PRP Records

Probable Primes Top 10000

(301429 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 ?
30012^588912-113519177281Enzo Doria08/2014
3002(682*10^177266-7)/9177268Robert Price08/2021
300315^150706+2177245Robert Price06/2015
30042^588403+335931177127Enzo Doria09/2024
3005(31208^39601-1)/(31208^199-1)177084Ryan Propper11/2023
30062^588194-1861001177065Enzo Doria11/2015
30075*10^177016-37177017Robert Price11/2021
3008fibonacci(846926)-4176997Jon Grantham08/2023
3009(23*10^176964-47)/3176965Robert Price09/2019
301020530^41031+41031^20530176942Norbert Schneider07/2022
3011(19*10^176932+521)/9176933Robert Price05/2018
3012(8*10^176908+43)/3176909Robert Price06/2018
3013(85*10^176900+203)/9176901Robert Price09/2020
30142^587560-113699176874Enzo Doria09/2014
301520596^40995+40995^20596176844Norbert Schneider07/2022
3016(101*10^176815-17)/3176817Robert Price02/2020
3017(25*10^176715-37)/3176716Robert Price10/2019
30185^252763-12862176674Enzo Doria05/2014
301938442^38531+38531^38442176658Norbert Schneider09/2022
30202^586829+23961176654Enzo Doria10/2023
30212^586804+81721176646Enzo Doria08/2016
3022(10^176584+77)/3176584Robert Price01/2018
30232^586570+1874419176576Enzo Doria06/2016
3024(157*10^176482-1)/3176484Robert Price01/2022
30255*2^586202+3176466Jon Grantham07/2023
302627122^39799-39799^27122176442Frank Doornink01/2024
30272^585994-3311176402Yves Minet12/2014
30288*10^176383-81176384Robert Price02/2021
3029(23*10^176357+61)/3176358Robert Price01/2022
30302^585832-112799176354Enzo Doria07/2014
3031fibonacci(843383)+4176257Jon Grantham08/2023
3032(29*10^176240+49)/3176241Robert Price09/2021
3033(2^585387-11)/3176219Stefano Morozzi08/2022
30342^585336-461039176204Enzo Doria06/2015
3035(25*10^176164+143)/3176165Robert Price08/2020
30362^585095-1848127176132Enzo Doria08/2015
3037(5*10^176101-311)/9176101Robert Price12/2021
30386*10^176092+77176093Robert Price06/2020
30392^584950-115451176088Enzo Doria07/2015
3040(646*10^176044+11)/9176046Robert Price10/2021
3041(7^208283-5^208283)/2176020Jon Grantham08/2023
30422^584671-3697176004Yves Minet03/2017
3043(13*10^175965-37)/3175966Robert Price01/2019
304431728^39089-39089^31728175957Frank Doornink01/2024
30452*10^175860-87175861Robert Price04/2018
304627009^39670-39670^27009175798Frank Doornink01/2024
3047(86*10^175774-221)/9175775Robert Price09/2019
30482^583614+216037175686Enzo Doria11/2023
30499*10^175654+47175655Robert Price01/2022
305025430^39869-39869^25430175637Frank Doornink01/2024
305110^175608+2971175609Mike Oakes05/2010
305210^175608-55829175608Patrick De Geest09/2013
30532^583051+1879793175516Enzo Doria09/2016
3054(76*10^175514+491)/9175515Robert Price10/2021
30562^582860-23829175459Enzo Doria08/2013
3055(200^76253-1)/199175459Anonymous06/2024
3057(8*10^175428-53)/9175428Serge Batalov11/2022
3058(28*10^175417-67)/3175418Robert Price10/2020
30592^582670-23913175402Enzo Doria08/2013
30602^582573-29563175372Enzo Doria08/2015
30612^582435-1862767175331Enzo Doria12/2015
306210^175295-40000001175295Robert Price07/2022
306331093^39018-39018^31093175295Frank Doornink01/2024
