PRP Records

Probable Primes Top 10000

(271067 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 ?
65016*10^88571+7788572Robert Price06/2020
6502(2^294145+1346)/288547Stefano Morozzi01/2020
6503(2*10^88545+7)/988545Erik Branger03/2011
65042^294137-13388545Lelio R Paula10/2012
6505(2^294109+3494)/288536Stefano Morozzi01/2020
650623515^5818+5818^2351588529Hans Havermann08/2020
6507(2^294092-1017)/117188528Lelio R Paula01/2013
65094^147036+147036^4+188525Robert Price04/2014
650822541^8458+8458^2254188525Hans Havermann08/2020
6510(14^77213-5^77213)/988496Robert Price04/2013
65112^293965+279337788493Enzo Doria03/2016
6512(2^293956+3306)/288490Stefano Morozzi01/2020
651311^84971-15088489Enzo Doria08/2012
6514(2^293944+1066)/288486Stefano Morozzi01/2020
651548^52626-4788478Norbert Schneider08/2018
6516(2^293956-1017)/3985137669667788476Lelio R Paula01/2013
651711^84958-219088475Enzo Doria12/2012
6518(2^293902+3070)/288474Stefano Morozzi01/2020
65192^293880-11134788467Enzo Doria05/2014
6520(106*10^88459-1)/388461Serge Batalov12/2014
652110^88457+27873388458Patrick De Geest07/2017
652210^88457-40188457Robert Price06/2017
6523(2^293834+3018)/288453Stefano Morozzi01/2020
6524(2^293747+1626)/288427Stefano Morozzi01/2020
652522080^10109+10109^2208088424Hans Havermann08/2020
652611^84908-168088423Enzo Doria12/2012
6527(2^293703+3486)/288414Stefano Morozzi01/2020
65282^293679-11207588407Enzo Doria06/2014
65296^113608-6588405Lelio R Paula12/2015
65302^293624+8287588390Lelio R Paula10/2013
6531(2^293618+918)/288388Stefano Morozzi01/2020
65322^293612-11233788387Enzo Doria06/2014
6533758^30693+30693^75888386Norbert Schneider05/2017
6534gcd(V(1062695),5*F(212539)*(F(212539)-1)+1)88383Serge Batalov04/2015
65355*10^88377+7788378Robert Price06/2016
6536(2^293584+1558)/288378Stefano Morozzi01/2020
6537(5*2^293526+1)/30388359Lelio R Paula01/2013
653820918^16743+16743^2091888355Hans Havermann08/2020
6539(2^293499+2390)/288352Stefano Morozzi01/2020
654020727^18292+18292^2072788344Hans Havermann08/2020
65412^293461-278584388341Enzo Doria03/2016
65432^293416-103788328Yves Minet11/2012
65426*10^88327+4388328Robert Price07/2020
654425109^3292+3292^2510988320Hans Havermann08/2020
6545(2^293384-7)/388317Lelio R Paula01/2013
6546(3^185092-5)/488311Lelio R Paula01/2013
6547(5*10^88303-173)/388304Robert Price11/2017
654814^77039-5788297Lelio R Paula11/2015
65493*10^88293-5988294Robert Price10/2017
65505^126303+4288283Lelio R Paula10/2015
655219^69025-1888266Theodore Burton01/2006
6551140^41128+13988266Norbert Schneider04/2019
65535*10^88261-388262Dmitry Domanov11/2010
6554(2^293195+2238)/288261Stefano Morozzi01/2020
65558^97731-7^(97731-1)88260Robert Price04/2016
65565*10^88254+5988255Robert Price09/2016
65584*3^184968-788253Lelio R Paula08/2014
655734*10^88251-988253Robert Price06/2020
65597^104426+8888251Lelio R Paula10/2015
65602^293142+9988245Lelio R Paula10/2012
656111^84736-213088244Enzo Doria12/2012
656223884^4945+4945^2388488232Hans Havermann08/2020
