PRP Records

Probable Primes Top 10000

(291910 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 ?
55014*10^106914-93106915Robert Price07/2020
55024*10^106892-3106893Robert Price10/2015
5503(66^58741+1)/67106881Paul Bourdelais08/2017
55042^354946-3106850M. Frind & P. Underwood08/2002
5505(2^354945+3134)/2106849Stefano Morozzi09/2020
55062^354873-18693106828Enzo Doria05/2013
5507(2^354831+3186)/2106815Stefano Morozzi09/2020
55092^354828+4257106814Lelio R Paula01/2017
550825216^17217+17217^25216106814Hans Havermann10/2020
5510(2^354799+1218)/2106805Stefano Morozzi09/2020
5511436^40459+40459^436106791Norbert Schneider03/2019
5512(21^80761+1)/22106783Paul Bourdelais03/2010
5513(115*10^106772-7)/9106774Robert Price02/2020
55142^354640-354640+1106758Robert Price10/2014
5515(2^354603+2606)/2106746Stefano Morozzi09/2020
55162^354585+95106741Lelio R Paula10/2011
5517(206*10^106737+1)/9106739Robert Price04/2022
55182^354553+189106732Lelio R Paula10/2011
5520(2^354546+1338)/2106729Stefano Morozzi02/2021
5519(8*10^106729-71)/9106729Serge Batalov11/2022
55212^354514-109031106720Enzo Doria04/2014
55222^354509-109465106718Enzo Doria04/2014
5523(15*2^354478-1)/26983106706Lelio R Paula03/2014
5524Phi(217618,10)/899798636917106693Makoto Kamada06/2019
552515^90710+28106684Lelio R Paula04/2017
55267^126237+34106683Lelio R Paula03/2017
55272^354385-115315106681Enzo Doria06/2015
55282^354327-19305106664Enzo Doria06/2013
5529(35*10^106649+1)/9106650Serge Batalov11/2010
553010^106636+97106637Lelio R Paula02/2017
553110^106636-22923106636Patrick De Geest03/2017
55322^354220-57106631Lelio R Paula10/2011
5533(68*10^106628-329)/9106629Robert Price03/2021
5534(29*10^106620-77)/3106621Robert Price02/2020
5535(746*10^106618+1)/9106620Robert Price03/2020
55362*10^106613+29106614Robert Price02/2021
55372^354157-17041106612Enzo Doria05/2013
553812^98778+73106600Lelio R Paula02/2017
553933333^1576+1576^33333106585Hans Havermann11/2020
55402^354064+1870651106584Enzo Doria05/2016
554124568^21779+21779^24568106577Hans Havermann11/2020
55422^353992-57106563Lelio R Paula10/2011
55439*10^106559+59106560Robert Price01/2020
55447*10^106553+27106554Robert Price11/2020
554528847^4938+4938^28847106548Hans Havermann10/2020
5546NSW(139160)106535Robert Price12/2018
5547(7*10^106516+113)/3106517Robert Price02/2018
55482^353832-1853849106515Enzo Doria09/2015
5549(7^126037-1)/6106513Paul Bourdelais09/2008
55502^353794-18453106503Enzo Doria05/2013
5551(2^353761+2094)/2106493Stefano Morozzi09/2020
55522^353728+7695106483Lelio R Paula01/2017
555326476^10509+10509^26476106475Hans Havermann10/2020
55542^353672-303106466Yves Minet02/2012
55556^136811+101106460Lelio R Paula02/2017
55562^353641+1871981106457Enzo Doria05/2016
5557(8*10^106454-29)/3106455Robert Price07/2018
555827845^6654+6654^27845106454Hans Havermann11/2020
555910^106449-700001106449Robert Price08/2021
556025316^16017+16017^25316106444Hans Havermann11/2020
55612^353553+54615106431Lelio R Paula01/2017
