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 ?
3251(25*2^442379-1)/71133169Lelio R Paula07/2015
325234240^7737+7737^34240133145Hans Havermann03/2021
3253452^50145+50145^452133142Norbert Schneider09/2020
325430659^21796+21796^30659133011Hans Havermann04/2021
325533276^9935+9935^33276133010Hans Havermann04/2021
325630111^26122+26122^30111133001Hans Havermann04/2021
325730790^20869+20869^30790132998Hans Havermann04/2021
3259(2^441799+78557)/5132995Lelio R Paula07/2015
32588*10^132994-27132995Robert Price10/2021
3260(109*10^132992+11)/3132994Robert Price06/2022
32612^441781-2787883132990Enzo Doria03/2016
3262(3*2^441685+1)/749132959Lelio R Paula07/2015
32632^441618+37132941Lelio R Paula08/2017
326434857^6514+6514^34857132940Hans Havermann04/2021
326534065^7988+7988^34065132937Hans Havermann04/2021
326635571^5452+5452^35571132914Hans Havermann04/2021
32672^441521-113575132912Enzo Doria08/2014
32687*10^132884-99132885Robert Price06/2019
3269(103*10^132879+17)/3132881Robert Price08/2020
32702^441396-65132874Lelio R Paula08/2017
327133350^9633+9633^33350132859Hans Havermann04/2021
32722^441330+1871959132854Enzo Doria05/2016
32732^441063+383132774Lelio R Paula06/2012
3274(10^132753+7)/17/19132751Alfred Reich06/2021
3275(22*10^132746+53)/3132747Robert Price07/2019
3276(77*10^132744-149)/9132745Robert Price03/2022
3277(22*10^132732+119)/3132733Robert Price04/2021
32782^440846+1870909132708Enzo Doria05/2016
32792^440656-113489132651Enzo Doria08/2014
3280numbpart(14180123587)132646Serge Batalov04/2017
328132950^10591+10591^32950132622Hans Havermann04/2021
328233302^9597+9597^33302132614Hans Havermann04/2021
3283(19*10^132550+191)/3132551Robert Price05/2019
3284(2^440399-1)/(16210820281161978209*31518475633*880799)132538Dario Alpern01/2015
3285(38^83891+1)/39132529Robert Price09/2013
32862*10^132493-43132494Robert Price04/2018
328731352^16809+16809^31352132480Hans Havermann04/2021
3288(418*10^132441+23)/9132443Robert Price02/2020
32892^439931-21132433Lelio R Paula08/2017
329047^79201-46^79201132432Robert Price10/2012
32912^439897-113653132423Enzo Doria08/2014
329235505^5362+5362^35505132410Hans Havermann03/2021
329330079^25222+25222^30079132402Hans Havermann04/2021
3294(5*2^439822+1)/9132400Lelio R Paula06/2015
3295(695*10^132356+7)/9132358Robert Price12/2021
3296(112*10^132337-1)/3132339Serge Batalov12/2014
32972^439576-113247132326Enzo Doria07/2014
329830059^25230+25230^30059132318Hans Havermann04/2021
32992^439497-29143132302Enzo Doria07/2015
33002^439409-114193132276Enzo Doria12/2014
3301(44*10^132233-233)/9132234Robert Price01/2019
33029*10^132148-7132149Robert Price09/2015
3303(47*10^132125-119)/9132126Robert Price05/2019
33042^438845+1870217132106Enzo Doria05/2016
33052^438789+87855132089Lelio R Paula01/2016
33062^438774-2786411132085Enzo Doria03/2016
33072^438755-1848205132079Enzo Doria07/2015
330830502^21381+21381^30502132075Hans Havermann04/2021
33092^438739-112087132074Enzo Doria06/2014
3310(2^438438+100280245065)131983Paul Bourdelais05/2022
331135872^4777+4777^35872131979Hans Havermann04/2021
331231198^16945+16945^31198131938Hans Havermann03/2021
