687623874^5165+5165^2387488646Hans Havermann08/2020
6877(2^294469+1466)/288644Stefano Morozzi01/2020
68787*10^88634-2788635Dylan Delgado08/2019
687920^68120-5388627Lelio R Paula01/2016
6880122^42477-12188623Norbert Schneider10/2018
68812^294391-11325788621Enzo Doria07/2014
68825^126784-1547688619Enzo Doria02/2013
6883(2^294335+554)/288604Stefano Morozzi01/2020
68842^294327+988602Lelio R Paula10/2012
68852^294320+1891588600Lelio R Paula10/2013
6886(98*10^88595-89)/9988595Ray Chandler07/2011
688720723^18834+18834^2072388590Hans Havermann08/2020
6888(2^294268+1402)/288584Stefano Morozzi01/2020
6889(17*2^294262-1)/1388582Lelio R Paula02/2014
68906*10^88571+7788572Robert Price06/2020
6891(2^294145+1346)/288547Stefano Morozzi01/2020
6892(2*10^88545+7)/988545Erik Branger03/2011
68932^294137-13388545Lelio R Paula10/2012
6894(2^294109+3494)/288536Stefano Morozzi01/2020
689523515^5818+5818^2351588529Hans Havermann08/2020
6896(2^294092-1017)/117188528Lelio R Paula01/2013
68984^147036+147036^4+188525Robert Price04/2014
689722541^8458+8458^2254188525Hans Havermann08/2020
6899(14^77213-5^77213)/988496Robert Price04/2013
69002^293965+279337788493Enzo Doria03/2016
6901(2^293956+3306)/288490Stefano Morozzi01/2020
690211^84971-15088489Enzo Doria08/2012
6903(2^293944+1066)/288486Stefano Morozzi01/2020
69049*10^88485+9188486Robert Price10/2020
690548^52626-4788478Norbert Schneider08/2018
6906(2^293956-1017)/3985137669667788476Lelio R Paula01/2013
690711^84958-219088475Enzo Doria12/2012
6908(2^293902+3070)/288474Stefano Morozzi01/2020
69092^293880-11134788467Enzo Doria05/2014
6910(106*10^88459-1)/388461Serge Batalov12/2014
691110^88457+27873388458Patrick De Geest07/2017
691210^88457-40188457Robert Price06/2017
6913(2^293834+3018)/288453Stefano Morozzi01/2020
6914(2^293747+1626)/288427Stefano Morozzi01/2020
691522080^10109+10109^2208088424Hans Havermann08/2020
691611^84908-168088423Enzo Doria12/2012
6917(2^293703+3486)/288414Stefano Morozzi01/2020
69182^293679-11207588407Enzo Doria06/2014
69196^113608-6588405Lelio R Paula12/2015
69202^293624+8287588390Lelio R Paula10/2013
6921(2^293618+918)/288388Stefano Morozzi01/2020
69222^293612-11233788387Enzo Doria06/2014
6923758^30693+30693^75888386Norbert Schneider05/2017
6924gcd(V(1062695),5*F(212539)*(F(212539)-1)+1)88383Serge Batalov04/2015
69265*10^88377+7788378Robert Price06/2016
6925(2^293584+1558)/288378Stefano Morozzi01/2020
6927(5*2^293526+1)/30388359Lelio R Paula01/2013
692820918^16743+16743^2091888355Hans Havermann08/2020
6929(2^293499+2390)/288352Stefano Morozzi01/2020
693020727^18292+18292^2072788344Hans Havermann08/2020
69312^293461-278584388341Enzo Doria03/2016
69332^293416-103788328Yves Minet11/2012
69326*10^88327+4388328Robert Price07/2020
693425109^3292+3292^2510988320Hans Havermann08/2020
6935(2^293384-7)/388317Lelio R Paula01/2013
6936(3^185092-5)/488311Lelio R Paula01/2013
6937(5*10^88303-173)/388304Robert Price11/2017
693814^77039-5788297Lelio R Paula11/2015
69393*10^88293-5988294Robert Price10/2017
69405^126303+4288283Lelio R Paula10/2015