55622^353544-18897106428Enzo Doria05/2013
556328894^4823+4823^28894106426Hans Havermann11/2020
5564(19*10^106422+29)/3106423Robert Price12/2021
5565(694*10^106418+53)/9106420Robert Price02/2022
55666*10^106412-13106413Robert Price07/2022
556725696^13829+13829^25696106402Hans Havermann11/2020
55686^136729-133106396Lelio R Paula02/2017
55692^353418+1605106390Lelio R Paula01/2017
55702^353387+65106381Lelio R Paula10/2011
55712^353372+74311106376Enzo Doria04/2016
55722^353344-3693106368Yves Minet03/2017
5573(772*10^106365-7)/9106367Robert Price06/2022
5574(56*10^106351+619)/9106352Robert Price05/2021
55762^353277-20089106347Enzo Doria06/2013
55752^353275+72173106347Enzo Doria04/2016
55772^353268-17705106345Enzo Doria05/2013
55782^353267-19857106344Enzo Doria06/2013
5579(46*10^106343+143)/9106344Robert Price01/2019
5580(2^353189+3054)/2106321Stefano Morozzi09/2020
558135087^1072+1072^35087106321Hans Havermann10/2020
5582(2^353184+1290)/2106319Stefano Morozzi01/2021
558326985^8684+8684^26985106287Hans Havermann10/2020
5584(2^353051+606)/2106279Stefano Morozzi09/2020
5586222748^3+3^222748106278Anatoly F. Selevich12/2010
5585(46*10^106277+107)/9106278Robert Price06/2022
5587(9179*2^353019-1)/9106273Lelio R Paula05/2015
55882^353025+72257106272Enzo Doria04/2016
55912^352932-20345106244Enzo Doria06/2013
5589(2^353011-3)/745325861246794515484535106244Lelio R Paula12/2013
559025628^13983+13983^25628106244Hans Havermann10/2020
55922^352883-187106229Lelio R Paula10/2011
559320^81649-19^81649106228Jean-Louis Charton03/2011
5594(55*10^106222+377)/9106223Robert Price02/2019
55952^352814-131106208Lelio R Paula10/2011
55962^352752+73951106189Enzo Doria04/2016
55976^136434+5106167Lelio R Paula11/2014
559825296^15737+15737^25296106166Hans Havermann09/2020
55998*10^106157-13106158Robert Price08/2019
56007*5^151872-8106155Lelio R Paula11/2014
5601105^52520-2106153Lelio R Paula10/2017
5602(23*10^106152-29)/3106153Robert Price03/2022
56032^352601-1604809106144Enzo Doria05/2015
560412^98353-43106141Lelio R Paula02/2017
56052^352585-18901106139Enzo Doria05/2013
560626363^10614+10614^26363106135Hans Havermann09/2020
5607(2^352554-3)/193106128Lelio R Paula12/2013
56082^352540+15015106126Lelio R Paula01/2017
560925068^17119+17119^25068106125Hans Havermann09/2020
56102^352524-3149106121Yves Minet10/2014
5611(7*10^106119-67)/3106120Robert Price10/2021
56122^352486-1858781106109Enzo Doria04/2016
56132^352444+12705106097Lelio R Paula01/2017
561428561^5182+5182^28561106090Hans Havermann10/2020
5615(182*10^106083+43)/9106085Robert Price02/2020
5616(266*10^106066+1)/3106068Robert Price04/2020
5617(7*10^106066-187)/9106066Tyler Busby01/2023
56182^352228-18953106032Enzo Doria05/2013
5619(2^352223+1118)/2106030Stefano Morozzi09/2020
5620(2^352212+2250)/2106027Stefano Morozzi01/2021
5621(2^352136+2638)/2106004Stefano Morozzi09/2020
56222^352107+1872533105995Enzo Doria05/2016
5623(2^352096+2086)/2105992Stefano Morozzi09/2020
56242^352066-2591105983Yves Minet07/2014
56252^352030+715105972Lelio R Paula10/2011
