PRP Records

Probable Primes Top 10000

(302955 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 ?
55012^440846+1870909132708Enzo Doria05/2016
5502(948^44579-1)/947132701Jinyuan Wang04/2023
55032^440656-113489132651Enzo Doria08/2014
5504numbpart(14180123587)132646Serge Batalov04/2017
550532950^10591+10591^32950132622Hans Havermann04/2021
550633302^9597+9597^33302132614Hans Havermann04/2021
5507(19*10^132550+191)/3132551Robert Price05/2019
5508(2^440399-1)/(16210820281161978209*31518475633*880799)132538Dario Alpern01/2015
5509(38^83891+1)/39132529Robert Price09/2013
55102*10^132493-43132494Robert Price04/2018
551131352^16809+16809^31352132480Hans Havermann04/2021
5512(418*10^132441+23)/9132443Robert Price02/2020
55132^439931-21132433Lelio R Paula08/2017
551447^79201-46^79201132432Robert Price10/2012
55152^439897-113653132423Enzo Doria08/2014
551635505^5362+5362^35505132410Hans Havermann03/2021
551730079^25222+25222^30079132402Hans Havermann04/2021
5518(5*2^439822+1)/9132400Lelio R Paula06/2015
5519(695*10^132356+7)/9132358Robert Price12/2021
5520(112*10^132337-1)/3132339Serge Batalov12/2014
55212^439576-113247132326Enzo Doria07/2014
5522(7^156589-1)/65346468774132323Paul Vanderveen05/2025
552330059^25230+25230^30059132318Hans Havermann04/2021
55242^439497-29143132302Enzo Doria07/2015
55252^439409-114193132276Enzo Doria12/2014
5526(39^83137+2^83137)/41132275Robert Price12/2024
5527(44*10^132233-233)/9132234Robert Price01/2019
552825507^30000-30000^25507132200Frank Doornink02/2024
55299*10^132148-7132149Robert Price09/2015
5530V(790390)132144Serge Batalov07/2024
5531(47*10^132125-119)/9132126Robert Price05/2019
55322^438900+214051132123Enzo Doria10/2023
55332^438845+1870217132106Enzo Doria05/2016
5534Phi(293229,-5)132106Henri Lifchitz02/2026
55352^438789+87855132089Lelio R Paula01/2016
55362^438774-2786411132085Enzo Doria03/2016
55372^438755-1848205132079Enzo Doria07/2015
553830502^21381+21381^30502132075Hans Havermann04/2021
55392^438739-112087132074Enzo Doria06/2014
5540(588859*29^90289-19)/28132043Eric Chen06/2025
5541(2^438438+100280245065)131983Paul Bourdelais05/2022
554235872^4777+4777^35872131979Hans Havermann04/2021
554331198^16945+16945^31198131938Hans Havermann03/2021
554413907#+(318259#)/(13907#)131923Makoto Morimoto10/2017
5545L(631181)131910Henri Lifchitz09/2008
5546(47*10^131886-119)/9131887Robert Price05/2019
55475*2^438096-3131881Jon Grantham07/2023
5548(3*2^438121+1)/4308193883131879Lelio R Paula06/2015
55492^438079-1863877131875Enzo Doria03/2016
5550(16*10^131872-37)/3131873Robert Price05/2021
5551(2^438067+5)/329131869Lelio R Paula06/2015
55522^437908-113855131824Enzo Doria09/2014
55532^437884-286349131817Enzo Doria07/2015
555415^112072+14131807Alfred Reich10/2023
55555^188558+4131797Tyler NeSmith05/2021
5556(11*10^131784-17)/3131785Robert Price06/2018
5557(166^59357-1)/165131777Anonymous06/2024
55584*10^131719-93131720Robert Price07/2020
555931629^14606+14606^31629131720Hans Havermann04/2021
55603^276062-112292131716Enzo Doria07/2014
55612^437539+2025131713Henri Lifchitz01/2025
556211*31^88313+322688131708Eric Chen05/2024
5563(7*10^131682+89)/3131683Robert Price08/2020
