PRP Records

Probable Primes Top 10000

(301692 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 ?
32512^575871+28733173355Enzo Doria01/2024
3252515^63898+63898^515173280Norbert Schneider12/2022
32532^575614+9173278Stefano Morozzi04/2021
32542^575606-219533173275Enzo Doria03/2024
3255(16*10^173251+107)/3173252Robert Price03/2019
325626618^39149-39149^26618173242Frank Doornink03/2024
32572^575196-114053173152Enzo Doria11/2014
32587*10^173135-53173136Robert Price06/2020
3259(301*10^173047+23)/9173049Robert Price06/2021
32602^574591-115387172970Enzo Doria07/2015
326125210^39297-39297^25210172969Frank Doornink12/2023
3262(202*10^172940-13)/9172942Robert Price01/2020
326345^104608+104608^45172940Norbert Schneider06/2021
32642^574328+81121172890Enzo Doria07/2016
3265(115*10^172862-1)/3172864Serge Batalov12/2014
32663*10^172812+13172813Robert Price07/2018
32674*5^247217-9172798Lelio R Paula10/2015
32686*10^172772-31172773Robert Price07/2020
326969061#+(467617#)/(69061#)172766Makoto Morimoto10/2017
3270(34*10^172693-547)/9172694Robert Price03/2021
32715*10^172692+57172693Robert Price12/2018
32722^573668-2782319172692Enzo Doria09/2015
32732^573444-1855109172624Enzo Doria09/2015
327425500^39173-39173^25500172618Frank Doornink02/2024
327527180^38917-38917^27180172568Frank Doornink01/2024
3276(14*10^172532-29)/3172533Robert Price09/2021
32773^361608+2172531Robert Price08/2014
3278(54^99563+1)/55172481Paul Bourdelais11/2017
32792^572592-114893172368Enzo Doria05/2015
32804*10^172354-39172355Robert Price09/2020
328137535^37674+37674^37535172338Norbert Schneider05/2022
3282(11*10^172322-119)/9172323Robert Price11/2021
32835^246497-4^246497172295Jean-Louis Charton11/2008
3284(38^109037-1)/37172254Paul Bourdelais10/2017
3285(4*10^172241+89)/3172242Robert Price08/2021
32863*10^172219+73172220Robert Price08/2018
32872^571810+28549172132Enzo Doria01/2024
3288A352736(15)172032Kellen Shenton05/2022
328932298^38149-38149^32298172021Frank Doornink02/2024
32902^571300+25861171979Enzo Doria11/2023
3291(36^110503+1)/37171975Lelio R Paula04/2017
32928*10^171934+71171935Robert Price05/2022
3293(11*10^171933+601)/9171934Robert Price02/2022
3294(22*10^171929-73)/3171930Robert Price04/2019
3295(49*10^171892-319)/9171893Robert Price10/2021
32964*10^171891-63171892Robert Price10/2018
329767*10^171882-9171884Robert Price03/2021
32982^570980-2782289171883Enzo Doria09/2015
3299(25*10^171849-37)/3171850Robert Price10/2019
330010^171832+387909171833Patrick De Geest08/2021
330110^171832-10001171832Robert Price02/2021
3303(2^(12*47563+13)-9)/7171818Kevin Acres11/2013
3302(2^570769-9)/7171818Stefano Morozzi08/2022
33042^570545+11025171752Henri Lifchitz01/2025
330524^124375-124375^24171664Henri Lifchitz08/2024
3306(74*10^171651-29)/9171652Robert Price06/2022
3307(536*10^171601-23)/9171603Robert Price02/2020
33087*10^171535-99171536Robert Price06/2019
3309(28*10^171534+101)/3171535Robert Price09/2020
33102^569563-1854607171456Enzo Doria09/2015
331132133^38042-38042^32133171454Frank Doornink02/2024
33123*10^171391+59171392Robert Price08/2018