331313907#+(318259#)/(13907#)131923Makoto Morimoto10/2017
3314L(631181)131910Henri Lifchitz09/2008
3315(47*10^131886-119)/9131887Robert Price05/2019
3316(3*2^438121+1)/4308193883131879Lelio R Paula06/2015
33172^438079-1863877131875Enzo Doria03/2016
3318(16*10^131872-37)/3131873Robert Price05/2021
3319(2^438067+5)/329131869Lelio R Paula06/2015
33202^437908-113855131824Enzo Doria09/2014
33212^437884-286349131817Enzo Doria07/2015
33225^188558+4131797Tyler NeSmith05/2021
3323(11*10^131784-17)/3131785Robert Price06/2018
33254*10^131719-93131720Robert Price07/2020
332431629^14606+14606^31629131720Hans Havermann04/2021
33263^276062-112292131716Enzo Doria07/2014
3327(7*10^131682+89)/3131683Robert Price08/2020
332829512^28969+28969^29512131681Hans Havermann03/2021
33292^437343+75953131654Enzo Doria04/2016
333035^85243-34^85243131621Robert Price05/2012
3331(28*10^131586+59)/3131587Robert Price05/2021
3332(59*10^131575+391)/9131576Robert Price03/2021
333339984^1945+1945^39984131505Hans Havermann03/2021
3334(203*10^131457+1)/3131459Robert Price03/2020
33357*10^131421-41131422Robert Price08/2021
333687309^32+32^87309131414Hans Havermann03/2021
3337(68^71713+1)/69131413Paul Bourdelais09/2017
33382^436451+1884713131385Enzo Doria03/2017
33392^436365+35131359Robert Price11/2015
33402^436300+1866871131340Enzo Doria03/2016
3341(7*10^131339+179)/3131340Robert Price09/2018
334214^114592-3131338Paul Bourdelais12/2020
334336197^4236+4236^36197131285Hans Havermann04/2021
3344(37*10^131270+341)/9131271Robert Price08/2018
334529863^24790+24790^29863131227Hans Havermann03/2021
3346(5*10^131223-29)/3131224Robert Price03/2018
334729524^27825+27825^29524131218Hans Havermann03/2021
3348(23*2^435891-1)/699131215Lelio R Paula07/2015
3349(11*2^435879+1)/3337131211Lelio R Paula06/2015
335030639^19136+19136^30639131192Hans Havermann04/2021
3351(2^435808+1)/641/6700417131182Lelio R Paula02/2012
3352(2^435808+1)/4294967297131182Serge Batalov12/2016
33532^435773+1875557131181Enzo Doria06/2016
3355(16*10^131180+167)/3131181Robert Price06/2019
3354(26*10^131180-77)/3131181Robert Price11/2019
3356(25*10^131144-7)/9131145Robert Price05/2018
335729299^29358-29358^29299131138Norbert Schneider03/2022
33582^435612-2789939131133Enzo Doria12/2015
335933976^7231+7231^33976131121Hans Havermann03/2021
336033715^7746+7746^33715131121Hans Havermann03/2021
336166^72047-65^72047131093Robert Price09/2013
3362(5*10^131090+37)/3131091Robert Price03/2018
33632^435468+75631131089Enzo Doria04/2016
336437^83588-2131083Lelio R Paula08/2015
3365(4^217720+11)/3131081Robert Price02/2017
336630407^20448+20448^30407131074Hans Havermann04/2021
3367(22*10^131070+179)/3131071Robert Price02/2022
336829487^27836+27836^29487131059Hans Havermann04/2021
336929962^23615+23615^29962131030Hans Havermann03/2021
33702^435202-113193131009Enzo Doria07/2014
337141705^1384+1384^41705131002Hans Havermann04/2021
33729*10^130998-19130999Robert Price07/2019
337336243^4108+4108^36243130969Hans Havermann04/2021
3374floor((sqrt(5)-1)/2*10^130911)130911Serge Batalov06/2017
33752^434835-111937130899Enzo Doria05/2014
3376(62*10^130895-629)/9130896Robert Price07/2021
33772^434685+72257130854Enzo Doria04/2016