556429512^28969+28969^29512131681Hans Havermann03/2021
55652^437343+75953131654Enzo Doria04/2016
556635^85243-34^85243131621Robert Price05/2012
5567(28*10^131586+59)/3131587Robert Price05/2021
5568(59*10^131575+391)/9131576Robert Price03/2021
5569Phi(51051,-17#)131513Henri Lifchitz12/2025
557039984^1945+1945^39984131505Hans Havermann03/2021
557125842^29801-29801^25842131492Frank Doornink03/2024
557228592^29505-29505^28592131482Frank Doornink05/2024
557325647^29818-29818^25647131469Frank Doornink02/2024
5574(203*10^131457+1)/3131459Robert Price03/2020
55757*10^131421-41131422Robert Price08/2021
557687309^32+32^87309131414Hans Havermann03/2021
5577(68^71713+1)/69131413Paul Bourdelais09/2017
55782^436521+224885131406Enzo Doria07/2024
5579(650*10^131391+43)/9131393Tyler Busby01/2023
55802^436451+1884713131385Enzo Doria03/2017
55812^436365+35131359Robert Price11/2015
55832^436300+1866871131340Enzo Doria03/2016
5582(7*10^131339+179)/3131340Robert Price09/2018
558414^114592-3131338Paul Bourdelais12/2020
558536197^4236+4236^36197131285Hans Havermann04/2021
5586(37*10^131270+341)/9131271Robert Price08/2018
558729863^24790+24790^29863131227Hans Havermann03/2021
5588(5*10^131223-29)/3131224Robert Price03/2018
558929524^27825+27825^29524131218Hans Havermann03/2021
5590(23*2^435891-1)/699131215Lelio R Paula07/2015
5591(11*2^435879+1)/3337131211Lelio R Paula06/2015
559230639^19136+19136^30639131192Hans Havermann04/2021
5593(2^435808+1)/641/6700417131182Lelio R Paula02/2012
5594(2^435808+1)/4294967297131182Serge Batalov12/2016
55952^435773+1875557131181Enzo Doria06/2016
5597(16*10^131180+167)/3131181Robert Price06/2019
5596(26*10^131180-77)/3131181Robert Price11/2019
5598(25*10^131144-7)/9131145Robert Price05/2018
559929299^29358-29358^29299131138Norbert Schneider03/2022
56002^435612-2789939131133Enzo Doria12/2015
560133976^7231+7231^33976131121Hans Havermann03/2021
560233715^7746+7746^33715131121Hans Havermann03/2021
560366^72047-65^72047131093Robert Price09/2013
5604(5*10^131090+37)/3131091Robert Price03/2018
56052^435468+75631131089Enzo Doria04/2016
560637^83588-2131083Lelio R Paula08/2015
5607(4^217720+11)/3131081Robert Price02/2017
560830407^20448+20448^30407131074Hans Havermann04/2021
5609(22*10^131070+179)/3131071Robert Price02/2022
561028831^29388-29388^28831131067Frank Doornink05/2024
561129487^27836+27836^29487131059Hans Havermann04/2021
561229962^23615+23615^29962131030Hans Havermann03/2021
56132^435202-113193131009Enzo Doria07/2014
561441705^1384+1384^41705131002Hans Havermann04/2021
56159*10^130998-19130999Robert Price07/2019
561636243^4108+4108^36243130969Hans Havermann04/2021
5617(445^49433+1)/446130914Jinyuan Wang05/2024
5618floor((sqrt(5)-1)/2*10^130911)130911Serge Batalov06/2017
56192^434835-111937130899Enzo Doria05/2014
5620(62*10^130895-629)/9130896Robert Price07/2021
56212^434807+225130890Henri Lifchitz11/2024
56222^434685+72257130854Enzo Doria04/2016
5623Phi(64497,-1105)130853Henri Lifchitz12/2025
5624(7*10^130825+113)/3130826Robert Price02/2018
56252^434539-29317130810Enzo Doria07/2015
5626(74*10^130791+637)/9130792Robert Price01/2022
56272^434469-114259130789Enzo Doria01/2015
5628(5*10^130763+103)/9130763Robert Price04/2022