3313(13*10^171306-37)/3171307Robert Price01/2019
33148*10^171296+87171297Robert Price10/2019
3315(55^98419-1)/54171284Paul Bourdelais12/2017
3316(29*10^171275+67)/3171276Robert Price12/2019
3317(457*10^171248-7)/9171250Robert Price09/2022
3318(194*10^171193+1)/3171195Robert Price01/2022
33192^568642+1876129171179Enzo Doria07/2016
33204*10^171146-47171147Robert Price10/2021
3321(19*10^170970+131)/3170971Robert Price06/2020
3322(46*10^170932+143)/9170933Robert Price01/2019
3323(79*10^170901-1)/3170903Robert Price02/2020
3324(58*10^170842+221)/9170843Robert Price02/2017
3325(29*10^170830+583)/9170831Robert Price06/2021
33263*10^170800+73170801Robert Price08/2018
3327(29*10^170799-119)/9170800Robert Price12/2021
332811^164009-270170798Enzo Doria10/2012
33292*10^170767+41170768Robert Price05/2018
33303^357706-112358170670Enzo Doria07/2014
3331TheodorusPrime(170657)170657Eric W. Weisstein08/2013
33322^566871+1876163170646Enzo Doria07/2016
3333(10657#+(404267#)/(10657#))/(1675379)170624Makoto Morimoto10/2017
33342^566496+7170533Donovan Johnson07/2006
3335(7^201653+1)/8170416Paul Bourdelais02/2010
333632150^37807-37807^32150170403Frank Doornink02/2024
33377*10^170348+33170349Robert Price06/2020
33382^565799+216011170323Enzo Doria12/2023
33392^565183-352021170138Enzo Doria07/2015
33402^565143-114457170125Enzo Doria02/2015
33413*2^565024-5170090Jon Grantham07/2023
33422^564976-49869170075Enzo Doria10/2015
33432^564561+225169950Henri Lifchitz11/2024
3344(7*10^169944+23)/3169945Robert Price06/2020
3345(37*10^169943+251)/9169944Robert Price09/2021
33462^564526-351401169940Enzo Doria07/2015
33473^355902+4169809Aurel Gibier10/2024
33484*10^169759+19169760Robert Price10/2018
3349(2^563903-13)/5169752Stefano Morozzi08/2022
335021^128327-20^128327169677Jean-Louis Charton11/2014
33512^563583+89169656Stefano Morozzi04/2021
33522^563311+215813169574Enzo Doria11/2023
3353(4*10^169559+83)/3169560Robert Price02/2018
3354(194*10^169461-17)/3169463Robert Price09/2020
33552^562749+2793047169405Enzo Doria02/2016
3356(154*10^169337-1)/9169339Serge Batalov12/2014
3357(109*10^169337+11)/3169339Robert Price06/2022
3358(56*10^169311+691)/9169312Robert Price05/2019
33592^562369-29503169290Enzo Doria08/2015
3360(17*10^169283+19)/9169284Robert Price03/2021
3361390151#-2322911169082Hayden Chesnut07/2024
336210^169074-5000000001169074Robert Price09/2022
33638*10^169071+59169072Robert Price11/2021
3364(10^169044+173)/3169044Robert Price05/2021
3365(22*10^169019+383)/9169020Robert Price05/2018
3366(64*10^168935+143)/9168936Robert Price05/2021
3367(22*10^168906+47)/3168907Robert Price06/2021
33685*10^168807+87168808Robert Price02/2019
3369(77*10^168803-149)/9168804Robert Price03/2022
33704*10^168788-47168789Robert Price10/2021
3371(154*10^168781+17)/9168783Robert Price06/2022
3372(418*10^168751-31)/9168753Robert Price05/2022
3373(29*10^168711+691)/9168712Robert Price08/2021
33742^560405-39943168699Enzo Doria09/2015
3375(397*10^168634+17)/9168636Robert Price03/2022
33762^560189+36587168634Enzo Doria09/2024
337789*10^168614-7168616Robert Price04/2020