656322080^9907+9907^2208088231Hans Havermann08/2020
6564(10^110315+1)/(10^22063+1)/582481268216764857846028164188225Makoto Kamada04/2019
65652^293068-8988223Lelio R Paula10/2012
65662126^26511+26511^212688218Norbert Schneider02/2020
65672^293014-10965588207Enzo Doria04/2014
65688*7^104371-388205Lelio R Paula10/2014
65692^292995-214588201Lelio R Paula10/2013
657028534^1233+1233^2853488198Hans Havermann08/2020
65715*10^88182+7788183Robert Price06/2016
65732^292929+4387788181Donovan Johnson04/2005
65726^113321+13188181Lelio R Paula12/2015
6574(2^292919+3366)/288178Stefano Morozzi01/2020
65752^292904-58394988173Paul Bourdelais04/2013
65762^292894-11185188170Enzo Doria05/2014
65772^292872-279734988164Enzo Doria03/2016
6578(2^292864+1042)/288161Stefano Morozzi01/2020
65792^292860-10968588160Enzo Doria04/2014
65809*6^113288-588157Lelio R Paula10/2014
6581(2^292735+2166)/288122Stefano Morozzi01/2020
6582(2^292735+2346)/288122Stefano Morozzi01/2020
6583(2^292705+1934)/288113Stefano Morozzi01/2020
6584(2*10^88112-23)/388112Robert Price09/2017
658529622^943+943^2962288111Hans Havermann08/2020
6586(73*10^88105+17)/988106Robert Price10/2015
6587(2^292673+3026)/288104Stefano Morozzi01/2020
658811^84588+7888090Lelio R Paula11/2015
6589(265*10^88077+11)/388079Robert Price03/2017
659091^44959-90^4495988077Robert Price07/2015
65916^113177-5^11317788069Jean-Louis Charton01/2009
65921316^28233+28233^131688066Norbert Schneider07/2020
6593(2^292543+2234)/288064Stefano Morozzi01/2020
6594(10^88020+101)/388020Robert Price04/2016
659552^51285-5188006Norbert Schneider09/2018
659621002^15501+15501^2100288006Hans Havermann08/2020
659720466^19951+19951^2046688004Hans Havermann08/2020
6598(2^292324+2346)/287998Stefano Morozzi01/2020
659921634^11683+11683^2163487998Hans Havermann08/2020
6600(6340^23143-1)/633987988Serge Batalov08/2020
660120674^18013+18013^2067487980Hans Havermann08/2020
6602(10^(2*43982+1)-6*10^43982-1)/387965Robert Price02/2016
6603(424*10^87930-1)/987932Robert Price11/2017
6604(2^292100+3070)/287931Stefano Morozzi01/2020
6605p(18225)#/2+12887929Robert Price04/2017
6606(10607^21841-1)/1060687919Serge Batalov08/2020
6607(2^292047+1550)/287915Stefano Morozzi01/2020
66084*6^112977+787914Lelio R Paula10/2014
6609(2^292016+1062)/287906Stefano Morozzi01/2020
6610(11359^21673-1)/1135887888Serge Batalov08/2020
661114^76677+6987882Lelio R Paula11/2015
6612(22*10^87863-1)/387864Robert Price12/2014
66132^291822-279781187848Enzo Doria04/2016
6614(2^291730+1614)/287820Stefano Morozzi01/2020
66152^291716-11138987816Enzo Doria05/2014
6616(782*10^87809-71)/987811Robert Price06/2017
66173^184039+182087809Lelio R Paula12/2015
661812^81356+4187798Lelio R Paula11/2015
661921307^13188+13188^2130787789Hans Havermann08/2020
6620(2527^25801-1)/252687788Serge Batalov08/2020
6621(2^291596+1986)/287779Stefano Morozzi01/2020
66236^112792-1898387770Enzo Doria03/2013
6622(3123^25117-1)/312287770Serge Batalov08/2020
66243*6^112787-587766Lelio R Paula10/2014
