PRP Records

Probable Primes Top 10000

(301352 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 ?
30018*10^176383-81176384Robert Price02/2021
3002(23*10^176357+61)/3176358Robert Price01/2022
30032^585832-112799176354Enzo Doria07/2014
3004fibonacci(843383)+4176257Jon Grantham08/2023
3005(29*10^176240+49)/3176241Robert Price09/2021
3006(2^585387-11)/3176219Stefano Morozzi08/2022
30072^585336-461039176204Enzo Doria06/2015
3008(25*10^176164+143)/3176165Robert Price08/2020
30092^585095-1848127176132Enzo Doria08/2015
3010(5*10^176101-311)/9176101Robert Price12/2021
30116*10^176092+77176093Robert Price06/2020
30122^584950-115451176088Enzo Doria07/2015
3013(646*10^176044+11)/9176046Robert Price10/2021
3014(7^208283-5^208283)/2176020Jon Grantham08/2023
30152^584671-3697176004Yves Minet03/2017
3016(13*10^175965-37)/3175966Robert Price01/2019
301731728^39089-39089^31728175957Frank Doornink01/2024
30182*10^175860-87175861Robert Price04/2018
301927009^39670-39670^27009175798Frank Doornink01/2024
3020(86*10^175774-221)/9175775Robert Price09/2019
30212^583614+216037175686Enzo Doria11/2023
30229*10^175654+47175655Robert Price01/2022
302325430^39869-39869^25430175637Frank Doornink01/2024
302410^175608+2971175609Mike Oakes05/2010
302510^175608-55829175608Patrick De Geest09/2013
30262^583051+1879793175516Enzo Doria09/2016
3027(76*10^175514+491)/9175515Robert Price10/2021
30292^582860-23829175459Enzo Doria08/2013
3028(200^76253-1)/199175459Anonymous06/2024
3030(8*10^175428-53)/9175428Serge Batalov11/2022
3031(28*10^175417-67)/3175418Robert Price10/2020
30322^582670-23913175402Enzo Doria08/2013
30332^582573-29563175372Enzo Doria08/2015
30342^582435-1862767175331Enzo Doria12/2015
303510^175295-40000001175295Robert Price07/2022
303631093^39018-39018^31093175295Frank Doornink01/2024
3037(11*10^175250-149)/3175251Robert Price09/2018
3038(29*10^175236+31)/3175237Robert Price04/2021
30392^582072-1848599175222Enzo Doria08/2015
3040(404267#+465)/(3^4*5^2*31)175208Makoto Morimoto06/2019
3041Phi(262767,10)/259613797175168Makoto Kamada12/2022
3042(2^581871-15)/7175160Stefano Morozzi08/2022
3043(5*10^175117-311)/9175117Robert Price12/2021
304431193^38966-38966^31193175116Frank Doornink01/2024
30452^581695+225893175108Enzo Doria08/2024
304610^175093-89175093Riley Fisher10/2023
3047(220221^32768+1)/2175075Serge Batalov03/2018
30482^581560+1874911175068Enzo Doria06/2016
3049(25*10^174987-97)/9174988Robert Price01/2022
3050(75^93307-1)/74174955Paul Bourdelais09/2017
305126446^39555-39555^26446174927Frank Doornink03/2024
305231522^38883-38883^31522174920Frank Doornink01/2024
3053(27398^39601-1)/(27398^199-1)174855Ryan Propper11/2023
3054(861^59557-1)/860174798Jinyuan Wang11/2023
305531492^38859-38859^31492174796Frank Doornink01/2024
3056(47*10^174790+493)/9174791Robert Price03/2019
30572^580528-114035174757Enzo Doria11/2014
3058(19*10^174754+737)/9174755Robert Price07/2018
3059V(1045270)/4181081/12543241/81333115129561174730Serge Batalov07/2024
3060(35*10^174704-377)/9174705Robert Price07/2018
