PRP Records

Probable Primes Top 10000

(294627 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 ?
65012^352524-3149106121Yves Minet10/2014
6502(7*10^106119-67)/3106120Robert Price10/2021
65032^352486-1858781106109Enzo Doria04/2016
65042^352444+12705106097Lelio R Paula01/2017
650528561^5182+5182^28561106090Hans Havermann10/2020
6506(182*10^106083+43)/9106085Robert Price02/2020
6507(266*10^106066+1)/3106068Robert Price04/2020
6508(7*10^106066-187)/9106066Tyler Busby01/2023
65092^352228-18953106032Enzo Doria05/2013
6510(2^352223+1118)/2106030Stefano Morozzi09/2020
6511(2^352212+2250)/2106027Stefano Morozzi01/2021
6512(2^352136+2638)/2106004Stefano Morozzi09/2020
65132^352107+1872533105995Enzo Doria05/2016
6514(2^352096+2086)/2105992Stefano Morozzi09/2020
65152^352066-2591105983Yves Minet07/2014
65162^352030+715105972Lelio R Paula10/2011
65179*6^136176-5105967Lelio R Paula11/2014
651817099*2^351991+58329105965Paul Vanderveen12/2017
651928582^5097+5097^28582105963Hans Havermann09/2020
6520155^48377+2105962Lelio R Paula08/2013
6521(23*10^105944-119)/3105945Robert Price07/2021
65222^351865+1869707105922Enzo Doria05/2016
652324974^17427+17427^24974105921Hans Havermann09/2020
652425163^16194+16194^25163105920Hans Havermann09/2020
65252^351831+23105912Lelio R Paula10/2011
6526(2^351818+3798)/2105908Stefano Morozzi02/2021
65279*2^351784-5105899Lelio R Paula09/2014
6528(2^351776+2766)/2105895Stefano Morozzi01/2021
6529(85*10^105881+203)/9105882Robert Price09/2020
65302^351671-112387105864Enzo Doria06/2014
65312^351669-109501105863Enzo Doria04/2014
65322^351644+74731105856Enzo Doria04/2016
653313^95025-42105853Lelio R Paula12/2016
65342^351599+15015105842Lelio R Paula01/2017
653519^82763+90105834Lelio R Paula01/2017
6536(205*10^105831-1)/3105833Robert Price11/2021
653726050^11551+11551^26050105832Hans Havermann09/2020
6538(9179*2^351540-1)/221105826Lelio R Paula05/2015
653920^81329-51105812Lelio R Paula01/2017
6540(5*10^105811+211)/9105811Robert Price02/2018
65412^351483+28425105807Lelio R Paula01/2017
654225231^15610+15610^25231105804Hans Havermann09/2020
654315^89960+86105802Lelio R Paula02/2017
65442^351460-17289105801Enzo Doria05/2013
654519^82735+22105798Lelio R Paula01/2017
65462^351435-109077105793Enzo Doria04/2014
65472^351393+1089105780Lelio R Paula01/2017
65482^351364+72631105772Enzo Doria04/2016
6549(2^351333+3626)/2105762Stefano Morozzi09/2020
655026818^8783+8783^26818105761Hans Havermann09/2020
65532^351305+1872467105754Enzo Doria05/2016
65523^221649+16105754Lelio R Paula11/2016
655132511^1790+1790^32511105754Hans Havermann09/2020
65548*3^221637-5105749Lelio R Paula09/2014
65552^351279-2780449105746Enzo Doria03/2016
6556(2^351263+3198)/2105741Stefano Morozzi09/2020
655715^89903-26105735Lelio R Paula02/2017
65592^351213-73105726Lelio R Paula10/2011
6558(2^351214+1210)/2105726Stefano Morozzi09/2020
65602^351192-4589105720Yves Minet07/2011
656120^81250-33105709Lelio R Paula12/2016
6562(2^351133+3530)/2105702Stefano Morozzi09/2020