694219^69025-1888266Theodore Burton01/2006
6941140^41128+13988266Norbert Schneider04/2019
69435*10^88261-388262Dmitry Domanov11/2010
6944(2^293195+2238)/288261Stefano Morozzi01/2020
69458^97731-7^(97731-1)88260Robert Price04/2016
69465*10^88254+5988255Robert Price09/2016
69484*3^184968-788253Lelio R Paula08/2014
694734*10^88251-988253Robert Price06/2020
69497^104426+8888251Lelio R Paula10/2015
69502^293142+9988245Lelio R Paula10/2012
695111^84736-213088244Enzo Doria12/2012
695223884^4945+4945^2388488232Hans Havermann08/2020
695322080^9907+9907^2208088231Hans Havermann08/2020
6954(10^110315+1)/(10^22063+1)/582481268216764857846028164188225Makoto Kamada04/2019
69552^293068-8988223Lelio R Paula10/2012
69562126^26511+26511^212688218Norbert Schneider02/2020
69572^293014-10965588207Enzo Doria04/2014
69588*7^104371-388205Lelio R Paula10/2014
69592^292995-214588201Lelio R Paula10/2013
696028534^1233+1233^2853488198Hans Havermann08/2020
69615*10^88182+7788183Robert Price06/2016
69632^292929+4387788181Donovan Johnson04/2005
69626^113321+13188181Lelio R Paula12/2015
6964(2^292919+3366)/288178Stefano Morozzi01/2020
69652^292904-58394988173Paul Bourdelais04/2013
69662^292894-11185188170Enzo Doria05/2014
69672^292872-279734988164Enzo Doria03/2016
6968(2^292864+1042)/288161Stefano Morozzi01/2020
69692^292860-10968588160Enzo Doria04/2014
69709*6^113288-588157Lelio R Paula10/2014
6971(2^292735+2166)/288122Stefano Morozzi01/2020
6972(2^292735+2346)/288122Stefano Morozzi01/2020
6973(2^292705+1934)/288113Stefano Morozzi01/2020
6974(2*10^88112-23)/388112Robert Price09/2017
697529622^943+943^2962288111Hans Havermann08/2020
6976(73*10^88105+17)/988106Robert Price10/2015
6977(2^292673+3026)/288104Stefano Morozzi01/2020
697811^84588+7888090Lelio R Paula11/2015
6979(265*10^88077+11)/388079Robert Price03/2017
698091^44959-90^4495988077Robert Price07/2015
69816^113177-5^11317788069Jean-Louis Charton01/2009
69821316^28233+28233^131688066Norbert Schneider07/2020
6983(2^292543+2234)/288064Stefano Morozzi01/2020
6984(10^88020+101)/388020Robert Price04/2016
698552^51285-5188006Norbert Schneider09/2018
698621002^15501+15501^2100288006Hans Havermann08/2020
698720466^19951+19951^2046688004Hans Havermann08/2020
6988(2^292324+2346)/287998Stefano Morozzi01/2020
698921634^11683+11683^2163487998Hans Havermann08/2020
6990(6340^23143-1)/633987988Serge Batalov08/2020
699120674^18013+18013^2067487980Hans Havermann08/2020
6992(10^(2*43982+1)-6*10^43982-1)/387965Robert Price02/2016
6993(424*10^87930-1)/987932Robert Price11/2017
6994(2^292100+3070)/287931Stefano Morozzi01/2020
6995p(18225)#/2+12887929Robert Price04/2017
6996(10607^21841-1)/1060687919Serge Batalov08/2020
6997(2^292047+1550)/287915Stefano Morozzi01/2020
69984*6^112977+787914Lelio R Paula10/2014
6999(2^292016+1062)/287906Stefano Morozzi01/2020
7000(11359^21673-1)/1135887888Serge Batalov08/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 25 2021 11:23 (Time in France)

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