PRP Records

Probable Primes Top 10000

(301745 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 ?
32512^580046-459161174612Enzo Doria05/2015
32522^579992-39779174595Enzo Doria09/2015
325325613^39582-39582^25613174496Frank Doornink02/2024
3254(29*10^174481-149)/3174482Robert Price08/2022
3255(4*10^174423+101)/3174424Robert Price11/2021
3256(2^579371-17)/3174408Stefano Morozzi08/2022
3257(2*10^174301-71)/3174301Robert Price12/2017
325814^152048+3174267Paul Bourdelais12/2020
3259(2^578696+1)/257174203Lelio R Paula09/2015
32602^578656-1851809174193Enzo Doria08/2015
32612^578583-113917174171Enzo Doria10/2014
32622^578434-83174126Yves Minet07/2017
326315^148048-2174118Robert Price06/2015
32645*10^174101+81174102Robert Price03/2019
32652^578346+2794249174100Enzo Doria03/2016
326610^173947+1372429173948Patrick De Geest08/2021
326810^173947-500000001173947Robert Price12/2020
326710^173947-286391173947Patrick De Geest08/2021
32695*10^173904-13173905Robert Price01/2019
3270(8*10^173862-59)/3173863Robert Price08/2021
3271(71*10^173854-287)/9173855Robert Price09/2019
3272(43*10^173826+101)/9173827Robert Price11/2018
32742*10^173809-87173810Robert Price04/2018
3273(17^141263-1)/27122512173810Paul Vanderveen05/2025
3275(2^577372-23)/7173806Stefano Morozzi08/2022
3276(L!41532)/2173772Serge Batalov07/2017
32772^577146-49877173739Enzo Doria10/2015
32782^576889+49727173661Enzo Doria09/2016
3279(19^173604)%(10^173604)173604Henri Lifchitz05/2025
3280(167*10^173571-17)/3173573Robert Price03/2020
328137803^37916+37916^37803173562Norbert Schneider06/2022
32825*10^173534+29173535Robert Price12/2020
3283(2^576551-1)/4612409/64758208321/242584327930759173528Dario Alpern06/2014
32844*10^173509+99173510Robert Price12/2020
3285(13*10^173467-37)/3173468Robert Price01/2019
32862^576016-113919173399Enzo Doria11/2014
32872^575911-1849387173367Enzo Doria08/2015
328821554^40005-40005^21554173363Norbert Schneider04/2025
32892^575879+215843173357Enzo Doria11/2023
32902^575871+28733173355Enzo Doria01/2024
3291515^63898+63898^515173280Norbert Schneider12/2022
32922^575614+9173278Stefano Morozzi04/2021
32932^575606-219533173275Enzo Doria03/2024
3294(16*10^173251+107)/3173252Robert Price03/2019
329526618^39149-39149^26618173242Frank Doornink03/2024
32962^575196-114053173152Enzo Doria11/2014
32977*10^173135-53173136Robert Price06/2020
3298(301*10^173047+23)/9173049Robert Price06/2021
32992^574591-115387172970Enzo Doria07/2015
330025210^39297-39297^25210172969Frank Doornink12/2023
3301(202*10^172940-13)/9172942Robert Price01/2020
330245^104608+104608^45172940Norbert Schneider06/2021
33032^574328+81121172890Enzo Doria07/2016
3304(115*10^172862-1)/3172864Serge Batalov12/2014
33053*10^172812+13172813Robert Price07/2018
33064*5^247217-9172798Lelio R Paula10/2015
33076*10^172772-31172773Robert Price07/2020
330869061#+(467617#)/(69061#)172766Makoto Morimoto10/2017
3309(34*10^172693-547)/9172694Robert Price03/2021
33105*10^172692+57172693Robert Price12/2018
33112^573668-2782319172692Enzo Doria09/2015
33122^573444-1855109172624Enzo Doria09/2015
331325500^39173-39173^25500172618Frank Doornink02/2024
331427180^38917-38917^27180172568Frank Doornink01/2024
3315(14*10^172532-29)/3172533Robert Price09/2021
33163^361608+2172531Robert Price08/2014
3317(54^99563+1)/55172481Paul Bourdelais11/2017
33182^572592-114893172368Enzo Doria05/2015
33194*10^172354-39172355Robert Price09/2020
332037535^37674+37674^37535172338Norbert Schneider05/2022
3321(11*10^172322-119)/9172323Robert Price11/2021
33225^246497-4^246497172295Jean-Louis Charton11/2008
3323(38^109037-1)/37172254Paul Bourdelais10/2017
3324(4*10^172241+89)/3172242Robert Price08/2021
33253*10^172219+73172220Robert Price08/2018
33262^571810+28549172132Enzo Doria01/2024
3327A352736(15)172032Kellen Shenton05/2022
332832298^38149-38149^32298172021Frank Doornink02/2024
33292^571300+25861171979Enzo Doria11/2023
3330(36^110503+1)/37171975Lelio R Paula04/2017
33318*10^171934+71171935Robert Price05/2022
3332(11*10^171933+601)/9171934Robert Price02/2022
3333(22*10^171929-73)/3171930Robert Price04/2019
