PRP Records

Probable Primes Top 10000

(291192 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 ?
5501(2^351333+3626)/2105762Stefano Morozzi09/2020
550226818^8783+8783^26818105761Hans Havermann09/2020
55052^351305+1872467105754Enzo Doria05/2016
55043^221649+16105754Lelio R Paula11/2016
550332511^1790+1790^32511105754Hans Havermann09/2020
55068*3^221637-5105749Lelio R Paula09/2014
55072^351279-2780449105746Enzo Doria03/2016
5508(2^351263+3198)/2105741Stefano Morozzi09/2020
550915^89903-26105735Lelio R Paula02/2017
55112^351213-73105726Lelio R Paula10/2011
5510(2^351214+1210)/2105726Stefano Morozzi09/2020
55122^351192-4589105720Yves Minet07/2011
551320^81250-33105709Lelio R Paula12/2016
5514(2^351133+3530)/2105702Stefano Morozzi09/2020
5515(2^351103+534)/2105693Stefano Morozzi09/2020
55162^351076-113159105685Enzo Doria07/2014
551793^53688-2105684Lelio R Paula09/2013
55182^351060-4559105680Yves Minet07/2011
5519((10^52836-1)*10000/9+5927)*10^52836+(10^52836-1)/9105676Hans Havermann08/2019
552011^101473-750105674Enzo Doria11/2012
55213*5^151181-8105672Lelio R Paula11/2014
552215^89831-34105650Lelio R Paula02/2017
552411^101448-360105648Enzo Doria08/2012
55233*7^125011+4105648Lelio R Paula11/2014
55252^350943-113269105645Enzo Doria07/2014
55262*10^105636-91105637Robert Price04/2020
552724231^22880+22880^24231105634Hans Havermann09/2020
552835296^983+983^35296105626Hans Havermann09/2020
55292^350868-19725105622Enzo Doria06/2013
55302^350858-59291105619Enzo Doria10/2015
55312^350851+135105617Lelio R Paula10/2011
55322^350841-741105614Lelio R Paula01/2017
55333*10^105582+77105583Robert Price09/2018
553424915^17284+17284^24915105581Hans Havermann09/2020
5535(5*10^105576-53)/3105577Robert Price09/2020
55368*10^105571+3105572Robert Price08/2015
55372^350674-78557105564Jorge Menendez03/2018
55382*5^151026-3105563Lelio R Paula11/2014
5539(2^350702+5)/34264674063105562Lelio R Paula12/2013
55406^135647-5^135647105554Jean-Louis Charton02/2009
55413^221211+236105545Lelio R Paula11/2016
5542(32*10^105530-77)/9105531Robert Price06/2018
554310^105515+33105516Lelio R Paula11/2016
554424644^19125+19125^24644105516Hans Havermann10/2020
554510^105515-41033105515Patrick De Geest12/2016
5546(29*2^350473-1)/267927105499Lelio R Paula03/2014
55472^350455-430567105498Harrison Mesh06/2022
554817^85732-72105489Lelio R Paula01/2017
5549(2^350399+3618)/2105481Stefano Morozzi09/2020
5550(2^350379+1010)/2105475Stefano Morozzi09/2020
555125233^15118+15118^25233105462Hans Havermann09/2020
555226261^10366+10366^26261105454Hans Havermann09/2020
55532^350307-110329105453Enzo Doria05/2014
55542^350253-20365105437Enzo Doria06/2013
5555(3*29^72089-1075)/4105423Curtis Bright05/2015
5556(2^350187+2658)/2105417Stefano Morozzi09/2020
55574*10^105415-69105416Robert Price01/2022
5558(22*10^105407+179)/3105408Robert Price02/2022
55592^350139-109009105403Enzo Doria04/2014
5560(2^350129+3026)/2105400Stefano Morozzi09/2020
5561(2^350097+2070)/2105390Stefano Morozzi09/2020