56269*6^136176-5105967Lelio R Paula11/2014
562717099*2^351991+58329105965Paul Vanderveen12/2017
562828582^5097+5097^28582105963Hans Havermann09/2020
5629155^48377+2105962Lelio R Paula08/2013
5630(23*10^105944-119)/3105945Robert Price07/2021
56312^351865+1869707105922Enzo Doria05/2016
563224974^17427+17427^24974105921Hans Havermann09/2020
563325163^16194+16194^25163105920Hans Havermann09/2020
56342^351831+23105912Lelio R Paula10/2011
5635(2^351818+3798)/2105908Stefano Morozzi02/2021
56369*2^351784-5105899Lelio R Paula09/2014
5637(2^351776+2766)/2105895Stefano Morozzi01/2021
5638(85*10^105881+203)/9105882Robert Price09/2020
56392^351671-112387105864Enzo Doria06/2014
56402^351669-109501105863Enzo Doria04/2014
56412^351644+74731105856Enzo Doria04/2016
564213^95025-42105853Lelio R Paula12/2016
56432^351599+15015105842Lelio R Paula01/2017
564419^82763+90105834Lelio R Paula01/2017
5645(205*10^105831-1)/3105833Robert Price11/2021
564626050^11551+11551^26050105832Hans Havermann09/2020
5647(9179*2^351540-1)/221105826Lelio R Paula05/2015
564820^81329-51105812Lelio R Paula01/2017
5649(5*10^105811+211)/9105811Robert Price02/2018
56502^351483+28425105807Lelio R Paula01/2017
565125231^15610+15610^25231105804Hans Havermann09/2020
565215^89960+86105802Lelio R Paula02/2017
56532^351460-17289105801Enzo Doria05/2013
565419^82735+22105798Lelio R Paula01/2017
56552^351435-109077105793Enzo Doria04/2014
56562^351393+1089105780Lelio R Paula01/2017
56572^351364+72631105772Enzo Doria04/2016
5658(2^351333+3626)/2105762Stefano Morozzi09/2020
565926818^8783+8783^26818105761Hans Havermann09/2020
56622^351305+1872467105754Enzo Doria05/2016
56613^221649+16105754Lelio R Paula11/2016
566032511^1790+1790^32511105754Hans Havermann09/2020
56638*3^221637-5105749Lelio R Paula09/2014
56642^351279-2780449105746Enzo Doria03/2016
5665(2^351263+3198)/2105741Stefano Morozzi09/2020
566615^89903-26105735Lelio R Paula02/2017
56682^351213-73105726Lelio R Paula10/2011
5667(2^351214+1210)/2105726Stefano Morozzi09/2020
56692^351192-4589105720Yves Minet07/2011
567020^81250-33105709Lelio R Paula12/2016
5671(2^351133+3530)/2105702Stefano Morozzi09/2020
5672(2^351103+534)/2105693Stefano Morozzi09/2020
56732^351076-113159105685Enzo Doria07/2014
567493^53688-2105684Lelio R Paula09/2013
56752^351060-4559105680Yves Minet07/2011
5676((10^52836-1)*10000/9+5927)*10^52836+(10^52836-1)/9105676Hans Havermann08/2019
567711^101473-750105674Enzo Doria11/2012
56783*5^151181-8105672Lelio R Paula11/2014
567915^89831-34105650Lelio R Paula02/2017
568111^101448-360105648Enzo Doria08/2012
56803*7^125011+4105648Lelio R Paula11/2014
56822^350943-113269105645Enzo Doria07/2014
56832*10^105636-91105637Robert Price04/2020
568424231^22880+22880^24231105634Hans Havermann09/2020
568535296^983+983^35296105626Hans Havermann09/2020
56862^350868-19725105622Enzo Doria06/2013
56872^350858-59291105619Enzo Doria10/2015
56882^350851+135105617Lelio R Paula10/2011
56892^350841-741105614Lelio R Paula01/2017
