PRP Records

Probable Primes Top 10000

(280932 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 ?
4501(55*10^106222+377)/9106223Robert Price02/2019
45022^352814-131106208Lelio R Paula10/2011
45032^352752+73951106189Enzo Doria04/2016
45046^136434+5106167Lelio R Paula11/2014
450525296^15737+15737^25296106166Hans Havermann09/2020
45068*10^106157-13106158Robert Price08/2019
45077*5^151872-8106155Lelio R Paula11/2014
4508105^52520-2106153Lelio R Paula10/2017
45092^352601-1604809106144Enzo Doria05/2015
451012^98353-43106141Lelio R Paula02/2017
45112^352585-18901106139Enzo Doria05/2013
451226363^10614+10614^26363106135Hans Havermann09/2020
4513(2^352554-3)/193106128Lelio R Paula12/2013
45142^352540+15015106126Lelio R Paula01/2017
451525068^17119+17119^25068106125Hans Havermann09/2020
45162^352524-3149106121Yves Minet10/2014
45172^352486-1858781106109Enzo Doria04/2016
45182^352444+12705106097Lelio R Paula01/2017
451928561^5182+5182^28561106090Hans Havermann10/2020
4520(182*10^106083+43)/9106085Robert Price02/2020
4521(266*10^106066+1)/3106068Robert Price04/2020
45222^352228-18953106032Enzo Doria05/2013
4523(2^352223+1118)/2106030Stefano Morozzi09/2020
4524(2^352212+2250)/2106027Stefano Morozzi01/2021
4525(2^352136+2638)/2106004Stefano Morozzi09/2020
45262^352107+1872533105995Enzo Doria05/2016
4527(2^352096+2086)/2105992Stefano Morozzi09/2020
45282^352066-2591105983Yves Minet07/2014
45292^352030+715105972Lelio R Paula10/2011
45309*6^136176-5105967Lelio R Paula11/2014
453117099*2^351991+58329105965Paul Vanderveen12/2017
453228582^5097+5097^28582105963Hans Havermann09/2020
4533155^48377+2105962Lelio R Paula08/2013
45342^351865+1869707105922Enzo Doria05/2016
453524974^17427+17427^24974105921Hans Havermann09/2020
453625163^16194+16194^25163105920Hans Havermann09/2020
45372^351831+23105912Lelio R Paula10/2011
4538(2^351818+3798)/2105908Stefano Morozzi02/2021
45399*2^351784-5105899Lelio R Paula09/2014
4540(2^351776+2766)/2105895Stefano Morozzi01/2021
4541(85*10^105881+203)/9105882Robert Price09/2020
45422^351671-112387105864Enzo Doria06/2014
45432^351669-109501105863Enzo Doria04/2014
45442^351644+74731105856Enzo Doria04/2016
454513^95025-42105853Lelio R Paula12/2016
45462^351599+15015105842Lelio R Paula01/2017
454719^82763+90105834Lelio R Paula01/2017
454826050^11551+11551^26050105832Hans Havermann09/2020
4549(9179*2^351540-1)/221105826Lelio R Paula05/2015
455020^81329-51105812Lelio R Paula01/2017
4551(5*10^105811+211)/9105811Robert Price02/2018
45522^351483+28425105807Lelio R Paula01/2017
455325231^15610+15610^25231105804Hans Havermann09/2020
455415^89960+86105802Lelio R Paula02/2017
45552^351460-17289105801Enzo Doria05/2013
455619^82735+22105798Lelio R Paula01/2017
45572^351435-109077105793Enzo Doria04/2014
45582^351393+1089105780Lelio R Paula01/2017
45592^351364+72631105772Enzo Doria04/2016
4560(2^351333+3626)/2105762Stefano Morozzi09/2020
456126818^8783+8783^26818105761Hans Havermann09/2020
45642^351305+1872467105754Enzo Doria05/2016