3378(23*10^168608-83)/3168609Robert Price08/2019
3379(94*10^168541+11)/3168543Robert Price04/2020
33802^559686-350471168483Enzo Doria06/2015
33812^559672-1855889168479Enzo Doria09/2015
3382(5*10^168379-473)/9168379Robert Price01/2018
33832024^50920+3168353Martin Hopf01/2024
33842^559000-59939168276Enzo Doria11/2015
33852^558830+25009168225Enzo Doria11/2023
3386(16*10^168181+41)/3168182Robert Price03/2019
3387(19*10^168173+77)/3168174Robert Price05/2019
3388(74*10^168170+529)/9168171Robert Price02/2022
33892^558640-114149168168Enzo Doria12/2014
33902^558498-1849277168125Enzo Doria08/2015
33912^558476-1850249168119Enzo Doria08/2015
3392(7*10^168067+71)/3168068Robert Price05/2018
33932^558150-1852211168020Enzo Doria08/2015
33942^558125-113661168013Enzo Doria09/2014
3395393^64747-392^64747167980Jean-Louis Charton08/2012
3396(8*10^167965-11)/3167966Robert Price07/2023
33972^557916+216151167950Enzo Doria12/2023
3398(13*10^167911+179)/3167912Robert Price11/2018
3399(26*10^167861-167)/3167862Robert Price10/2019
340036^107827-107827167812Kellen Shenton06/2023
340132027^37242-37242^32027167795Frank Doornink01/2024
340239^105456+2167788Robert Price04/2015
34032^557322+217519167771Enzo Doria01/2024
3404(28^115877-1)/27167691Paul Bourdelais12/2017
34056*10^167662-13167663Robert Price07/2022
340610^167639+121911167640Patrick De Geest07/2018
340710^167639-8001167639Robert Price03/2018
34082^556504-462059167525Enzo Doria07/2015
3409(88*10^167522-637)/9167523Robert Price11/2020
34105*10^167510+9167511Robert Price08/2015
34117*10^167437-93167438Robert Price08/2020
3412(43^102451-1)/7138097213378082167335Paul Vanderveen05/2025
341325455^37978-37978^25455167323Frank Doornink01/2024
341411^160663+6167314Paul Bourdelais02/2021
3415(7*10^167308-493)/9167308Robert Price04/2021
34162^555759+74333167301Enzo Doria07/2023
341726084^37871-37871^26084167253Frank Doornink03/2024
34182^555343+1874333167175Enzo Doria06/2016
34192^555210-461261167135Enzo Doria07/2015
34209*10^166996+59166997Robert Price01/2020
3421(68*10^166976-329)/9166977Robert Price03/2021
3422(64*10^166901+683)/9166902Robert Price06/2022
34232^554372+1880527166883Enzo Doria11/2016
34242^554299+72173166861Enzo Doria04/2016
3425(185*10^166837+7)/3166839Robert Price03/2020
3426(14*10^166813+139)/9166814Robert Price11/2021
342726084^37767-37767^26084166794Frank Doornink03/2024
34282^554037-2797063166782Enzo Doria03/2016
342931861^37028-37028^31861166747Frank Doornink01/2024
3430(49*10^166721-139)/9166722Robert Price03/2019
34312*10^166646+69166647Robert Price06/2020
34322^553484-29819166616Enzo Doria08/2015
3433(188*10^166611+7)/3166613Robert Price03/2020
34342^553383-2784217166585Enzo Doria10/2015
34352^553069+76427166491Enzo Doria05/2016
343625218^37819-37819^25218166469Frank Doornink12/2023
34372*10^166458+51166459Robert Price05/2018
3438589^60089-588^60089166454Jean-Louis Charton09/2012
343925214^37799-37799^25214166378Frank Doornink11/2023
344011^159756-2424166369Mike Oakes06/2010
34412^552649-361275166364Enzo Doria05/2014