66257^103848+8287762Lelio R Paula10/2015
6626(19*2^291534-1)/17869639587754Lelio R Paula02/2014
6627(2^291506+918)/287752Stefano Morozzi01/2020
662824411^3932+3932^2441187749Hans Havermann08/2020
6629(3^183915+5)/12887748Lelio R Paula01/2013
663019^68619+2487747Lelio R Paula12/2015
66322^291480+118587745Lelio R Paula10/2013
66312^291482+186736987745Enzo Doria03/2016
66332^291467-93787741Yves Minet05/2013
6634(25*10^87726+161)/387727Robert Price01/2017
663511^84239-285087726Enzo Doria12/2012
663610^87720+21554187721Patrick De Geest01/2011
663710^87720-387720Markus Tervooren07/2010
6638(2^291383+3078)/287715Stefano Morozzi01/2020
6640(5*10^87712-473)/987712Robert Price12/2017
6639(2^291373+2946)/287712Stefano Morozzi01/2020
664122591^7630+7630^2259187711Hans Havermann08/2020
664222081^9378+9378^2208187709Hans Havermann08/2020
6643(2^291357+5)/684787704Lelio R Paula01/2013
6644(2^291280+462)/287684Stefano Morozzi01/2020
664520749^16816+16816^2074987680Hans Havermann08/2020
664793^44541-287679Lelio R Paula09/2013
66462^291261-10956187679Enzo Doria04/2014
6648(4*10^87669+149)/987669Robert Price03/2017
66492^291217+425787666Lelio R Paula10/2013
665022748^7137+7137^2274887660Hans Havermann08/2020
66512*12^81214-5^8121487645Mike Oakes12/2010
6652(5005^23689-1)/500487632Serge Batalov08/2020
6653(5*10^87622-473)/987622Robert Price12/2017
665412^81188+8587617Lelio R Paula11/2015
6655(2^291030+3462)/287609Stefano Morozzi01/2020
6656(21*2^290980-1)/587595Lelio R Paula02/2014
6657(2^290980+1150)/287594Stefano Morozzi01/2020
66582^290958+12787588Lelio R Paula09/2012
665978531!4-887580Robert Price11/2019
66602^290923-6787577Lelio R Paula09/2012
66613*10^87573-9787574Robert Price08/2017
6662(13*10^87565+11)/387566Robert Price05/2015
6663(2^290881+1022)/287564Stefano Morozzi01/2020
6664(2^290857-7)/5587555Lelio R Paula01/2013
6665(2^290808+1498)/287542Stefano Morozzi01/2020
66662^290802+8287587541Lelio R Paula10/2013
6667(509203*2^290792-1)/756098787536Lelio R Paula04/2015
66683^183441+23687524Lelio R Paula12/2015
66692^290618-3387485Lelio R Paula09/2012
6670(184*10^87473-1)/387475Robert Price02/2017
66712^290534-11515187460Enzo Doria06/2015
66722^290512-10975787453Enzo Doria04/2014
6673(32*10^87448-41)/987449Robert Price05/2015
6674(2^290493+3074)/287447Stefano Morozzi01/2020
6675(2^290491+9)/317987444Lelio R Paula01/2013
6676(25*2^290489-1)/5180987443Lelio R Paula02/2014
66772^290426+8287587427Lelio R Paula11/2013
66783*2^290415-787425Lelio R Paula08/2014
668110^87408+5787409Robert Price03/2011
66802^290366+7477987409Enzo Doria04/2016
667922284^8365+8365^2228487409Hans Havermann08/2020
668210^87408-12356987408Patrick De Geest07/2013
668321517^11536+11536^2151787404Hans Havermann08/2020
66846*10^87396+7787397Robert Price06/2020
6685(2^290268+3882)/287380Stefano Morozzi01/2020
66862^290265+5890587379Lelio R Paula10/2013
66877^103391+1687376Lelio R Paula10/2015
6688(115*10^87368-7)/987370Robert Price11/2017
