PRP Records

Probable Primes Top 10000

(293510 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 ?
37512*10^132493-43132494Robert Price04/2018
375231352^16809+16809^31352132480Hans Havermann04/2021
3753(418*10^132441+23)/9132443Robert Price02/2020
37542^439931-21132433Lelio R Paula08/2017
375547^79201-46^79201132432Robert Price10/2012
37562^439897-113653132423Enzo Doria08/2014
375735505^5362+5362^35505132410Hans Havermann03/2021
375830079^25222+25222^30079132402Hans Havermann04/2021
3759(5*2^439822+1)/9132400Lelio R Paula06/2015
3760(695*10^132356+7)/9132358Robert Price12/2021
3761(112*10^132337-1)/3132339Serge Batalov12/2014
37622^439576-113247132326Enzo Doria07/2014
376330059^25230+25230^30059132318Hans Havermann04/2021
37642^439497-29143132302Enzo Doria07/2015
37652^439409-114193132276Enzo Doria12/2014
3766(44*10^132233-233)/9132234Robert Price01/2019
37679*10^132148-7132149Robert Price09/2015
3768(47*10^132125-119)/9132126Robert Price05/2019
37692^438845+1870217132106Enzo Doria05/2016
37702^438789+87855132089Lelio R Paula01/2016
37712^438774-2786411132085Enzo Doria03/2016
37722^438755-1848205132079Enzo Doria07/2015
377330502^21381+21381^30502132075Hans Havermann04/2021
37742^438739-112087132074Enzo Doria06/2014
3775(2^438438+100280245065)131983Paul Bourdelais05/2022
377635872^4777+4777^35872131979Hans Havermann04/2021
377731198^16945+16945^31198131938Hans Havermann03/2021
377813907#+(318259#)/(13907#)131923Makoto Morimoto10/2017
3779L(631181)131910Henri Lifchitz09/2008
3780(47*10^131886-119)/9131887Robert Price05/2019
37815*2^438096-3131881Jon Grantham07/2023
3782(3*2^438121+1)/4308193883131879Lelio R Paula06/2015
37832^438079-1863877131875Enzo Doria03/2016
3784(16*10^131872-37)/3131873Robert Price05/2021
3785(2^438067+5)/329131869Lelio R Paula06/2015
37862^437908-113855131824Enzo Doria09/2014
37872^437884-286349131817Enzo Doria07/2015
37885^188558+4131797Tyler NeSmith05/2021
3789(11*10^131784-17)/3131785Robert Price06/2018
37914*10^131719-93131720Robert Price07/2020
379031629^14606+14606^31629131720Hans Havermann04/2021
37923^276062-112292131716Enzo Doria07/2014
3793(7*10^131682+89)/3131683Robert Price08/2020
379429512^28969+28969^29512131681Hans Havermann03/2021
37952^437343+75953131654Enzo Doria04/2016
379635^85243-34^85243131621Robert Price05/2012
3797(28*10^131586+59)/3131587Robert Price05/2021
3798(59*10^131575+391)/9131576Robert Price03/2021
379939984^1945+1945^39984131505Hans Havermann03/2021
3800(203*10^131457+1)/3131459Robert Price03/2020
38017*10^131421-41131422Robert Price08/2021
380287309^32+32^87309131414Hans Havermann03/2021
3803(68^71713+1)/69131413Paul Bourdelais09/2017
3804(650*10^131391+43)/9131393Tyler Busby01/2023
38052^436451+1884713131385Enzo Doria03/2017
38062^436365+35131359Robert Price11/2015
38072^436300+1866871131340Enzo Doria03/2016
3808(7*10^131339+179)/3131340Robert Price09/2018
380914^114592-3131338Paul Bourdelais12/2020
381036197^4236+4236^36197131285Hans Havermann04/2021
3811(37*10^131270+341)/9131271Robert Price08/2018
381229863^24790+24790^29863131227Hans Havermann03/2021
3813(5*10^131223-29)/3131224Robert Price03/2018