55623*5^150763+4105380Lelio R Paula11/2014
556312^97643+91105375Lelio R Paula02/2017
55646*5^150744-7105367Lelio R Paula11/2014
5565(2^350018+2074)/2105366Stefano Morozzi09/2020
55664*10^105364-39105365Robert Price09/2020
55682^349996-112169105360Enzo Doria06/2014
5567(2^349997+3702)/2105360Stefano Morozzi09/2020
5569(418*10^105343+23)/9105345Robert Price02/2020
557025490^13563+13563^25490105334Hans Havermann10/2020
557111^101142-1080105329Enzo Doria12/2012
5572(68*10^105320-41)/9105321Robert Price10/2013
557324800^17649+17649^24800105319Hans Havermann09/2020
55743^220712-9934105307Enzo Doria05/2014
55757*10^105296+9105297Robert Price09/2015
557689*10^105284-7105286Robert Price04/2020
55772^349739+1873373105282Enzo Doria06/2016
55787^124574+24105278Lelio R Paula11/2016
55792^349708-20957105273Enzo Doria06/2013
558034115^1218+1218^34115105267Hans Havermann09/2020
55812^349649-20469105255Enzo Doria06/2013
55822^349607-20109105243Enzo Doria06/2013
5583(85*10^105242+473)/9105243Robert Price01/2020
55842^349594-19085105239Enzo Doria05/2013
55852^349530+1874479105220Enzo Doria06/2016
5586(3^220528+8)/8081105215Lelio R Paula12/2013
5587(106*10^105199+17)/3105201Robert Price04/2021
5588(2^349452+3570)/2105196Stefano Morozzi09/2020
55893^220464-112852105189Enzo Doria07/2014
55902^349419-17349105186Enzo Doria05/2013
55912^349400-2579105180Yves Minet07/2014
55928*5^150471+3105176Lelio R Paula11/2014
5593(2^349359+2298)/2105168Stefano Morozzi02/2021
5594655^37342+37342^655105165Norbert Schneider08/2018
559513^94403+94105160Lelio R Paula12/2016
55962^349301-112309105151Enzo Doria06/2014
559730291^2960+2960^30291105149Hans Havermann09/2020
559827350^6981+6981^27350105132Hans Havermann09/2020
56009*2^349220+5105127Lelio R Paula09/2014
5599(2^349225+3122)/2105127Stefano Morozzi09/2020
56017*3^220317+8105119Lelio R Paula09/2014
56027^124386+88105119Lelio R Paula11/2016
5603(2^349197+570)/2105119Stefano Morozzi09/2020
56042^349171-19657105111Enzo Doria06/2013
5605(2^349115+590)/2105094Stefano Morozzi09/2020
5606(2^(6*58185+1)-5)/3105093Kevin Acres11/2013
5607(2^349111-5)/3105093Lelio R Paula12/2013
5608675^37142+37142^675105087Norbert Schneider08/2018
56092^348981-2797573105054Enzo Doria04/2016
56102^348869-6555105021Lelio R Paula01/2017
56115^150217+78104998Lelio R Paula11/2016
5612(88*10^104989-1)/3104991Robert Price04/2020
5613(28*10^104972+149)/3104973Robert Price12/2019
561424927^16262+16262^24927104972Hans Havermann10/2020
56152^348703-113005104971Enzo Doria06/2014
5616(191*10^104956-17)/3104958Robert Price11/2021
56182^348612-809104943Yves Minet05/2013
5617(73*10^104942-1)/9104943Robert Price01/2015
56192^348583-350407104934Enzo Doria06/2015
56202^348531-949104919Yves Minet05/2012
562120^80636-59104910Lelio R Paula12/2016
56228*10^104893-13104894Robert Price08/2019
56242^348437+35104890Lelio R Paula09/2011
562325208^14487+14487^25208104890Hans Havermann09/2020
56252^348348+135104864Lelio R Paula09/2011
5626(29*10^104858+349)/9104859Robert Price06/2021