3062(49*10^174681+293)/9174682Robert Price03/2021
30616*10^174681+11174682Robert Price07/2022
30633*10^174665-97174666Robert Price07/2018
30642^580046-459161174612Enzo Doria05/2015
30652^579992-39779174595Enzo Doria09/2015
306625613^39582-39582^25613174496Frank Doornink02/2024
3067(29*10^174481-149)/3174482Robert Price08/2022
3068(4*10^174423+101)/3174424Robert Price11/2021
3069(2^579371-17)/3174408Stefano Morozzi08/2022
3070(2*10^174301-71)/3174301Robert Price12/2017
307114^152048+3174267Paul Bourdelais12/2020
3072(2^578696+1)/257174203Lelio R Paula09/2015
30732^578656-1851809174193Enzo Doria08/2015
30742^578583-113917174171Enzo Doria10/2014
30752^578434-83174126Yves Minet07/2017
307615^148048-2174118Robert Price06/2015
30775*10^174101+81174102Robert Price03/2019
30782^578346+2794249174100Enzo Doria03/2016
307910^173947+1372429173948Patrick De Geest08/2021
308110^173947-500000001173947Robert Price12/2020
308010^173947-286391173947Patrick De Geest08/2021
30825*10^173904-13173905Robert Price01/2019
3083(8*10^173862-59)/3173863Robert Price08/2021
3084(71*10^173854-287)/9173855Robert Price09/2019
3085(43*10^173826+101)/9173827Robert Price11/2018
30862*10^173809-87173810Robert Price04/2018
3087(2^577372-23)/7173806Stefano Morozzi08/2022
3088(L!41532)/2173772Serge Batalov07/2017
30892^577146-49877173739Enzo Doria10/2015
30902^576889+49727173661Enzo Doria09/2016
3091(167*10^173571-17)/3173573Robert Price03/2020
309237803^37916+37916^37803173562Norbert Schneider06/2022
30935*10^173534+29173535Robert Price12/2020
3094(2^576551-1)/4612409/64758208321/242584327930759173528Dario Alpern06/2014
30954*10^173509+99173510Robert Price12/2020
3096(13*10^173467-37)/3173468Robert Price01/2019
30972^576016-113919173399Enzo Doria11/2014
30982^575911-1849387173367Enzo Doria08/2015
309921554^40005-40005^21554173363Norbert Schneider04/2025
31002^575879+215843173357Enzo Doria11/2023
31012^575871+28733173355Enzo Doria01/2024
3102515^63898+63898^515173280Norbert Schneider12/2022
31032^575614+9173278Stefano Morozzi04/2021
31042^575606-219533173275Enzo Doria03/2024
3105(16*10^173251+107)/3173252Robert Price03/2019
310626618^39149-39149^26618173242Frank Doornink03/2024
31072^575196-114053173152Enzo Doria11/2014
31087*10^173135-53173136Robert Price06/2020
3109(301*10^173047+23)/9173049Robert Price06/2021
31102^574591-115387172970Enzo Doria07/2015
311125210^39297-39297^25210172969Frank Doornink12/2023
3112(202*10^172940-13)/9172942Robert Price01/2020
311345^104608+104608^45172940Norbert Schneider06/2021
31142^574328+81121172890Enzo Doria07/2016
3115(115*10^172862-1)/3172864Serge Batalov12/2014
31163*10^172812+13172813Robert Price07/2018
31174*5^247217-9172798Lelio R Paula10/2015
31186*10^172772-31172773Robert Price07/2020
311969061#+(467617#)/(69061#)172766Makoto Morimoto10/2017
3120(34*10^172693-547)/9172694Robert Price03/2021
31215*10^172692+57172693Robert Price12/2018
31222^573668-2782319172692Enzo Doria09/2015
31232^573444-1855109172624Enzo Doria09/2015
312425500^39173-39173^25500172618Frank Doornink02/2024