3334(49*10^171892-319)/9171893Robert Price10/2021
33354*10^171891-63171892Robert Price10/2018
333667*10^171882-9171884Robert Price03/2021
33372^570980-2782289171883Enzo Doria09/2015
3338(25*10^171849-37)/3171850Robert Price10/2019
333910^171832+387909171833Patrick De Geest08/2021
334010^171832-10001171832Robert Price02/2021
3342(2^(12*47563+13)-9)/7171818Kevin Acres11/2013
3341(2^570769-9)/7171818Stefano Morozzi08/2022
33432^570545+11025171752Henri Lifchitz01/2025
334424^124375-124375^24171664Henri Lifchitz08/2024
3345(74*10^171651-29)/9171652Robert Price06/2022
3346(536*10^171601-23)/9171603Robert Price02/2020
33477*10^171535-99171536Robert Price06/2019
3348(28*10^171534+101)/3171535Robert Price09/2020
33492^569563-1854607171456Enzo Doria09/2015
335032133^38042-38042^32133171454Frank Doornink02/2024
33513*10^171391+59171392Robert Price08/2018
3352(13*10^171306-37)/3171307Robert Price01/2019
33538*10^171296+87171297Robert Price10/2019
3354(55^98419-1)/54171284Paul Bourdelais12/2017
3355(29*10^171275+67)/3171276Robert Price12/2019
3356(457*10^171248-7)/9171250Robert Price09/2022
3357(194*10^171193+1)/3171195Robert Price01/2022
33582^568642+1876129171179Enzo Doria07/2016
33594*10^171146-47171147Robert Price10/2021
3360(19*10^170970+131)/3170971Robert Price06/2020
3361(46*10^170932+143)/9170933Robert Price01/2019
3362(79*10^170901-1)/3170903Robert Price02/2020
3363(58*10^170842+221)/9170843Robert Price02/2017
3364(29*10^170830+583)/9170831Robert Price06/2021
33653*10^170800+73170801Robert Price08/2018
3366(29*10^170799-119)/9170800Robert Price12/2021
336711^164009-270170798Enzo Doria10/2012
33682*10^170767+41170768Robert Price05/2018
33693^357706-112358170670Enzo Doria07/2014
3370TheodorusPrime(170657)170657Eric W. Weisstein08/2013
33712^566871+1876163170646Enzo Doria07/2016
3372(10657#+(404267#)/(10657#))/(1675379)170624Makoto Morimoto10/2017
33732^566496+7170533Donovan Johnson07/2006
3374(7^201653+1)/8170416Paul Bourdelais02/2010
337532150^37807-37807^32150170403Frank Doornink02/2024
33767*10^170348+33170349Robert Price06/2020
33772^565799+216011170323Enzo Doria12/2023
33782^565183-352021170138Enzo Doria07/2015
33792^565143-114457170125Enzo Doria02/2015
33803*2^565024-5170090Jon Grantham07/2023
33812^564976-49869170075Enzo Doria10/2015
33822^564561+225169950Henri Lifchitz11/2024
3383(7*10^169944+23)/3169945Robert Price06/2020
3384(37*10^169943+251)/9169944Robert Price09/2021
33852^564526-351401169940Enzo Doria07/2015
33863^355902+4169809Aurel Gibier10/2024
33874*10^169759+19169760Robert Price10/2018
3388(2^563903-13)/5169752Stefano Morozzi08/2022
338921^128327-20^128327169677Jean-Louis Charton11/2014
33902^563583+89169656Stefano Morozzi04/2021
33912^563311+215813169574Enzo Doria11/2023
3392(4*10^169559+83)/3169560Robert Price02/2018
3393(194*10^169461-17)/3169463Robert Price09/2020
33942^562749+2793047169405Enzo Doria02/2016
3395(154*10^169337-1)/9169339Serge Batalov12/2014
3396(109*10^169337+11)/3169339Robert Price06/2022
3397(56*10^169311+691)/9169312Robert Price05/2019
33982^562369-29503169290Enzo Doria08/2015
3399(17*10^169283+19)/9169284Robert Price03/2021
3400390151#-2322911169082Hayden Chesnut07/2024
340110^169074-5000000001169074Robert Price09/2022
34028*10^169071+59169072Robert Price11/2021
3403(10^169044+173)/3169044Robert Price05/2021
3404(22*10^169019+383)/9169020Robert Price05/2018
3405(64*10^168935+143)/9168936Robert Price05/2021
3406(22*10^168906+47)/3168907Robert Price06/2021
34075*10^168807+87168808Robert Price02/2019
3408(77*10^168803-149)/9168804Robert Price03/2022
34094*10^168788-47168789Robert Price10/2021
3410(154*10^168781+17)/9168783Robert Price06/2022
3411(418*10^168751-31)/9168753Robert Price05/2022
3412(29*10^168711+691)/9168712Robert Price08/2021
34132^560405-39943168699Enzo Doria09/2015
3414(397*10^168634+17)/9168636Robert Price03/2022
34152^560189+36587168634Enzo Doria09/2024
341689*10^168614-7168616Robert Price04/2020
3417(23*10^168608-83)/3168609Robert Price08/2019
3418(94*10^168541+11)/3168543Robert Price04/2020
34192^559686-350471168483Enzo Doria06/2015