3378(7*10^130825+113)/3130826Robert Price02/2018
33792^434539-29317130810Enzo Doria07/2015
3380(74*10^130791+637)/9130792Robert Price01/2022
33812^434469-114259130789Enzo Doria01/2015
3382(5*10^130763+103)/9130763Robert Price04/2022
33832^434246+33130722Robert Price11/2015
338430156^21599+21599^30156130710Hans Havermann04/2021
3385(17*10^130695-161)/9130695Robert Price02/2021
338630513^19148+19148^30513130661Hans Havermann03/2021
338729736^24761+24761^29736130654Hans Havermann04/2021
33889*10^130638+41130639Robert Price08/2020
33892^433911-91130621Lelio R Paula06/2017
339030786^17449+17449^30786130588Hans Havermann03/2021
33912^433744-114419130570Enzo Doria02/2015
33932^433708+1869451130560Enzo Doria05/2016
33922^433710+93130560Lelio R Paula06/2017
3394(9629^32768+1)/120501441265666130520Kellen Shenton05/2021
3395(29*2^433547-1)/27130511Lelio R Paula06/2015
33963^273521+10130503Tyler NeSmith01/2021
339741659^1356+1356^41659130487Hans Havermann03/2021
33984*10^130480+9130481Robert Price05/2015
3399(23*2^433449-1)/75130481Lelio R Paula06/2015
3400(23*2^433334-1)/3731130445Lelio R Paula06/2015
3401(31*10^130414-49)/9130415Robert Price11/2021
340233481^7848+7848^33481130401Hans Havermann03/2021
3403(22*10^130392+203)/9130393Robert Price10/2021
340429773^23950+23950^29773130386Hans Havermann04/2021
34052^433023-113497130353Enzo Doria08/2014
340631175^15178+15178^31175130350Hans Havermann04/2021
34072^433002+1179379130347Enzo Doria06/2016
34082^432974+19130339Robert Price08/2015
340931903^12168+12168^31903130331Hans Havermann04/2021
341029387^27112+27112^29387130278Hans Havermann04/2021
341129577^25370+25370^29577130267Hans Havermann04/2021
341231738^12685+12685^31738130231Hans Havermann03/2021
341344235^878+878^44235130206Hans Havermann04/2021
341432160^11171+11171^32160130187Hans Havermann04/2021
341529489^25956+25956^29489130172Hans Havermann04/2021
3416(2^432457-1)/1672739247834685086279697130159Tony Prest / Never Odd Or Even09/2013
341733005^8766+8766^33005130133Hans Havermann04/2021
3418(35*10^130132-611)/9130133Robert Price02/2022
34192^432217+41130111Lelio R Paula06/2017
3420(2^216089*(2^216091-1)-339)/25130098Makoto Morimoto03/2017
3421((2^216091+1066)^2+(2^216091+1066)+41)/47/2069130095Makoto Morimoto05/2016
342297^65480-2130094Lelio R Paula05/2017
342336007^4102+4102^36007130094Hans Havermann04/2021
34244*10^130088-89130089Robert Price11/2018
34252^432117-113215130081Enzo Doria07/2014
34262^431804+72511129986Enzo Doria04/2016
3427(13*10^129896+137)/3129897Robert Price06/2021
3428(13*10^129890+71)/3129891Robert Price06/2021
342929048^29101-29101^29048129882Norbert Schneider03/2022
343037832^2709+2709^37832129871Hans Havermann04/2021
343131055^15184+15184^31055129853Hans Havermann04/2021
3432(3^272141-3^136071+1)/7129844Serge Batalov03/2014
343331385^13702+13702^31385129833Hans Havermann04/2021
343428901^29102-29102^28901129822Norbert Schneider03/2022
3435(47*10^129789-119)/9129790Robert Price05/2019
3436(9*2^431141+1)/17129787Lelio R Paula06/2015
3437(166*10^129712+17)/3129714Robert Price07/2022
3438(29*2^430881-1)/21129709Lelio R Paula06/2015