381429524^27825+27825^29524131218Hans Havermann03/2021
3815(23*2^435891-1)/699131215Lelio R Paula07/2015
3816(11*2^435879+1)/3337131211Lelio R Paula06/2015
381730639^19136+19136^30639131192Hans Havermann04/2021
3818(2^435808+1)/641/6700417131182Lelio R Paula02/2012
3819(2^435808+1)/4294967297131182Serge Batalov12/2016
38202^435773+1875557131181Enzo Doria06/2016
3822(16*10^131180+167)/3131181Robert Price06/2019
3821(26*10^131180-77)/3131181Robert Price11/2019
3823(25*10^131144-7)/9131145Robert Price05/2018
382429299^29358-29358^29299131138Norbert Schneider03/2022
38252^435612-2789939131133Enzo Doria12/2015
382633976^7231+7231^33976131121Hans Havermann03/2021
382733715^7746+7746^33715131121Hans Havermann03/2021
382866^72047-65^72047131093Robert Price09/2013
3829(5*10^131090+37)/3131091Robert Price03/2018
38302^435468+75631131089Enzo Doria04/2016
383137^83588-2131083Lelio R Paula08/2015
3832(4^217720+11)/3131081Robert Price02/2017
383330407^20448+20448^30407131074Hans Havermann04/2021
3834(22*10^131070+179)/3131071Robert Price02/2022
383529487^27836+27836^29487131059Hans Havermann04/2021
383629962^23615+23615^29962131030Hans Havermann03/2021
38372^435202-113193131009Enzo Doria07/2014
383841705^1384+1384^41705131002Hans Havermann04/2021
38399*10^130998-19130999Robert Price07/2019
384036243^4108+4108^36243130969Hans Havermann04/2021
3841floor((sqrt(5)-1)/2*10^130911)130911Serge Batalov06/2017
38422^434835-111937130899Enzo Doria05/2014
3843(62*10^130895-629)/9130896Robert Price07/2021
38442^434685+72257130854Enzo Doria04/2016
3845(7*10^130825+113)/3130826Robert Price02/2018
38462^434539-29317130810Enzo Doria07/2015
3847(74*10^130791+637)/9130792Robert Price01/2022
38482^434469-114259130789Enzo Doria01/2015
3849(5*10^130763+103)/9130763Robert Price04/2022
38502^434246+33130722Robert Price11/2015
385130156^21599+21599^30156130710Hans Havermann04/2021
3852(17*10^130695-161)/9130695Robert Price02/2021
385330513^19148+19148^30513130661Hans Havermann03/2021
385429736^24761+24761^29736130654Hans Havermann04/2021
38559*10^130638+41130639Robert Price08/2020
38562^433911-91130621Lelio R Paula06/2017
385730786^17449+17449^30786130588Hans Havermann03/2021
38582^433744-114419130570Enzo Doria02/2015
38602^433708+1869451130560Enzo Doria05/2016
38592^433710+93130560Lelio R Paula06/2017
38617*10^130535-27130536Robert Price11/2022
3862(9629^32768+1)/120501441265666130520Kellen Shenton05/2021
3863804*34^85220+713130516Eric Chen08/2023
3864(29*2^433547-1)/27130511Lelio R Paula06/2015
38653^273521+10130503Tyler NeSmith01/2021
386641659^1356+1356^41659130487Hans Havermann03/2021
38674*10^130480+9130481Robert Price05/2015
3868(23*2^433449-1)/75130481Lelio R Paula06/2015
38693*2^433422+5130474Jon Grantham07/2023
3870(23*2^433334-1)/3731130445Lelio R Paula06/2015
3871(31*10^130414-49)/9130415Robert Price11/2021
387233481^7848+7848^33481130401Hans Havermann03/2021
3873(17*10^130393+7)/3130394Robert Price06/2023
3874(22*10^130392+203)/9130393Robert Price10/2021
387529773^23950+23950^29773130386Hans Havermann04/2021
38762^433023-113497130353Enzo Doria08/2014