34202^559672-1855889168479Enzo Doria09/2015
3421(5*10^168379-473)/9168379Robert Price01/2018
34222024^50920+3168353Martin Hopf01/2024
34232^559000-59939168276Enzo Doria11/2015
34242^558830+25009168225Enzo Doria11/2023
3425(16*10^168181+41)/3168182Robert Price03/2019
3426(19*10^168173+77)/3168174Robert Price05/2019
3427(74*10^168170+529)/9168171Robert Price02/2022
34282^558640-114149168168Enzo Doria12/2014
34292^558498-1849277168125Enzo Doria08/2015
34302^558476-1850249168119Enzo Doria08/2015
3431(7*10^168067+71)/3168068Robert Price05/2018
34322^558150-1852211168020Enzo Doria08/2015
34332^558125-113661168013Enzo Doria09/2014
3434393^64747-392^64747167980Jean-Louis Charton08/2012
3435(8*10^167965-11)/3167966Robert Price07/2023
34362^557916+216151167950Enzo Doria12/2023
3437(13*10^167911+179)/3167912Robert Price11/2018
3438(26*10^167861-167)/3167862Robert Price10/2019
343936^107827-107827167812Kellen Shenton06/2023
344032027^37242-37242^32027167795Frank Doornink01/2024
344139^105456+2167788Robert Price04/2015
34422^557322+217519167771Enzo Doria01/2024
3443(28^115877-1)/27167691Paul Bourdelais12/2017
34446*10^167662-13167663Robert Price07/2022
344510^167639+121911167640Patrick De Geest07/2018
344610^167639-8001167639Robert Price03/2018
34472^556504-462059167525Enzo Doria07/2015
3448(88*10^167522-637)/9167523Robert Price11/2020
34495*10^167510+9167511Robert Price08/2015
34507*10^167437-93167438Robert Price08/2020
3451(43^102451-1)/7138097213378082167335Paul Vanderveen05/2025
345225455^37978-37978^25455167323Frank Doornink01/2024
345311^160663+6167314Paul Bourdelais02/2021
3454(7*10^167308-493)/9167308Robert Price04/2021
34552^555759+74333167301Enzo Doria07/2023
345626084^37871-37871^26084167253Frank Doornink03/2024
34572^555343+1874333167175Enzo Doria06/2016
34582^555210-461261167135Enzo Doria07/2015
34599*10^166996+59166997Robert Price01/2020
3460(68*10^166976-329)/9166977Robert Price03/2021
3461(64*10^166901+683)/9166902Robert Price06/2022
34622^554372+1880527166883Enzo Doria11/2016
34632^554299+72173166861Enzo Doria04/2016
3464(185*10^166837+7)/3166839Robert Price03/2020
3465(14*10^166813+139)/9166814Robert Price11/2021
346626084^37767-37767^26084166794Frank Doornink03/2024
34672^554037-2797063166782Enzo Doria03/2016
346831861^37028-37028^31861166747Frank Doornink01/2024
3469(49*10^166721-139)/9166722Robert Price03/2019
34702*10^166646+69166647Robert Price06/2020
34712^553484-29819166616Enzo Doria08/2015
3472(188*10^166611+7)/3166613Robert Price03/2020
34732^553383-2784217166585Enzo Doria10/2015
34742^553069+76427166491Enzo Doria05/2016
347525218^37819-37819^25218166469Frank Doornink12/2023
34762*10^166458+51166459Robert Price05/2018
3477589^60089-588^60089166454Jean-Louis Charton09/2012
347825214^37799-37799^25214166378Frank Doornink11/2023
347911^159756-2424166369Mike Oakes06/2010
34802^552649-361275166364Enzo Doria05/2014
34812^552628-113669166358Enzo Doria09/2014
3482(19*10^166325+137)/3166326Robert Price03/2022
348310^166324+550603166325Patrick De Geest07/2018
348410^166324-801166324Robert Price02/2018
3485(85*10^166297-1)/3166299Robert Price02/2020
3486(19*10^166280-7)/3166281Robert Price12/2023
348725533^37726-37726^25533166263Frank Doornink02/2024
34888*10^166227+87166228Robert Price10/2019
34892^552137+1879397166210Enzo Doria09/2016
3490262273205671539190984629()252475512364409752762433166141Anonymous01/2025
3491490079063773165613318095()218182139934160868002603166141Anonymous01/2025
3492140717254840416411192803()712689271538459396766869166140Anonymous01/2025
3493122398296040696255481419()271117913237372866926417166140Anonymous01/2025
3494(103*10^166126+11)/3166128Robert Price01/2021
3495(22*10^166077+179)/3166078Robert Price02/2022
3496(23^121949-1)/22166061Paul Bourdelais10/2017
34972^551576+236221166041Enzo Doria05/2025
34982^551542+19249166031Payam Samidoost08/2002
34992^551535-23821166029Enzo Doria08/2013
35002^551507-23557166021Enzo Doria08/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 15 2025 20:38 (Time in France)

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