56276*10^104852-31104853Robert Price07/2020
5629(2^348284+9)/25104843Lelio R Paula12/2013
562875^55914-74104843Norbert Schneider01/2015
56302^348268+255255104840Lelio R Paula01/2017
563135540^891+891^35540104839Hans Havermann09/2020
56325^149985-52104836Lelio R Paula11/2016
56332^348224-20249104826Enzo Doria06/2013
5634(2^348217+2522)/2104824Stefano Morozzi09/2020
56352^348212-20105104823Enzo Doria06/2013
563624647^17898+17898^24647104819Hans Havermann10/2020
563720^80562+19104814Lelio R Paula12/2016
56382*10^104811-87104812Robert Price04/2018
56392^348149-20053104804Enzo Doria06/2013
56402^348095-171104788Lelio R Paula09/2011
564125383^13412+13412^25383104769Hans Havermann09/2020
56422^348003-20377104760Enzo Doria06/2013
56432^347994-741104757Lelio R Paula12/2016
5644(2^347993+2234)/2104757Stefano Morozzi01/2021
5645(2^347990+790)/2104756Stefano Morozzi09/2020
564625137^14702+14702^25137104756Hans Havermann09/2020
5647(13*2^347972-1)/282309104746Lelio R Paula03/2014
564812883^25484-25484^12883104740Norbert Schneider08/2022
56492^347910-109937104732Enzo Doria04/2014
5650(88*10^104709-637)/9104710Robert Price11/2020
5651(13*10^104702+71)/3104703Robert Price06/2021
56525^149794+28104702Lelio R Paula11/2016
5653105^51800-2104698Lelio R Paula10/2017
5654(16^86939+3^86939)/19104684Robert Price06/2013
5655(15^89009-1)/14104682Paul Bourdelais03/2010
56562^347731-18609104678Enzo Doria05/2013
56574*6^134519+7104677Lelio R Paula11/2014
5658(34*10^104672-259)/9104673Robert Price12/2021
565925321^13588+13588^25321104656Hans Havermann09/2020
56602^347612-18545104642Enzo Doria05/2013
56636^134465+95104635Lelio R Paula11/2016
5661(2^347588+3718)/2104635Stefano Morozzi09/2020
5662(166*10^104633-7)/3104635Robert Price11/2020
56642^347517-17301104614Enzo Doria05/2013
5665(2^347493+3186)/2104606Stefano Morozzi09/2020
5666(2^347490+2574)/2104605Stefano Morozzi09/2020
56673^219222-310104596Lelio R Paula11/2016
566825993^10554+10554^25993104581Hans Havermann09/2020
5669(15*2^347399-1)/13104578Lelio R Paula03/2014
56702^347372-17853104570Enzo Doria05/2013
56712^347314+99104552Lelio R Paula09/2011
56722^347300-22233104548Enzo Doria06/2013
56732^347287-19845104544Enzo Doria06/2013
56742^347258-231191104536Harrison Mesh06/2022
5675(31*2^347254-1)/891104533Lelio R Paula03/2014
56765*F(250091)*(F(250091)-1)+1104532Serge Batalov04/2015
56777*2^347239-3104531Lelio R Paula09/2014
5678(3^219098-8)/514147439969104525Lelio R Paula12/2013
56795*3^219047+8104513Lelio R Paula09/2014
56802^347148-109073104502Enzo Doria04/2014
56812^347129-20145104497Enzo Doria06/2013
56824*10^104461-57104462Robert Price10/2018
5683(2^346989+590)/2104454Stefano Morozzi09/2020
56842^346923-19585104435Enzo Doria05/2013
5685(11*2^346864-1)/175104416Lelio R Paula03/2014
56862^346854+346854^2+1104414Robert Price06/2014
56872^346834+11715104408Lelio R Paula04/2015
568824276^19961+19961^24276104392Hans Havermann09/2020
568979^55009+78104387Norbert Schneider02/2015
56903^218744+58104368Lelio R Paula11/2016