6689(92^44491-1)/9187369Paul Bourdelais08/2017
66908*7^103379+387367Lelio R Paula10/2014
6691(2^290226+7)/7187365Lelio R Paula01/2013
6692(3216^24907-1)/321587354Serge Batalov08/2020
6693(2^290160+2686)/287347Stefano Morozzi01/2020
669413^78407-3087341Lelio R Paula11/2015
66954*10^87337-9987338Robert Price12/2016
66967*10^87319+3987320Robert Price07/2016
66973*5^124921+287317Lelio R Paula10/2014
669878315!4-1687316Robert Price11/2019
66993^182984+8887306Lelio R Paula12/2015
6700(10^87323-1)/(9*33909262597306826117)87303Alfred Reich02/2019
6701(2^290008+958)/287301Stefano Morozzi01/2020
6702(10536^21701-1)/1053587293Serge Batalov08/2020
67034*10^87287-9987288Robert Price12/2016
670511^83813-186087283Enzo Doria12/2012
6704(3068^25033-1)/306787283Serge Batalov08/2020
6706734^30453+30453^73487270Norbert Schneider04/2017
670712^80855+2987258Lelio R Paula11/2015
670822209^8482+8482^2220987249Hans Havermann08/2020
67093*6^112119-587247Lelio R Paula10/2014
671012^80806+7987205Lelio R Paula11/2015
671191382^9+9^9138287201Andrey Kulsha11/2004
6712(21181*2^289657+1)/8187198Lelio R Paula06/2014
67136^112054-4787195Lelio R Paula12/2015
6714(55459*2^289632+1)/5587191Lelio R Paula06/2014
671515^74131-6887185Lelio R Paula11/2015
67162^289583-74187174Lelio R Paula10/2013
67177^103146+1287169Lelio R Paula10/2015
6718(2^289562+2182)/287167Stefano Morozzi01/2020
67195*2^289556-387166Lelio R Paula08/2014
67202^289543-11273587162Enzo Doria06/2014
672120204^20243-20243^2020487155Norbert Schneider04/2020
67228*3^182655-787150Lelio R Paula08/2014
67232*10^87144+8187145Robert Price01/2017
672420541^17468+17468^2054187140Hans Havermann07/2020
67257^103106+2*3^10310687135Mike Oakes08/2010
67268*3^182614+787130Lelio R Paula08/2014
6727(4982^23563-1)/498187119Serge Batalov08/2020
6728(2^289368-509203)/987108Lelio R Paula01/2013
67293^182566+1487107Robert Price09/2013
67301738^26881+26881^173887096Norbert Schneider04/2020
673124290^3849+3849^2429087089Hans Havermann08/2020
6732(3^182385-5)/287020Lelio R Paula01/2013
673311^83534-886992Lelio R Paula11/2015
67344^144479-1426786986Mike Oakes03/2011
6735(145*10^86982-1)/986984Serge Batalov12/2014
6737(151*10^86963-1)/386965Robert Price04/2017
6736(2^288892+826)/286965Stefano Morozzi01/2020
673815^73940-5886961Lelio R Paula11/2015
67392^288761-11314386926Enzo Doria07/2014
674024440^3603+3603^2444086925Hans Havermann08/2020
67422^288747+308386922Yves Minet03/2011
6741(2^288749+3102)/286922Stefano Morozzi01/2020
674330^58842+2986917Norbert Schneider03/2017
6744(2^288705+2186)/286909Stefano Morozzi01/2020
6745(10^86906-13)/386906Robert Price02/2017
67462^288692-11002786905Enzo Doria04/2014
6747(2^288682+7)/25989544986894Lelio R Paula01/2013
6748(26*10^86885+79)/386886Robert Price09/2020
6749(2^288636+47)/129386885Lelio R Paula01/2013
67503^182089-3486879Robert Price11/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 30 2020 10:03 (Time in France)

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