6563(2^351103+534)/2105693Stefano Morozzi09/2020
65642^351076-113159105685Enzo Doria07/2014
656593^53688-2105684Lelio R Paula09/2013
65662^351060-4559105680Yves Minet07/2011
6567((10^52836-1)*10000/9+5927)*10^52836+(10^52836-1)/9105676Hans Havermann08/2019
656811^101473-750105674Enzo Doria11/2012
65693*5^151181-8105672Lelio R Paula11/2014
657015^89831-34105650Lelio R Paula02/2017
657211^101448-360105648Enzo Doria08/2012
65713*7^125011+4105648Lelio R Paula11/2014
65732^350943-113269105645Enzo Doria07/2014
65742*10^105636-91105637Robert Price04/2020
657524231^22880+22880^24231105634Hans Havermann09/2020
657635296^983+983^35296105626Hans Havermann09/2020
65772^350868-19725105622Enzo Doria06/2013
65782^350858-59291105619Enzo Doria10/2015
65792^350851+135105617Lelio R Paula10/2011
65802^350841-741105614Lelio R Paula01/2017
65813*10^105582+77105583Robert Price09/2018
658224915^17284+17284^24915105581Hans Havermann09/2020
6583(5*10^105576-53)/3105577Robert Price09/2020
65848*10^105571+3105572Robert Price08/2015
65852^350674-78557105564Jorge Menendez03/2018
65862*5^151026-3105563Lelio R Paula11/2014
6587(2^350702+5)/34264674063105562Lelio R Paula12/2013
65886^135647-5^135647105554Jean-Louis Charton02/2009
65893^221211+236105545Lelio R Paula11/2016
6590(32*10^105530-77)/9105531Robert Price06/2018
659110^105515+33105516Lelio R Paula11/2016
659224644^19125+19125^24644105516Hans Havermann10/2020
659310^105515-41033105515Patrick De Geest12/2016
6594(29*2^350473-1)/267927105499Lelio R Paula03/2014
65952^350455-430567105498Harrison Mesh06/2022
659617^85732-72105489Lelio R Paula01/2017
6597(2^350399+3618)/2105481Stefano Morozzi09/2020
6598(2^350379+1010)/2105475Stefano Morozzi09/2020
65992^350356+24241105468Enzo Doria10/2023
660025233^15118+15118^25233105462Hans Havermann09/2020
660126261^10366+10366^26261105454Hans Havermann09/2020
66022^350307-110329105453Enzo Doria05/2014
66032^350253-20365105437Enzo Doria06/2013
6604(3*29^72089-1075)/4105423Curtis Bright05/2015
6605(2^350187+2658)/2105417Stefano Morozzi09/2020
66064*10^105415-69105416Robert Price01/2022
6607(22*10^105407+179)/3105408Robert Price02/2022
66082^350139-109009105403Enzo Doria04/2014
6609(2^350129+3026)/2105400Stefano Morozzi09/2020
6610(2^350097+2070)/2105390Stefano Morozzi09/2020
66113*5^150763+4105380Lelio R Paula11/2014
661212^97643+91105375Lelio R Paula02/2017
66136*5^150744-7105367Lelio R Paula11/2014
6614(2^350018+2074)/2105366Stefano Morozzi09/2020
66154*10^105364-39105365Robert Price09/2020
66172^349996-112169105360Enzo Doria06/2014
6616(2^349997+3702)/2105360Stefano Morozzi09/2020
6618(418*10^105343+23)/9105345Robert Price02/2020
661925490^13563+13563^25490105334Hans Havermann10/2020
662011^101142-1080105329Enzo Doria12/2012
6621(68*10^105320-41)/9105321Robert Price10/2013
662224800^17649+17649^24800105319Hans Havermann09/2020
66233^220712-9934105307Enzo Doria05/2014
66247*10^105296+9105297Robert Price09/2015
662589*10^105284-7105286Robert Price04/2020