56919*10^104361+89104362Robert Price11/2019
569225048^14665+14665^25048104358Hans Havermann09/2020
56932^346649+65104352Lelio R Paula09/2011
56942^346638-17265104349Enzo Doria05/2013
5695(2^346606+2082)/2104339Stefano Morozzi09/2020
5696(2^346607+2070)/2104339Stefano Morozzi09/2020
5697(2^346582+3202)/2104332Stefano Morozzi09/2020
569826092^9967+9967^26092104331Hans Havermann09/2020
56995*10^104326+77104327Robert Price12/2018
5700(2^346564+2026)/2104326Stefano Morozzi09/2020
57022^346527-111817104316Enzo Doria05/2014
57016^134055+101104316Lelio R Paula11/2016
570392105!4+8104312Robert Price09/2019
57046^134013+163104283Lelio R Paula11/2016
5705(22*10^104272-61)/3104273Robert Price03/2022
5706(2^346318+862)/2104252Stefano Morozzi02/2021
570818^83049-89104250Lelio R Paula01/2017
5707(2^346311+606)/2104250Stefano Morozzi09/2020
5709(166*10^104230+11)/3104232Robert Price03/2021
57102^346213+484049104221Enzo Doria04/2017
571118^83021-91104214Lelio R Paula01/2017
571210^104212+128779104213Patrick De Geest05/2016
571310^104212+237447104213Patrick De Geest05/2016
571410^104212+242139104213Patrick De Geest05/2016
571510^104212+269199104213Patrick De Geest05/2016
571624254^19803+19803^24254104213Hans Havermann09/2020
5717(10^104212-71)/1104212Serge Batalov12/2014
571823678^23821-23821^23678104202Norbert Schneider01/2020
57192^346078+7695104180Lelio R Paula12/2016
57202^346055-19537104173Enzo Doria05/2013
5721(3*2^346057+1)/77104173Lelio R Paula12/2013
57222^346037-20125104168Enzo Doria06/2013
5723(34*10^104168-7)/9/13/551179104162Makoto Morimoto05/2016
57246^133854-17993104159Enzo Doria03/2013
57252^345990+1874239104154Enzo Doria06/2016
57262^345988-20373104153Enzo Doria06/2013
5727(2^345965+2214)/2104146Stefano Morozzi09/2020
5728(26*10^104132-503)/9104133Robert Price07/2018
57293*5^148968+8104125Lelio R Paula11/2014
5730(7*10^104113+53)/3104114Robert Price05/2018
5731p(21253)#/2+8104113Robert Price01/2017
573233582^1259+1259^33582104106Hans Havermann09/2020
573332958^1441+1441^32958104104Hans Havermann09/2020
573429127^3748+3748^29127104095Hans Havermann09/2020
5735322^41507+41507^322104094Norbert Schneider12/2014
57366^133768-17423104092Enzo Doria03/2013
57372^345786-19557104092Enzo Doria05/2013
5738171^46606-2104072Lelio R Paula10/2017
5739(29*10^104071+91)/3104072Robert Price04/2020
5740norm(Mod(x,x^3-x-1)^852167-1)104070Paul Vanderveen09/2022
57412^345704-149104068Lelio R Paula09/2011
574225821^10712+10712^25821104056Hans Havermann09/2020
5743(2^345662+2038)/2104055Stefano Morozzi09/2020
57446^133704-17273104042Enzo Doria02/2013
5745(3*2^345590-1)/23104033Lelio R Paula03/2014
5746(19*2^345590+1)/33859104030Lelio R Paula12/2013
57472^345547+11104021Lelio R Paula09/2011
5748(19*10^104014-49)/3104015Robert Price05/2019
5749(2^345519+1794)/2104012Stefano Morozzi01/2021
57502^345504+723104008Lelio R Paula09/2011


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 22 2022 18:03 (Time in France)

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