56292^434246+33130722Robert Price11/2015
563030156^21599+21599^30156130710Hans Havermann04/2021
5631(41^81041-3^81041)/38130701Robert Price09/2025
5632(17*10^130695-161)/9130696Robert Price02/2021
563330513^19148+19148^30513130661Hans Havermann03/2021
563429736^24761+24761^29736130654Hans Havermann04/2021
56359*10^130638+41130639Robert Price08/2020
56362^433911-91130621Lelio R Paula06/2017
563730786^17449+17449^30786130588Hans Havermann03/2021
56382^433744-114419130570Enzo Doria02/2015
56402^433708+1869451130560Enzo Doria05/2016
56392^433710+93130560Lelio R Paula06/2017
56417*10^130535-27130536Robert Price11/2022
5642(17^130533)%(10^130533)130533Henri Lifchitz05/2025
5643(9629^32768+1)/120501441265666130520Kellen Shenton05/2021
5644804*34^85220+713130516Eric Chen08/2023
5645(29*2^433547-1)/27130511Lelio R Paula06/2015
56463^273521+10130503Tyler NeSmith01/2021
564741659^1356+1356^41659130487Hans Havermann03/2021
56484*10^130480+9130481Robert Price05/2015
5649(23*2^433449-1)/75130481Lelio R Paula06/2015
56503*2^433422+5130474Jon Grantham07/2023
5651(23*2^433334-1)/3731130445Lelio R Paula06/2015
5652(31*10^130414-49)/9130415Robert Price11/2021
565326462^29485-29485^26462130402Frank Doornink03/2024
565433481^7848+7848^33481130401Hans Havermann03/2021
5655(17*10^130393+7)/3130394Robert Price06/2023
5656(22*10^130392+203)/9130393Robert Price10/2021
565729773^23950+23950^29773130386Hans Havermann04/2021
56582^433023-113497130353Enzo Doria08/2014
565931175^15178+15178^31175130350Hans Havermann04/2021
56602^433002+1179379130347Enzo Doria06/2016
56612^432974+19130339Robert Price08/2015
566231903^12168+12168^31903130331Hans Havermann04/2021
56632^432917+22217130322Enzo Doria09/2023
566429387^27112+27112^29387130278Hans Havermann04/2021
56652^432768+213181130277Enzo Doria09/2023
566629577^25370+25370^29577130267Hans Havermann04/2021
566731738^12685+12685^31738130231Hans Havermann03/2021
566844235^878+878^44235130206Hans Havermann04/2021
566932160^11171+11171^32160130187Hans Havermann04/2021
567029489^25956+25956^29489130172Hans Havermann04/2021
5671(2^432457-1)/1672739247834685086279697130159Tony Prest / Never Odd Or Even09/2013
567233005^8766+8766^33005130133Hans Havermann04/2021
5673(35*10^130132-611)/9130133Robert Price02/2022
5674(444^49408+1)/(444^256+1)130125Martin Hopf12/2023
56752^432217+41130111Lelio R Paula06/2017
5676(2^216089*(2^216091-1)-339)/25130098Makoto Morimoto03/2017
5677((2^216091+1066)^2+(2^216091+1066)+41)/47/2069130095Makoto Morimoto05/2016
567897^65480-2130094Lelio R Paula05/2017
567936007^4102+4102^36007130094Hans Havermann04/2021
56804*10^130088-89130089Robert Price11/2018
56812^432117-113215130081Enzo Doria07/2014
5682(4*10^130080+41)/9130080Serge Batalov11/2022
56839583*29^88890+736129997Eric Chen06/2025
56842^431804+72511129986Enzo Doria04/2016
568527902^29237-29237^27902129978Frank Doornink03/2024
568633^85579+32129953Alfred Reich10/2025
5687(2313^38809-1)/(2313^197-1)129898Ryan Propper11/2023
5688(13*10^129896+137)/3129897Robert Price06/2021
5689(13*10^129890+71)/3129891Robert Price06/2021
569029048^29101-29101^29048129882Norbert Schneider03/2022