45633^221649+16105754Lelio R Paula11/2016
456232511^1790+1790^32511105754Hans Havermann09/2020
45658*3^221637-5105749Lelio R Paula09/2014
45662^351279-2780449105746Enzo Doria03/2016
4567(2^351263+3198)/2105741Stefano Morozzi09/2020
456815^89903-26105735Lelio R Paula02/2017
45702^351213-73105726Lelio R Paula10/2011
4569(2^351214+1210)/2105726Stefano Morozzi09/2020
45712^351192-4589105720Yves Minet07/2011
457220^81250-33105709Lelio R Paula12/2016
4573(2^351133+3530)/2105702Stefano Morozzi09/2020
4574(2^351103+534)/2105693Stefano Morozzi09/2020
45752^351076-113159105685Enzo Doria07/2014
457693^53688-2105684Lelio R Paula09/2013
45772^351060-4559105680Yves Minet07/2011
4578((10^52836-1)*10000/9+5927)*10^52836+(10^52836-1)/9105676Hans Havermann08/2019
457911^101473-750105674Enzo Doria11/2012
45803*5^151181-8105672Lelio R Paula11/2014
458115^89831-34105650Lelio R Paula02/2017
458311^101448-360105648Enzo Doria08/2012
45823*7^125011+4105648Lelio R Paula11/2014
45842^350943-113269105645Enzo Doria07/2014
45852*10^105636-91105637Robert Price04/2020
458624231^22880+22880^24231105634Hans Havermann09/2020
458735296^983+983^35296105626Hans Havermann09/2020
45882^350868-19725105622Enzo Doria06/2013
45892^350858-59291105619Enzo Doria10/2015
45902^350851+135105617Lelio R Paula10/2011
45912^350841-741105614Lelio R Paula01/2017
45923*10^105582+77105583Robert Price09/2018
459324915^17284+17284^24915105581Hans Havermann09/2020
4594(5*10^105576-53)/3105577Robert Price09/2020
45958*10^105571+3105572Robert Price08/2015
45962^350674-78557105564Jorge Menendez03/2018
45972*5^151026-3105563Lelio R Paula11/2014
4598(2^350702+5)/34264674063105562Lelio R Paula12/2013
45996^135647-5^135647105554Jean-Louis Charton02/2009
46003^221211+236105545Lelio R Paula11/2016
4601(32*10^105530-77)/9105531Robert Price06/2018
460310^105515+33105516Lelio R Paula11/2016
460224644^19125+19125^24644105516Hans Havermann10/2020
460410^105515-41033105515Patrick De Geest12/2016
4605(29*2^350473-1)/267927105499Lelio R Paula03/2014
460617^85732-72105489Lelio R Paula01/2017
4607(2^350399+3618)/2105481Stefano Morozzi09/2020
4608(2^350379+1010)/2105475Stefano Morozzi09/2020
460925233^15118+15118^25233105462Hans Havermann09/2020
461026261^10366+10366^26261105454Hans Havermann09/2020
46112^350307-110329105453Enzo Doria05/2014
46122^350253-20365105437Enzo Doria06/2013
4613(3*29^72089-1075)/4105423Curtis Bright05/2015
4614(2^350187+2658)/2105417Stefano Morozzi09/2020
46152^350139-109009105403Enzo Doria04/2014
4616(2^350129+3026)/2105400Stefano Morozzi09/2020
4617(2^350097+2070)/2105390Stefano Morozzi09/2020
46183*5^150763+4105380Lelio R Paula11/2014
461912^97643+91105375Lelio R Paula02/2017
46206*5^150744-7105367Lelio R Paula11/2014
4621(2^350018+2074)/2105366Stefano Morozzi09/2020
46224*10^105364-39105365Robert Price09/2020
46232^349996-112169105360Enzo Doria06/2014
4624(2^349997+3702)/2105360Stefano Morozzi09/2020
4625(418*10^105343+23)/9105345Robert Price02/2020