312527180^38917-38917^27180172568Frank Doornink01/2024
3126(14*10^172532-29)/3172533Robert Price09/2021
31273^361608+2172531Robert Price08/2014
3128(54^99563+1)/55172481Paul Bourdelais11/2017
31292^572592-114893172368Enzo Doria05/2015
31304*10^172354-39172355Robert Price09/2020
313137535^37674+37674^37535172338Norbert Schneider05/2022
3132(11*10^172322-119)/9172323Robert Price11/2021
31335^246497-4^246497172295Jean-Louis Charton11/2008
3134(38^109037-1)/37172254Paul Bourdelais10/2017
3135(4*10^172241+89)/3172242Robert Price08/2021
31363*10^172219+73172220Robert Price08/2018
31372^571810+28549172132Enzo Doria01/2024
3138A352736(15)172032Kellen Shenton05/2022
313932298^38149-38149^32298172021Frank Doornink02/2024
31402^571300+25861171979Enzo Doria11/2023
3141(36^110503+1)/37171975Lelio R Paula04/2017
31428*10^171934+71171935Robert Price05/2022
3143(11*10^171933+601)/9171934Robert Price02/2022
3144(22*10^171929-73)/3171930Robert Price04/2019
3145(49*10^171892-319)/9171893Robert Price10/2021
31464*10^171891-63171892Robert Price10/2018
314767*10^171882-9171884Robert Price03/2021
31482^570980-2782289171883Enzo Doria09/2015
3149(25*10^171849-37)/3171850Robert Price10/2019
315010^171832+387909171833Patrick De Geest08/2021
315110^171832-10001171832Robert Price02/2021
3153(2^(12*47563+13)-9)/7171818Kevin Acres11/2013
3152(2^570769-9)/7171818Stefano Morozzi08/2022
31542^570545+11025171752Henri Lifchitz01/2025
315524^124375-124375^24171664Henri Lifchitz08/2024
3156(74*10^171651-29)/9171652Robert Price06/2022
3157(536*10^171601-23)/9171603Robert Price02/2020
31587*10^171535-99171536Robert Price06/2019
3159(28*10^171534+101)/3171535Robert Price09/2020
31602^569563-1854607171456Enzo Doria09/2015
316132133^38042-38042^32133171454Frank Doornink02/2024
31623*10^171391+59171392Robert Price08/2018
3163(13*10^171306-37)/3171307Robert Price01/2019
31648*10^171296+87171297Robert Price10/2019
3165(55^98419-1)/54171284Paul Bourdelais12/2017
3166(29*10^171275+67)/3171276Robert Price12/2019
3167(457*10^171248-7)/9171250Robert Price09/2022
3168(194*10^171193+1)/3171195Robert Price01/2022
31692^568642+1876129171179Enzo Doria07/2016
31704*10^171146-47171147Robert Price10/2021
3171(19*10^170970+131)/3170971Robert Price06/2020
3172(46*10^170932+143)/9170933Robert Price01/2019
3173(79*10^170901-1)/3170903Robert Price02/2020
3174(58*10^170842+221)/9170843Robert Price02/2017
3175(29*10^170830+583)/9170831Robert Price06/2021
31763*10^170800+73170801Robert Price08/2018
3177(29*10^170799-119)/9170800Robert Price12/2021
317811^164009-270170798Enzo Doria10/2012
31792*10^170767+41170768Robert Price05/2018
31803^357706-112358170670Enzo Doria07/2014
3181TheodorusPrime(170657)170657Eric W. Weisstein08/2013
31822^566871+1876163170646Enzo Doria07/2016
3183(10657#+(404267#)/(10657#))/(1675379)170624Makoto Morimoto10/2017
31842^566496+7170533Donovan Johnson07/2006
3185(7^201653+1)/8170416Paul Bourdelais02/2010
318632150^37807-37807^32150170403Frank Doornink02/2024
31877*10^170348+33170349Robert Price06/2020
31882^565799+216011170323Enzo Doria12/2023