34392^430807+1869563129686Enzo Doria05/2016
34402^430721-21429129660Enzo Doria07/2013
3441(4*10^129618+89)/3129619Robert Price08/2021
34422^430415-276271129568Enzo Doria07/2015
344332282^10311+10311^32282129558Hans Havermann04/2021
344429486^24741+24741^29486129545Hans Havermann04/2021
3445(29*10^129543+313)/9129544Robert Price04/2021
344637095^3104+3104^37095129533Hans Havermann04/2021
344731132^14459+14459^31132129514Hans Havermann04/2021
344832582^9435+9435^32582129506Hans Havermann03/2021
344930442^17953+17953^30442129505Hans Havermann03/2021
3450(199*10^129487-7)/3129489Robert Price05/2020
34512^430142-2791721129486Enzo Doria03/2016
3452(7*10^129472-13)/3129473Robert Price07/2018
3453(8*10^129469+79)/3129470Robert Price10/2020
345431678^12213+12213^31678129463Hans Havermann04/2021
3455(772*10^129406-7)/9129408Robert Price06/2022
345631100^14439+14439^31100129362Hans Havermann04/2021
345733009^8288+8288^33009129345Hans Havermann04/2021
345829675^22804+22804^29675129324Hans Havermann04/2021
345929068^28099+28099^29068129315Hans Havermann04/2021
34602^429568-21017129313Enzo Doria07/2013
3461(10^129295+83)/3129295Robert Price08/2021
3462(853*10^129274-7)/9129276Robert Price07/2021
346330958^14961+14961^30958129249Hans Havermann04/2021
3464(11*10^129239-179)/3129240Robert Price09/2018
346528659^28988+28988^28659129208Norbert Schneider02/2021
346629423^24616+24616^29423129203Hans Havermann03/2021
34672^429194-112685129201Enzo Doria06/2014
34682^429145-2780449129186Enzo Doria04/2016
346932500^9427+9427^32500129168Hans Havermann04/2021
347033577^7014+7014^33577129136Hans Havermann03/2021
34712^428892-113453129110Enzo Doria07/2014
3472(11*2^428881-7)/15129106Renaud Lifchitz03/2011
34732^428727-113959129060Enzo Doria10/2014
3474(7*2^428725-1)/13129059Lelio R Paula05/2014
3475(10^129051-31)/3129051Serge Batalov12/2014
3476(134*10^129038+7)/3129040Robert Price02/2020
34772^428564+71161129011Enzo Doria04/2016
347828781^28930+28930^28781129002Norbert Schneider02/2021
347929065^27424+27424^29065128995Hans Havermann04/2021
34802^428502-113285128992Enzo Doria07/2014
34812^428421-21373128968Enzo Doria06/2013
3482L(616787)128901Henri Lifchitz09/2008
348320^99055-3128874Paul Bourdelais12/2020
348491^65772-2128851Lelio R Paula05/2017
34852^428022+43128848Lelio R Paula05/2017
34862^427999-459397128841Enzo Doria05/2015
34872^427993+76847128839Enzo Doria05/2016
348831059^14060+14060^31059128833Hans Havermann03/2021
348910^128805+152871128806Patrick De Geest05/2021
349010^128805-10001128805Robert Price02/2021
34912^427824-1851507128788Enzo Doria08/2015
34922^427807-21469128783Enzo Doria07/2013
349329082^26783+26783^29082128772Hans Havermann04/2021
349440055^1638+1638^40055128750Hans Havermann04/2021
349511^123594-240128710Enzo Doria09/2012
34962^427504-21503128692Enzo Doria07/2013
349737727^2574+2574^37727128673Hans Havermann04/2021
349829686^21591+21591^29686128668Hans Havermann04/2021
349910^128668-70000000001128668Robert Price08/2021
35002^427420+91128667Lelio R Paula05/2017


Find by discoverer :


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

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