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 ?
3751(2^352136+2638)/2106004Stefano Morozzi09/2020
37522^352107+1872533105995Enzo Doria05/2016
3753(2^352096+2086)/2105992Stefano Morozzi09/2020
37542^352066-2591105983Yves Minet07/2014
37552^352030+715105972Lelio R Paula10/2011
37569*6^136176-5105967Lelio R Paula11/2014
375717099*2^351991+58329105965Paul Vanderveen12/2017
375828582^5097+5097^28582105963Hans Havermann09/2020
3759155^48377+2105962Lelio R Paula08/2013
37602^351865+1869707105922Enzo Doria05/2016
376124974^17427+17427^24974105921Hans Havermann09/2020
376225163^16194+16194^25163105920Hans Havermann09/2020
37632^351831+23105912Lelio R Paula10/2011
37649*2^351784-5105899Lelio R Paula09/2014
3765(85*10^105881+203)/9105882Robert Price09/2020
37662^351671-112387105864Enzo Doria06/2014
37672^351669-109501105863Enzo Doria04/2014
37682^351644+74731105856Enzo Doria04/2016
376913^95025-42105853Lelio R Paula12/2016
37702^351599+15015105842Lelio R Paula01/2017
377119^82763+90105834Lelio R Paula01/2017
377226050^11551+11551^26050105832Hans Havermann09/2020
3773(9179*2^351540-1)/221105826Lelio R Paula05/2015
377420^81329-51105812Lelio R Paula01/2017
3775(5*10^105811+211)/9105811Robert Price02/2018
37762^351483+28425105807Lelio R Paula01/2017
377725231^15610+15610^25231105804Hans Havermann09/2020
377815^89960+86105802Lelio R Paula02/2017
37792^351460-17289105801Enzo Doria05/2013
378019^82735+22105798Lelio R Paula01/2017
37812^351435-109077105793Enzo Doria04/2014
37822^351393+1089105780Lelio R Paula01/2017
37832^351364+72631105772Enzo Doria04/2016
3784(2^351333+3626)/2105762Stefano Morozzi09/2020
378526818^8783+8783^26818105761Hans Havermann09/2020
37872^351305+1872467105754Enzo Doria05/2016
37883^221649+16105754Lelio R Paula11/2016
378632511^1790+1790^32511105754Hans Havermann09/2020
37898*3^221637-5105749Lelio R Paula09/2014
37902^351279-2780449105746Enzo Doria03/2016
3791(2^351263+3198)/2105741Stefano Morozzi09/2020
379215^89903-26105735Lelio R Paula02/2017
37942^351213-73105726Lelio R Paula10/2011
3793(2^351214+1210)/2105726Stefano Morozzi09/2020
37952^351192-4589105720Yves Minet07/2011
379620^81250-33105709Lelio R Paula12/2016
3797(2^351133+3530)/2105702Stefano Morozzi09/2020
3798(2^351103+534)/2105693Stefano Morozzi09/2020
37992^351076-113159105685Enzo Doria07/2014
380093^53688-2105684Lelio R Paula09/2013
38012^351060-4559105680Yves Minet07/2011
3802((10^52836-1)*10000/9+5927)*10^52836+(10^52836-1)/9105676Hans Havermann08/2019
380311^101473-750105674Enzo Doria11/2012
38043*5^151181-8105672Lelio R Paula11/2014
380515^89831-34105650Lelio R Paula02/2017
380711^101448-360105648Enzo Doria08/2012
38063*7^125011+4105648Lelio R Paula11/2014
38082^350943-113269105645Enzo Doria07/2014
38092*10^105636-91105637Robert Price04/2020
381024231^22880+22880^24231105634Hans Havermann09/2020
381135296^983+983^35296105626Hans Havermann09/2020
38122^350868-19725105622Enzo Doria06/2013
38132^350858-59291105619Enzo Doria10/2015
38142^350851+135105617Lelio R Paula10/2011
38152^350841-741105614Lelio R Paula01/2017
38163*10^105582+77105583Robert Price09/2018
381724915^17284+17284^24915105581Hans Havermann09/2020
3818(5*10^105576-53)/3105577Robert Price09/2020
38198*10^105571+3105572Robert Price08/2015
38202^350674-78557105564Jorge Menendez03/2018
38212*5^151026-3105563Lelio R Paula11/2014
3822(2^350702+5)/34264674063105562Lelio R Paula12/2013
38236^135647-5^135647105554Jean-Louis Charton02/2009
38243^221211+236105545Lelio R Paula11/2016
3825(32*10^105530-77)/9105531Robert Price06/2018
382610^105515+33105516Lelio R Paula11/2016
382710^105515-41033105515Patrick De Geest12/2016
3828(29*2^350473-1)/267927105499Lelio R Paula03/2014
382917^85732-72105489Lelio R Paula01/2017
3830(2^350399+3618)/2105481Stefano Morozzi09/2020
3831(2^350379+1010)/2105475Stefano Morozzi09/2020
383225233^15118+15118^25233105462Hans Havermann09/2020
383326261^10366+10366^26261105454Hans Havermann09/2020