31892^565183-352021170138Enzo Doria07/2015
31902^565143-114457170125Enzo Doria02/2015
31913*2^565024-5170090Jon Grantham07/2023
31922^564976-49869170075Enzo Doria10/2015
31932^564561+225169950Henri Lifchitz11/2024
3194(7*10^169944+23)/3169945Robert Price06/2020
3195(37*10^169943+251)/9169944Robert Price09/2021
31962^564526-351401169940Enzo Doria07/2015
31973^355902+4169809Aurel Gibier10/2024
31984*10^169759+19169760Robert Price10/2018
3199(2^563903-13)/5169752Stefano Morozzi08/2022
320021^128327-20^128327169677Jean-Louis Charton11/2014
32012^563583+89169656Stefano Morozzi04/2021
32022^563311+215813169574Enzo Doria11/2023
3203(4*10^169559+83)/3169560Robert Price02/2018
3204(194*10^169461-17)/3169463Robert Price09/2020
32052^562749+2793047169405Enzo Doria02/2016
3206(154*10^169337-1)/9169339Serge Batalov12/2014
3207(109*10^169337+11)/3169339Robert Price06/2022
3208(56*10^169311+691)/9169312Robert Price05/2019
32092^562369-29503169290Enzo Doria08/2015
3210(17*10^169283+19)/9169284Robert Price03/2021
3211390151#-2322911169082Hayden Chesnut07/2024
321210^169074-5000000001169074Robert Price09/2022
32138*10^169071+59169072Robert Price11/2021
3214(10^169044+173)/3169044Robert Price05/2021
3215(22*10^169019+383)/9169020Robert Price05/2018
3216(64*10^168935+143)/9168936Robert Price05/2021
3217(22*10^168906+47)/3168907Robert Price06/2021
32185*10^168807+87168808Robert Price02/2019
3219(77*10^168803-149)/9168804Robert Price03/2022
32204*10^168788-47168789Robert Price10/2021
3221(154*10^168781+17)/9168783Robert Price06/2022
3222(418*10^168751-31)/9168753Robert Price05/2022
3223(29*10^168711+691)/9168712Robert Price08/2021
32242^560405-39943168699Enzo Doria09/2015
3225(397*10^168634+17)/9168636Robert Price03/2022
32262^560189+36587168634Enzo Doria09/2024
322789*10^168614-7168616Robert Price04/2020
3228(23*10^168608-83)/3168609Robert Price08/2019
3229(94*10^168541+11)/3168543Robert Price04/2020
32302^559686-350471168483Enzo Doria06/2015
32312^559672-1855889168479Enzo Doria09/2015
3232(5*10^168379-473)/9168379Robert Price01/2018
32332024^50920+3168353Martin Hopf01/2024
32342^559000-59939168276Enzo Doria11/2015
32352^558830+25009168225Enzo Doria11/2023
3236(16*10^168181+41)/3168182Robert Price03/2019
3237(19*10^168173+77)/3168174Robert Price05/2019
3238(74*10^168170+529)/9168171Robert Price02/2022
32392^558640-114149168168Enzo Doria12/2014
32402^558498-1849277168125Enzo Doria08/2015
32412^558476-1850249168119Enzo Doria08/2015
3242(7*10^168067+71)/3168068Robert Price05/2018
32432^558150-1852211168020Enzo Doria08/2015
32442^558125-113661168013Enzo Doria09/2014
3245393^64747-392^64747167980Jean-Louis Charton08/2012
3246(8*10^167965-11)/3167966Robert Price07/2023
32472^557916+216151167950Enzo Doria12/2023
3248(13*10^167911+179)/3167912Robert Price11/2018
3249(26*10^167861-167)/3167862Robert Price10/2019
325036^107827-107827167812Kellen Shenton06/2023


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 24 2025 12:56 (Time in France)

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