387731175^15178+15178^31175130350Hans Havermann04/2021
38782^433002+1179379130347Enzo Doria06/2016
38792^432974+19130339Robert Price08/2015
388031903^12168+12168^31903130331Hans Havermann04/2021
38812^432917+22217130322Enzo Doria09/2023
388229387^27112+27112^29387130278Hans Havermann04/2021
38832^432768+213181130277Enzo Doria09/2023
388429577^25370+25370^29577130267Hans Havermann04/2021
388531738^12685+12685^31738130231Hans Havermann03/2021
388644235^878+878^44235130206Hans Havermann04/2021
388732160^11171+11171^32160130187Hans Havermann04/2021
388829489^25956+25956^29489130172Hans Havermann04/2021
3889(2^432457-1)/1672739247834685086279697130159Tony Prest / Never Odd Or Even09/2013
389033005^8766+8766^33005130133Hans Havermann04/2021
3891(35*10^130132-611)/9130133Robert Price02/2022
38922^432217+41130111Lelio R Paula06/2017
3893(2^216089*(2^216091-1)-339)/25130098Makoto Morimoto03/2017
3894((2^216091+1066)^2+(2^216091+1066)+41)/47/2069130095Makoto Morimoto05/2016
389597^65480-2130094Lelio R Paula05/2017
389636007^4102+4102^36007130094Hans Havermann04/2021
38974*10^130088-89130089Robert Price11/2018
38982^432117-113215130081Enzo Doria07/2014
3899(4*10^130080+41)/9130080Serge Batalov11/2022
39002^431804+72511129986Enzo Doria04/2016
3901(13*10^129896+137)/3129897Robert Price06/2021
3902(13*10^129890+71)/3129891Robert Price06/2021
390329048^29101-29101^29048129882Norbert Schneider03/2022
390437832^2709+2709^37832129871Hans Havermann04/2021
390531055^15184+15184^31055129853Hans Havermann04/2021
3906(3^272141-3^136071+1)/7129844Serge Batalov03/2014
390731385^13702+13702^31385129833Hans Havermann04/2021
3908(13*10^129826+41)/9129827Tyler Busby02/2023
390928901^29102-29102^28901129822Norbert Schneider03/2022
3910(47*10^129789-119)/9129790Robert Price05/2019
3911(9*2^431141+1)/17129787Lelio R Paula06/2015
3912(166*10^129712+17)/3129714Robert Price07/2022
3913(29*2^430881-1)/21129709Lelio R Paula06/2015
39142^430807+1869563129686Enzo Doria05/2016
39152^430721-21429129660Enzo Doria07/2013
3916(4*10^129618+89)/3129619Robert Price08/2021
3917(10^129587-7^129587)/3129587Jon Grantham07/2023
39182^430415-276271129568Enzo Doria07/2015
391932282^10311+10311^32282129558Hans Havermann04/2021
392029486^24741+24741^29486129545Hans Havermann04/2021
3921(29*10^129543+313)/9129544Robert Price04/2021
392237095^3104+3104^37095129533Hans Havermann04/2021
392331132^14459+14459^31132129514Hans Havermann04/2021
392432582^9435+9435^32582129506Hans Havermann03/2021
392530442^17953+17953^30442129505Hans Havermann03/2021
3926(199*10^129487-7)/3129489Robert Price05/2020
39272^430142-2791721129486Enzo Doria03/2016
3928(7*10^129472-13)/3129473Robert Price07/2018
3929(8*10^129469+79)/3129470Robert Price10/2020
393031678^12213+12213^31678129463Hans Havermann04/2021
393110620^32143-10619^32143129412Norbert Schneider08/2023
3932(772*10^129406-7)/9129408Robert Price06/2022
393331100^14439+14439^31100129362Hans Havermann04/2021
393433009^8288+8288^33009129345Hans Havermann04/2021
393529675^22804+22804^29675129324Hans Havermann04/2021
393629068^28099+28099^29068129315Hans Havermann04/2021
39372^429568-21017129313Enzo Doria07/2013