34422^552628-113669166358Enzo Doria09/2014
3443(19*10^166325+137)/3166326Robert Price03/2022
344410^166324+550603166325Patrick De Geest07/2018
344510^166324-801166324Robert Price02/2018
3446(85*10^166297-1)/3166299Robert Price02/2020
3447(19*10^166280-7)/3166281Robert Price12/2023
344825533^37726-37726^25533166263Frank Doornink02/2024
34498*10^166227+87166228Robert Price10/2019
34502^552137+1879397166210Enzo Doria09/2016
3451262273205671539190984629()252475512364409752762433166141Anonymous01/2025
3452490079063773165613318095()218182139934160868002603166141Anonymous01/2025
3453140717254840416411192803()712689271538459396766869166140Anonymous01/2025
3454122398296040696255481419()271117913237372866926417166140Anonymous01/2025
3455(103*10^166126+11)/3166128Robert Price01/2021
3456(22*10^166077+179)/3166078Robert Price02/2022
3457(23^121949-1)/22166061Paul Bourdelais10/2017
34582^551576+236221166041Enzo Doria05/2025
34592^551542+19249166031Payam Samidoost08/2002
34602^551535-23821166029Enzo Doria08/2013
34612^551507-23557166021Enzo Doria08/2013
346232030^36841-36841^32030165990Frank Doornink01/2024
346310^165947-7000000001165947Robert Price12/2021
34644*10^165938-47165939Robert Price10/2021
34657*10^165916-3165917Robert Price08/2015
3466(29*10^165796+67)/3165797Robert Price12/2019
346781^86837-80^86837165728Robert Price01/2015
3468(71*10^165716-17)/9165717Serge Batalov01/2023
3469fibonacci(792909)+3165708Jon Grantham08/2023
3470(71*10^165663-539)/9165664Robert Price07/2019
347125682^37567-37567^25682165657Frank Doornink02/2024
34722^550270-69551165648Enzo Doria12/2015
34732^550250+29329165642Enzo Doria03/2024
3474(202*10^165569-13)/9165571Robert Price01/2020
34752^550000-23625165567Enzo Doria08/2013
347631688^36783-36783^31688165557Frank Doornink01/2024
34772^549675-1852057165469Enzo Doria08/2015
34782^549663+212543165466Enzo Doria08/2023
3479(3^549633)%(2^549633)165456Henri Lifchitz06/2025
3480(529*10^165394-7)/9165396Robert Price08/2021
348126253^37424-37424^26253165384Frank Doornink03/2024
3482-tau(103^14938)165374Nik Lygeros / Olivier Rozier10/2013
3483(28*10^165358-1)/9165359Serge Batalov10/2014
34842^549278+1879669165350Enzo Doria09/2016
3485(7*10^165350-439)/9165350Robert Price02/2018
34862^549252-351269165342Enzo Doria06/2015
34872^549221+335931165332Enzo Doria09/2024
348867*10^165327-9165329Robert Price03/2021
3489(14*10^165282+73)/3165283Robert Price12/2018
3490(8*10^165283-629)/9165283Robert Price01/2022
34912^549049+2797607165281Enzo Doria04/2016
3492(218*10^165258+7)/9165260Robert Price06/2022
3493(7*10^165239+107)/3165240Robert Price02/2018
34942^548880+23961165230Enzo Doria10/2023
34955*2^548778+3165200Jon Grantham07/2023
3496(44^100511-1)/43165184Paul Bourdelais11/2017
3497(7*10^165134+107)/3165135Robert Price02/2018
3498(301*10^165082+23)/9165084Robert Price06/2021
3499(23*10^165060-83)/3165061Robert Price08/2019
35007*10^165023-27165024Robert Price11/2022


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 05 2025 13:49 (Time in France)

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