462625490^13563+13563^25490105334Hans Havermann10/2020
462711^101142-1080105329Enzo Doria12/2012
4628(68*10^105320-41)/9105321Robert Price10/2013
462924800^17649+17649^24800105319Hans Havermann09/2020
46303^220712-9934105307Enzo Doria05/2014
46317*10^105296+9105297Robert Price09/2015
463289*10^105284-7105286Robert Price04/2020
46332^349739+1873373105282Enzo Doria06/2016
46347^124574+24105278Lelio R Paula11/2016
46352^349708-20957105273Enzo Doria06/2013
463634115^1218+1218^34115105267Hans Havermann09/2020
46372^349649-20469105255Enzo Doria06/2013
46382^349607-20109105243Enzo Doria06/2013
4639(85*10^105242+473)/9105243Robert Price01/2020
46402^349594-19085105239Enzo Doria05/2013
46412^349530+1874479105220Enzo Doria06/2016
4642(3^220528+8)/8081105215Lelio R Paula12/2013
4643(2^349452+3570)/2105196Stefano Morozzi09/2020
46443^220464-112852105189Enzo Doria07/2014
46452^349419-17349105186Enzo Doria05/2013
46462^349400-2579105180Yves Minet07/2014
46478*5^150471+3105176Lelio R Paula11/2014
4648(2^349359+2298)/2105168Stefano Morozzi02/2021
4649655^37342+37342^655105165Norbert Schneider08/2018
465013^94403+94105160Lelio R Paula12/2016
46512^349301-112309105151Enzo Doria06/2014
465230291^2960+2960^30291105149Hans Havermann09/2020
465327350^6981+6981^27350105132Hans Havermann09/2020
46559*2^349220+5105127Lelio R Paula09/2014
4654(2^349225+3122)/2105127Stefano Morozzi09/2020
46567*3^220317+8105119Lelio R Paula09/2014
46587^124386+88105119Lelio R Paula11/2016
4657(2^349197+570)/2105119Stefano Morozzi09/2020
46592^349171-19657105111Enzo Doria06/2013
4660(2^349115+590)/2105094Stefano Morozzi09/2020
4661(2^(6*58185+1)-5)/3105093Kevin Acres11/2013
4662(2^349111-5)/3105093Lelio R Paula12/2013
4663675^37142+37142^675105087Norbert Schneider08/2018
46642^348981-2797573105054Enzo Doria04/2016
46652^348869-6555105021Lelio R Paula01/2017
46665^150217+78104998Lelio R Paula11/2016
4667(88*10^104989-1)/3104991Robert Price04/2020
4668(28*10^104972+149)/3104973Robert Price12/2019
466924927^16262+16262^24927104972Hans Havermann10/2020
46702^348703-113005104971Enzo Doria06/2014
46722^348612-809104943Yves Minet05/2013
4671(73*10^104942-1)/9104943Robert Price01/2015
46732^348583-350407104934Enzo Doria06/2015
46742^348531-949104919Yves Minet05/2012
467520^80636-59104910Lelio R Paula12/2016
46768*10^104893-13104894Robert Price08/2019
46782^348437+35104890Lelio R Paula09/2011
467725208^14487+14487^25208104890Hans Havermann09/2020
46792^348348+135104864Lelio R Paula09/2011
46806*10^104852-31104853Robert Price07/2020
4682(2^348284+9)/25104843Lelio R Paula12/2013
468175^55914-74104843Norbert Schneider01/2015
46832^348268+255255104840Lelio R Paula01/2017
468435540^891+891^35540104839Hans Havermann09/2020
46855^149985-52104836Lelio R Paula11/2016
46862^348224-20249104826Enzo Doria06/2013
4687(2^348217+2522)/2104824Stefano Morozzi09/2020
46882^348212-20105104823Enzo Doria06/2013
468924647^17898+17898^24647104819Hans Havermann10/2020