66262^349739+1873373105282Enzo Doria06/2016
66277^124574+24105278Lelio R Paula11/2016
66282^349708-20957105273Enzo Doria06/2013
662934115^1218+1218^34115105267Hans Havermann09/2020
66302^349649-20469105255Enzo Doria06/2013
66312^349607-20109105243Enzo Doria06/2013
6632(85*10^105242+473)/9105243Robert Price01/2020
66332^349594-19085105239Enzo Doria05/2013
66342^349530+1874479105220Enzo Doria06/2016
6635(3^220528+8)/8081105215Lelio R Paula12/2013
6636(106*10^105199+17)/3105201Robert Price04/2021
6637(2^349452+3570)/2105196Stefano Morozzi09/2020
66383^220464-112852105189Enzo Doria07/2014
66392^349419-17349105186Enzo Doria05/2013
66402^349400-2579105180Yves Minet07/2014
66418*5^150471+3105176Lelio R Paula11/2014
6642(2^349359+2298)/2105168Stefano Morozzi02/2021
6643655^37342+37342^655105165Norbert Schneider08/2018
664413^94403+94105160Lelio R Paula12/2016
66452^349301-112309105151Enzo Doria06/2014
664630291^2960+2960^30291105149Hans Havermann09/2020
664727350^6981+6981^27350105132Hans Havermann09/2020
66499*2^349220+5105127Lelio R Paula09/2014
6648(2^349225+3122)/2105127Stefano Morozzi09/2020
66507*3^220317+8105119Lelio R Paula09/2014
66517^124386+88105119Lelio R Paula11/2016
6652(2^349197+570)/2105119Stefano Morozzi09/2020
66532^349171-19657105111Enzo Doria06/2013
6654(2^349115+590)/2105094Stefano Morozzi09/2020
6655(2^(6*58185+1)-5)/3105093Kevin Acres11/2013
6656(2^349111-5)/3105093Lelio R Paula12/2013
6657675^37142+37142^675105087Norbert Schneider08/2018
66582^348981-2797573105054Enzo Doria04/2016
66592^348869-6555105021Lelio R Paula01/2017
66605^150217+78104998Lelio R Paula11/2016
6661(88*10^104989-1)/3104991Robert Price04/2020
6662(28*10^104972+149)/3104973Robert Price12/2019
666324927^16262+16262^24927104972Hans Havermann10/2020
66642^348703-113005104971Enzo Doria06/2014
6665(191*10^104956-17)/3104958Robert Price11/2021
66672^348612-809104943Yves Minet05/2013
6666(73*10^104942-1)/9104943Robert Price01/2015
66682^348583-350407104934Enzo Doria06/2015
66692^348531-949104919Yves Minet05/2012
667020^80636-59104910Lelio R Paula12/2016
66718*10^104893-13104894Robert Price08/2019
66732^348437+35104890Lelio R Paula09/2011
667225208^14487+14487^25208104890Hans Havermann09/2020
66742^348348+135104864Lelio R Paula09/2011
6675(29*10^104858+349)/9104859Robert Price06/2021
66766*10^104852-31104853Robert Price07/2020
6678(2^348284+9)/25104843Lelio R Paula12/2013
667775^55914-74104843Norbert Schneider01/2015
66792^348268+255255104840Lelio R Paula01/2017
668035540^891+891^35540104839Hans Havermann09/2020
66815^149985-52104836Lelio R Paula11/2016
66822^348224-20249104826Enzo Doria06/2013
6683(2^348217+2522)/2104824Stefano Morozzi09/2020
66842^348212-20105104823Enzo Doria06/2013
668524647^17898+17898^24647104819Hans Havermann10/2020
668620^80562+19104814Lelio R Paula12/2016
66872*10^104811-87104812Robert Price04/2018
66882^348149-20053104804Enzo Doria06/2013
66892^348095-171104788Lelio R Paula09/2011
669025383^13412+13412^25383104769Hans Havermann09/2020