3938(10^129295+83)/3129295Robert Price08/2021
3939(853*10^129274-7)/9129276Robert Price07/2021
394030958^14961+14961^30958129249Hans Havermann04/2021
3941(11*10^129239-179)/3129240Robert Price09/2018
394228659^28988+28988^28659129208Norbert Schneider02/2021
394329423^24616+24616^29423129203Hans Havermann03/2021
39442^429194-112685129201Enzo Doria06/2014
39452^429145-2780449129186Enzo Doria04/2016
394632500^9427+9427^32500129168Hans Havermann04/2021
394733577^7014+7014^33577129136Hans Havermann03/2021
39482^428892-113453129110Enzo Doria07/2014
3949(11*2^428881-7)/15129106Renaud Lifchitz03/2011
39502^428727-113959129060Enzo Doria10/2014
3951(7*2^428725-1)/13129059Lelio R Paula05/2014
3952(10^129051-31)/3129051Serge Batalov12/2014
3953(134*10^129038+7)/3129040Robert Price02/2020
39542^428564+71161129011Enzo Doria04/2016
395528781^28930+28930^28781129002Norbert Schneider02/2021
395629065^27424+27424^29065128995Hans Havermann04/2021
39572^428502-113285128992Enzo Doria07/2014
39582^428421-21373128968Enzo Doria06/2013
3959L(616787)128901Henri Lifchitz09/2008
396020^99055-3128874Paul Bourdelais12/2020
396191^65772-2128851Lelio R Paula05/2017
39622^428022+43128848Lelio R Paula05/2017
39632^427999-459397128841Enzo Doria05/2015
39642^427993+76847128839Enzo Doria05/2016
396531059^14060+14060^31059128833Hans Havermann03/2021
396610^128805+152871128806Patrick De Geest05/2021
396710^128805-10001128805Robert Price02/2021
39682^427824-1851507128788Enzo Doria08/2015
39692^427807-21469128783Enzo Doria07/2013
397029082^26783+26783^29082128772Hans Havermann04/2021
397140055^1638+1638^40055128750Hans Havermann04/2021
397211^123594-240128710Enzo Doria09/2012
39732^427504-21503128692Enzo Doria07/2013
397437727^2574+2574^37727128673Hans Havermann04/2021
397529686^21591+21591^29686128668Hans Havermann04/2021
397610^128668-70000000001128668Robert Price08/2021
39772^427420+91128667Lelio R Paula05/2017
39788*10^128651-37128652Robert Price03/2022
3979(68*10^128645-257)/9128646Robert Price07/2019
39802^427269-113635128621Enzo Doria08/2014
39812^427130+1877569128579Enzo Doria08/2016
39822^427068+20011128561Enzo Doria06/2023
39832^427016-115349128545Enzo Doria07/2015
3984(4*10^128510+137)/3128511Robert Price03/2018
39852^426889-112879128507Enzo Doria06/2014
39862^426804+1869931128481Enzo Doria05/2016
39872^426750+77635128465Enzo Doria05/2016
398836988^2969+2969^36988128445Hans Havermann03/2021
398936664^3185+3185^36664128439Hans Havermann03/2021
399032618^8649+8649^32618128416Hans Havermann04/2021
399128883^27874+27874^28883128391Hans Havermann04/2021
39922^426425-91128367Lelio R Paula05/2017
3993(15*2^426398-1)/11128359Lelio R Paula05/2014
39942^426352+74971128345Enzo Doria04/2016
3995(199*10^128343-7)/3128345Robert Price05/2020
39964*10^128343-21128344Robert Price09/2018
3997(65*10^128338+493)/9128339Robert Price08/2021
399835632^3997+3997^35632128337Hans Havermann04/2021
39992^426300-1863689128330Enzo Doria03/2016
40002^426293+1881017128327Enzo Doria11/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2023 15:19 (Time in France)

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