38342^350307-110329105453Enzo Doria05/2014
38352^350253-20365105437Enzo Doria06/2013
3836(3*29^72089-1075)/4105423Curtis Bright05/2015
3837(2^350187+2658)/2105417Stefano Morozzi09/2020
38382^350139-109009105403Enzo Doria04/2014
3839(2^350129+3026)/2105400Stefano Morozzi09/2020
3840(2^350097+2070)/2105390Stefano Morozzi09/2020
38413*5^150763+4105380Lelio R Paula11/2014
384212^97643+91105375Lelio R Paula02/2017
38436*5^150744-7105367Lelio R Paula11/2014
3844(2^350018+2074)/2105366Stefano Morozzi09/2020
38454*10^105364-39105365Robert Price09/2020
38472^349996-112169105360Enzo Doria06/2014
3846(2^349997+3702)/2105360Stefano Morozzi09/2020
3848(418*10^105343+23)/9105345Robert Price02/2020
384911^101142-1080105329Enzo Doria12/2012
3850(68*10^105320-41)/9105321Robert Price10/2013
385124800^17649+17649^24800105319Hans Havermann09/2020
38523^220712-9934105307Enzo Doria05/2014
38537*10^105296+9105297Robert Price09/2015
385489*10^105284-7105286Robert Price04/2020
38552^349739+1873373105282Enzo Doria06/2016
38567^124574+24105278Lelio R Paula11/2016
38572^349708-20957105273Enzo Doria06/2013
385834115^1218+1218^34115105267Hans Havermann09/2020
38592^349649-20469105255Enzo Doria06/2013
38602^349607-20109105243Enzo Doria06/2013
3861(85*10^105242+473)/9105243Robert Price01/2020
38622^349594-19085105239Enzo Doria05/2013
38632^349530+1874479105220Enzo Doria06/2016
3864(3^220528+8)/8081105215Lelio R Paula12/2013
3865(2^349452+3570)/2105196Stefano Morozzi09/2020
38663^220464-112852105189Enzo Doria07/2014
38672^349419-17349105186Enzo Doria05/2013
38682^349400-2579105180Yves Minet07/2014
38698*5^150471+3105176Lelio R Paula11/2014
3870655^37342+37342^655105165Norbert Schneider08/2018
387113^94403+94105160Lelio R Paula12/2016
38722^349301-112309105151Enzo Doria06/2014
387327350^6981+6981^27350105132Hans Havermann09/2020
38759*2^349220+5105127Lelio R Paula09/2014
3874(2^349225+3122)/2105127Stefano Morozzi09/2020
38767*3^220317+8105119Lelio R Paula09/2014
38777^124386+88105119Lelio R Paula11/2016
3878(2^349197+570)/2105119Stefano Morozzi09/2020
38792^349171-19657105111Enzo Doria06/2013
3880(2^349115+590)/2105094Stefano Morozzi09/2020
3881(2^(6*58185+1)-5)/3105093Kevin Acres11/2013
3882(2^349111-5)/3105093Lelio R Paula12/2013
3883675^37142+37142^675105087Norbert Schneider08/2018
38842^348981-2797573105054Enzo Doria04/2016
38852^348869-6555105021Lelio R Paula01/2017
38865^150217+78104998Lelio R Paula11/2016
3887(88*10^104989-1)/3104991Robert Price04/2020
3888(28*10^104972+149)/3104973Robert Price12/2019
38892^348703-113005104971Enzo Doria06/2014
38912^348612-809104943Yves Minet05/2013
3890(73*10^104942-1)/9104943Robert Price01/2015
38922^348583-350407104934Enzo Doria06/2015
38932^348531-949104919Yves Minet05/2012
389420^80636-59104910Lelio R Paula12/2016
38958*10^104893-13104894Robert Price08/2019
38972^348437+35104890Lelio R Paula09/2011
389625208^14487+14487^25208104890Hans Havermann09/2020
38982^348348+135104864Lelio R Paula09/2011
38996*10^104852-31104853Robert Price07/2020
3901(2^348284+9)/25104843Lelio R Paula12/2013
390075^55914-74104843Norbert Schneider01/2015
39022^348268+255255104840Lelio R Paula01/2017
390335540^891+891^35540104839Hans Havermann09/2020
39045^149985-52104836Lelio R Paula11/2016
39052^348224-20249104826Enzo Doria06/2013
3906(2^348217+2522)/2104824Stefano Morozzi09/2020
39072^348212-20105104823Enzo Doria06/2013
390820^80562+19104814Lelio R Paula12/2016
39092*10^104811-87104812Robert Price04/2018
39102^348149-20053104804Enzo Doria06/2013
39112^348095-171104788Lelio R Paula09/2011
391225383^13412+13412^25383104769Hans Havermann09/2020
39132^348003-20377104760Enzo Doria06/2013
39142^347994-741104757Lelio R Paula12/2016
3915(2^347990+790)/2104756Stefano Morozzi09/2020
391625137^14702+14702^25137104756Hans Havermann09/2020
3917(13*2^347972-1)/282309104746Lelio R Paula03/2014
39182^347910-109937104732Enzo Doria04/2014
39195^149794+28104702Lelio R Paula11/2016
3920105^51800-2104698Lelio R Paula10/2017