469020^80562+19104814Lelio R Paula12/2016
46912*10^104811-87104812Robert Price04/2018
46922^348149-20053104804Enzo Doria06/2013
46932^348095-171104788Lelio R Paula09/2011
469425383^13412+13412^25383104769Hans Havermann09/2020
46952^348003-20377104760Enzo Doria06/2013
46972^347994-741104757Lelio R Paula12/2016
4696(2^347993+2234)/2104757Stefano Morozzi01/2021
4698(2^347990+790)/2104756Stefano Morozzi09/2020
469925137^14702+14702^25137104756Hans Havermann09/2020
4700(13*2^347972-1)/282309104746Lelio R Paula03/2014
47012^347910-109937104732Enzo Doria04/2014
4702(88*10^104709-637)/9104710Robert Price11/2020
47035^149794+28104702Lelio R Paula11/2016
4704105^51800-2104698Lelio R Paula10/2017
4705(16^86939+3^86939)/19104684Robert Price06/2013
4706(15^89009-1)/14104682Paul Bourdelais03/2010
47072^347731-18609104678Enzo Doria05/2013
47084*6^134519+7104677Lelio R Paula11/2014
470925321^13588+13588^25321104656Hans Havermann09/2020
47102^347612-18545104642Enzo Doria05/2013
47136^134465+95104635Lelio R Paula11/2016
4711(2^347588+3718)/2104635Stefano Morozzi09/2020
4712(166*10^104633-7)/3104635Robert Price11/2020
47142^347517-17301104614Enzo Doria05/2013
4715(2^347493+3186)/2104606Stefano Morozzi09/2020
4716(2^347490+2574)/2104605Stefano Morozzi09/2020
47173^219222-310104596Lelio R Paula11/2016
471825993^10554+10554^25993104581Hans Havermann09/2020
4719(15*2^347399-1)/13104578Lelio R Paula03/2014
47202^347372-17853104570Enzo Doria05/2013
47212^347314+99104552Lelio R Paula09/2011
47222^347300-22233104548Enzo Doria06/2013
47232^347287-19845104544Enzo Doria06/2013
4724(31*2^347254-1)/891104533Lelio R Paula03/2014
47255*F(250091)*(F(250091)-1)+1104532Serge Batalov04/2015
47267*2^347239-3104531Lelio R Paula09/2014
4727(3^219098-8)/514147439969104525Lelio R Paula12/2013
47285*3^219047+8104513Lelio R Paula09/2014
47292^347148-109073104502Enzo Doria04/2014
47302^347129-20145104497Enzo Doria06/2013
47314*10^104461-57104462Robert Price10/2018
4732(2^346989+590)/2104454Stefano Morozzi09/2020
47332^346923-19585104435Enzo Doria05/2013
4734(11*2^346864-1)/175104416Lelio R Paula03/2014
47352^346854+346854^2+1104414Robert Price06/2014
47362^346834+11715104408Lelio R Paula04/2015
473724276^19961+19961^24276104392Hans Havermann09/2020
473879^55009+78104387Norbert Schneider02/2015
47393^218744+58104368Lelio R Paula11/2016
47409*10^104361+89104362Robert Price11/2019
474125048^14665+14665^25048104358Hans Havermann09/2020
47422^346649+65104352Lelio R Paula09/2011
47432^346638-17265104349Enzo Doria05/2013
4744(2^346606+2082)/2104339Stefano Morozzi09/2020
4745(2^346607+2070)/2104339Stefano Morozzi09/2020
4746(2^346582+3202)/2104332Stefano Morozzi09/2020
474726092^9967+9967^26092104331Hans Havermann09/2020
47485*10^104326+77104327Robert Price12/2018
4749(2^346564+2026)/2104326Stefano Morozzi09/2020
47506^134055+101104316Lelio R Paula11/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 13 2021 12:02 (Time in France)

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