66912^348003-20377104760Enzo Doria06/2013
66922^347994-741104757Lelio R Paula12/2016
6693(2^347993+2234)/2104757Stefano Morozzi01/2021
6694(2^347990+790)/2104756Stefano Morozzi09/2020
669525137^14702+14702^25137104756Hans Havermann09/2020
6696(13*2^347972-1)/282309104746Lelio R Paula03/2014
669712883^25484-25484^12883104740Norbert Schneider08/2022
66982^347910-109937104732Enzo Doria04/2014
6699(88*10^104709-637)/9104710Robert Price11/2020
6700(13*10^104702+71)/3104703Robert Price06/2021
67015^149794+28104702Lelio R Paula11/2016
6702105^51800-2104698Lelio R Paula10/2017
6703(16^86939+3^86939)/19104684Robert Price06/2013
6704(15^89009-1)/14104682Paul Bourdelais03/2010
67052^347731-18609104678Enzo Doria05/2013
67064*6^134519+7104677Lelio R Paula11/2014
6707(34*10^104672-259)/9104673Robert Price12/2021
670825321^13588+13588^25321104656Hans Havermann09/2020
67092^347625+5367104646Riley Fisher04/2023
67102^347612-18545104642Enzo Doria05/2013
67136^134465+95104635Lelio R Paula11/2016
6712(2^347588+3718)/2104635Stefano Morozzi09/2020
6711(166*10^104633-7)/3104635Robert Price11/2020
67142^347517-17301104614Enzo Doria05/2013
6715(2^347493+3186)/2104606Stefano Morozzi09/2020
6716(2^347490+2574)/2104605Stefano Morozzi09/2020
67173^219222-310104596Lelio R Paula11/2016
671825993^10554+10554^25993104581Hans Havermann09/2020
6719(15*2^347399-1)/13104578Lelio R Paula03/2014
67202^347372-17853104570Enzo Doria05/2013
67212^347314+99104552Lelio R Paula09/2011
67222^347300-22233104548Enzo Doria06/2013
67232^347287-19845104544Enzo Doria06/2013
67242^347258-231191104536Harrison Mesh06/2022
6725(31*2^347254-1)/891104533Lelio R Paula03/2014
67265*F(250091)*(F(250091)-1)+1104532Serge Batalov04/2015
67277*2^347239-3104531Lelio R Paula09/2014
6728(3^219098-8)/514147439969104525Lelio R Paula12/2013
67295*3^219047+8104513Lelio R Paula09/2014
67302^347148-109073104502Enzo Doria04/2014
67312^347129-20145104497Enzo Doria06/2013
67324*10^104461-57104462Robert Price10/2018
6733(7*10^(2*52227+1)+9*10^52227-7)/9104455Robert Price10/2023
6734(2^346989+590)/2104454Stefano Morozzi09/2020
67352^346923-19585104435Enzo Doria05/2013
6736(11*2^346864-1)/175104416Lelio R Paula03/2014
67372^346854+346854^2+1104414Robert Price06/2014
67382^346834+11715104408Lelio R Paula04/2015
673924276^19961+19961^24276104392Hans Havermann09/2020
674079^55009+78104387Norbert Schneider02/2015
67413^218744+58104368Lelio R Paula11/2016
67429*10^104361+89104362Robert Price11/2019
674325048^14665+14665^25048104358Hans Havermann09/2020
67442^346649+65104352Lelio R Paula09/2011
6745(19*33^68718-600883)/32104350Eric Chen05/2023
67462^346638-17265104349Enzo Doria05/2013
6747(2^346606+2082)/2104339Stefano Morozzi09/2020
6748(2^346607+2070)/2104339Stefano Morozzi09/2020
6749(2^346582+3202)/2104332Stefano Morozzi09/2020
675026092^9967+9967^26092104331Hans Havermann09/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 12 2024 13:37 (Time in France)

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