3921(16^86939+3^86939)/19104684Robert Price06/2013
3922(15^89009-1)/14104682Paul Bourdelais03/2010
39232^347731-18609104678Enzo Doria05/2013
39244*6^134519+7104677Lelio R Paula11/2014
392525321^13588+13588^25321104656Hans Havermann09/2020
39262^347612-18545104642Enzo Doria05/2013
39286^134465+95104635Lelio R Paula11/2016
3927(2^347588+3718)/2104635Stefano Morozzi09/2020
39292^347517-17301104614Enzo Doria05/2013
3930(2^347493+3186)/2104606Stefano Morozzi09/2020
3931(2^347490+2574)/2104605Stefano Morozzi09/2020
39323^219222-310104596Lelio R Paula11/2016
393325993^10554+10554^25993104581Hans Havermann09/2020
3934(15*2^347399-1)/13104578Lelio R Paula03/2014
39352^347372-17853104570Enzo Doria05/2013
39362^347314+99104552Lelio R Paula09/2011
39372^347300-22233104548Enzo Doria06/2013
39382^347287-19845104544Enzo Doria06/2013
3939(31*2^347254-1)/891104533Lelio R Paula03/2014
39405*F(250091)*(F(250091)-1)+1104532Serge Batalov04/2015
39417*2^347239-3104531Lelio R Paula09/2014
3942(3^219098-8)/514147439969104525Lelio R Paula12/2013
39435*3^219047+8104513Lelio R Paula09/2014
39442^347148-109073104502Enzo Doria04/2014
39452^347129-20145104497Enzo Doria06/2013
39464*10^104461-57104462Robert Price10/2018
3947(2^346989+590)/2104454Stefano Morozzi09/2020
39482^346923-19585104435Enzo Doria05/2013
3949(11*2^346864-1)/175104416Lelio R Paula03/2014
39502^346854+346854^2+1104414Robert Price06/2014
39512^346834+11715104408Lelio R Paula04/2015
395224276^19961+19961^24276104392Hans Havermann09/2020
395379^55009+78104387Norbert Schneider02/2015
39543^218744+58104368Lelio R Paula11/2016
39559*10^104361+89104362Robert Price11/2019
395625048^14665+14665^25048104358Hans Havermann09/2020
39572^346649+65104352Lelio R Paula09/2011
39582^346638-17265104349Enzo Doria05/2013
3959(2^346606+2082)/2104339Stefano Morozzi09/2020
3960(2^346607+2070)/2104339Stefano Morozzi09/2020
3961(2^346582+3202)/2104332Stefano Morozzi09/2020
396226092^9967+9967^26092104331Hans Havermann09/2020
39635*10^104326+77104327Robert Price12/2018
3964(2^346564+2026)/2104326Stefano Morozzi09/2020
39662^346527-111817104316Enzo Doria05/2014
39656^134055+101104316Lelio R Paula11/2016
396792105!4+8104312Robert Price09/2019
39686^134013+163104283Lelio R Paula11/2016
396918^83049-89104250Lelio R Paula01/2017
3970(2^346311+606)/2104250Stefano Morozzi09/2020
39712^346213+484049104221Enzo Doria04/2017
397218^83021-91104214Lelio R Paula01/2017
397310^104212+128779104213Patrick De Geest05/2016
397410^104212+237447104213Patrick De Geest05/2016
397510^104212+242139104213Patrick De Geest05/2016
397610^104212+269199104213Patrick De Geest05/2016
397724254^19803+19803^24254104213Hans Havermann09/2020
3978(10^104212-71)/1104212Serge Batalov12/2014
397923678^23821-23821^23678104202Norbert Schneider01/2020
39802^346078+7695104180Lelio R Paula12/2016
39812^346055-19537104173Enzo Doria05/2013
3982(3*2^346057+1)/77104173Lelio R Paula12/2013
39832^346037-20125104168Enzo Doria06/2013
3984(34*10^104168-7)/9/13/551179104162Makoto Morimoto05/2016
39856^133854-17993104159Enzo Doria03/2013
39862^345990+1874239104154Enzo Doria06/2016
39872^345988-20373104153Enzo Doria06/2013
3988(2^345965+2214)/2104146Stefano Morozzi09/2020
3989(26*10^104132-503)/9104133Robert Price07/2018
39903*5^148968+8104125Lelio R Paula11/2014
3991(7*10^104113+53)/3104114Robert Price05/2018
3992p(21253)#/2+8104113Robert Price01/2017
399333582^1259+1259^33582104106Hans Havermann09/2020
399432958^1441+1441^32958104104Hans Havermann09/2020
399529127^3748+3748^29127104095Hans Havermann09/2020
3996322^41507+41507^322104094Norbert Schneider12/2014
39976^133768-17423104092Enzo Doria03/2013
39982^345786-19557104092Enzo Doria05/2013
4000171^46606-2104072Lelio R Paula10/2017
3999(29*10^104071+91)/3104072Robert Price04/2020


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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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