569137832^2709+2709^37832129871Hans Havermann04/2021
569231055^15184+15184^31055129853Hans Havermann04/2021
5694(3^272141-3^136071+1)/7129844Serge Batalov03/2014
5693Phi(1632846L,3)129844Anonymous03/2025
569531385^13702+13702^31385129833Hans Havermann04/2021
5696(13*10^129826+41)/9129827Tyler Busby02/2023
569728901^29102-29102^28901129822Norbert Schneider03/2022
5698(47*10^129789-119)/9129790Robert Price05/2019
5699(9*2^431141+1)/17129787Lelio R Paula06/2015
570025999^29384-29384^25999129730Frank Doornink03/2024
570125771^29408-29408^25771129723Frank Doornink02/2024
5702(166*10^129712+17)/3129714Robert Price07/2022
5703(29*2^430881-1)/21129709Lelio R Paula06/2015
57042^430807+1869563129686Enzo Doria05/2016
57052^430721-21429129660Enzo Doria07/2013
5706Phi(326081,3)129648Henri Lifchitz12/2025
5707(4*10^129618+89)/3129619Robert Price08/2021
5708(142^60223-1)/141129616Anonymous06/2024
5709(10^129587-7^129587)/3129587Jon Grantham07/2023
57102^430415-276271129568Enzo Doria07/2015
571132282^10311+10311^32282129558Hans Havermann04/2021
571229486^24741+24741^29486129545Hans Havermann04/2021
5713(29*10^129543+313)/9129544Robert Price04/2021
571437095^3104+3104^37095129533Hans Havermann04/2021
571531132^14459+14459^31132129514Hans Havermann04/2021
571632582^9435+9435^32582129506Hans Havermann03/2021
571730442^17953+17953^30442129505Hans Havermann03/2021
5718(199*10^129487-7)/3129489Robert Price05/2020
57192^430142-2791721129486Enzo Doria03/2016
5720(7*10^129472-13)/3129473Robert Price07/2018
5721(8*10^129469+79)/3129470Robert Price10/2020
572231678^12213+12213^31678129463Hans Havermann04/2021
572310620^32143-10619^32143129412Norbert Schneider08/2023
5724(772*10^129406-7)/9129408Robert Price06/2022
5725(535^47431-1)/534129406Tom Wu09/2024
5726((3*20425-8193)*F(618977)-(20425-8193)*L(618977))/2129363Yaroslav Berezhko03/2025
572731100^14439+14439^31100129362Hans Havermann04/2021
572833009^8288+8288^33009129345Hans Havermann04/2021
572925895^29306-29306^25895129334Frank Doornink03/2024
5730(44^78697+43^78697)/87129333Aurel Gibier11/2023
573129675^22804+22804^29675129324Hans Havermann04/2021
573229068^28099+28099^29068129315Hans Havermann04/2021
57332^429568-21017129313Enzo Doria07/2013
5734(10^129295+83)/3129295Robert Price08/2021
5735(853*10^129274-7)/9129276Robert Price07/2021
5736998^43100+997129263Alfred Reich03/2026
573730958^14961+14961^30958129249Hans Havermann04/2021
5738(11*10^129239-179)/3129240Robert Price09/2018
573928659^28988+28988^28659129208Norbert Schneider02/2021
574029423^24616+24616^29423129203Hans Havermann03/2021
57412^429194-112685129201Enzo Doria06/2014
574231*35^83672+17398129197Eric Chen05/2025
57432^429145-2780449129186Enzo Doria04/2016
574432500^9427+9427^32500129168Hans Havermann04/2021
574533577^7014+7014^33577129136Hans Havermann03/2021
57462^428892-113453129110Enzo Doria07/2014
5747(11*2^428881-7)/15129106Renaud Lifchitz03/2011
57482^428727-113959129060Enzo Doria10/2014
5749(7*2^428725-1)/13129059Lelio R Paula05/2014
5750(10^129051-31)/3129051Serge Batalov12/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 24 2026 08:53 (Time in France)

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