56903*10^105582+77105583Robert Price09/2018
569124915^17284+17284^24915105581Hans Havermann09/2020
5692(5*10^105576-53)/3105577Robert Price09/2020
56938*10^105571+3105572Robert Price08/2015
56942^350674-78557105564Jorge Menendez03/2018
56952*5^151026-3105563Lelio R Paula11/2014
5696(2^350702+5)/34264674063105562Lelio R Paula12/2013
56976^135647-5^135647105554Jean-Louis Charton02/2009
56983^221211+236105545Lelio R Paula11/2016
5699(32*10^105530-77)/9105531Robert Price06/2018
570010^105515+33105516Lelio R Paula11/2016
570124644^19125+19125^24644105516Hans Havermann10/2020
570210^105515-41033105515Patrick De Geest12/2016
5703(29*2^350473-1)/267927105499Lelio R Paula03/2014
57042^350455-430567105498Harrison Mesh06/2022
570517^85732-72105489Lelio R Paula01/2017
5706(2^350399+3618)/2105481Stefano Morozzi09/2020
5707(2^350379+1010)/2105475Stefano Morozzi09/2020
570825233^15118+15118^25233105462Hans Havermann09/2020
570926261^10366+10366^26261105454Hans Havermann09/2020
57102^350307-110329105453Enzo Doria05/2014
57112^350253-20365105437Enzo Doria06/2013
5712(3*29^72089-1075)/4105423Curtis Bright05/2015
5713(2^350187+2658)/2105417Stefano Morozzi09/2020
57144*10^105415-69105416Robert Price01/2022
5715(22*10^105407+179)/3105408Robert Price02/2022
57162^350139-109009105403Enzo Doria04/2014
5717(2^350129+3026)/2105400Stefano Morozzi09/2020
5718(2^350097+2070)/2105390Stefano Morozzi09/2020
57193*5^150763+4105380Lelio R Paula11/2014
572012^97643+91105375Lelio R Paula02/2017
57216*5^150744-7105367Lelio R Paula11/2014
5722(2^350018+2074)/2105366Stefano Morozzi09/2020
57234*10^105364-39105365Robert Price09/2020
57252^349996-112169105360Enzo Doria06/2014
5724(2^349997+3702)/2105360Stefano Morozzi09/2020
5726(418*10^105343+23)/9105345Robert Price02/2020
572725490^13563+13563^25490105334Hans Havermann10/2020
572811^101142-1080105329Enzo Doria12/2012
5729(68*10^105320-41)/9105321Robert Price10/2013
573024800^17649+17649^24800105319Hans Havermann09/2020
57313^220712-9934105307Enzo Doria05/2014
57327*10^105296+9105297Robert Price09/2015
573389*10^105284-7105286Robert Price04/2020
57342^349739+1873373105282Enzo Doria06/2016
57357^124574+24105278Lelio R Paula11/2016
57362^349708-20957105273Enzo Doria06/2013
573734115^1218+1218^34115105267Hans Havermann09/2020
57382^349649-20469105255Enzo Doria06/2013
57392^349607-20109105243Enzo Doria06/2013
5740(85*10^105242+473)/9105243Robert Price01/2020
57412^349594-19085105239Enzo Doria05/2013
57422^349530+1874479105220Enzo Doria06/2016
5743(3^220528+8)/8081105215Lelio R Paula12/2013
5744(106*10^105199+17)/3105201Robert Price04/2021
5745(2^349452+3570)/2105196Stefano Morozzi09/2020
57463^220464-112852105189Enzo Doria07/2014
57472^349419-17349105186Enzo Doria05/2013
57482^349400-2579105180Yves Minet07/2014
57498*5^150471+3105176Lelio R Paula11/2014
5750(2^349359+2298)/2105168Stefano Morozzi02/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 02 2023 13:22 (Time in France)

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