3064(11*10^175250-149)/3175251Robert Price09/2018
3065(29*10^175236+31)/3175237Robert Price04/2021
30662^582072-1848599175222Enzo Doria08/2015
3067(404267#+465)/(3^4*5^2*31)175208Makoto Morimoto06/2019
3068Phi(262767,10)/259613797175168Makoto Kamada12/2022
3069(2^581871-15)/7175160Stefano Morozzi08/2022
3070(5*10^175117-311)/9175117Robert Price12/2021
307131193^38966-38966^31193175116Frank Doornink01/2024
30722^581695+225893175108Enzo Doria08/2024
307310^175093-89175093Riley Fisher10/2023
3074(220221^32768+1)/2175075Serge Batalov03/2018
30752^581560+1874911175068Enzo Doria06/2016
3076(25*10^174987-97)/9174988Robert Price01/2022
3077(75^93307-1)/74174955Paul Bourdelais09/2017
307826446^39555-39555^26446174927Frank Doornink03/2024
307931522^38883-38883^31522174920Frank Doornink01/2024
3080(27398^39601-1)/(27398^199-1)174855Ryan Propper11/2023
3081(861^59557-1)/860174798Jinyuan Wang11/2023
308231492^38859-38859^31492174796Frank Doornink01/2024
3083(47*10^174790+493)/9174791Robert Price03/2019
30842^580528-114035174757Enzo Doria11/2014
3085(19*10^174754+737)/9174755Robert Price07/2018
3086V(1045270)/4181081/12543241/81333115129561174730Serge Batalov07/2024
3087(35*10^174704-377)/9174705Robert Price07/2018
3089(49*10^174681+293)/9174682Robert Price03/2021
30886*10^174681+11174682Robert Price07/2022
30903*10^174665-97174666Robert Price07/2018
30912^580046-459161174612Enzo Doria05/2015
30922^579992-39779174595Enzo Doria09/2015
309325613^39582-39582^25613174496Frank Doornink02/2024
3094(29*10^174481-149)/3174482Robert Price08/2022
3095(4*10^174423+101)/3174424Robert Price11/2021
3096(2^579371-17)/3174408Stefano Morozzi08/2022
3097(2*10^174301-71)/3174301Robert Price12/2017
309814^152048+3174267Paul Bourdelais12/2020
3099(2^578696+1)/257174203Lelio R Paula09/2015
31002^578656-1851809174193Enzo Doria08/2015
31012^578583-113917174171Enzo Doria10/2014
31022^578434-83174126Yves Minet07/2017
310315^148048-2174118Robert Price06/2015
31045*10^174101+81174102Robert Price03/2019
31052^578346+2794249174100Enzo Doria03/2016
310610^173947+1372429173948Patrick De Geest08/2021
310810^173947-500000001173947Robert Price12/2020
310710^173947-286391173947Patrick De Geest08/2021
31095*10^173904-13173905Robert Price01/2019
3110(8*10^173862-59)/3173863Robert Price08/2021
3111(71*10^173854-287)/9173855Robert Price09/2019
3112(43*10^173826+101)/9173827Robert Price11/2018
31142*10^173809-87173810Robert Price04/2018
3113(17^141263-1)/27122512173810Paul Vanderveen05/2025
3115(2^577372-23)/7173806Stefano Morozzi08/2022
3116(L!41532)/2173772Serge Batalov07/2017
31172^577146-49877173739Enzo Doria10/2015
31182^576889+49727173661Enzo Doria09/2016
3119(19^173604)%(10^173604)173604Henri Lifchitz05/2025
3120(167*10^173571-17)/3173573Robert Price03/2020
312137803^37916+37916^37803173562Norbert Schneider06/2022
31225*10^173534+29173535Robert Price12/2020
3123(2^576551-1)/4612409/64758208321/242584327930759173528Dario Alpern06/2014
31244*10^173509+99173510Robert Price12/2020
3125(13*10^173467-37)/3173468Robert Price01/2019
31262^576016-113919173399Enzo Doria11/2014
31272^575911-1849387173367Enzo Doria08/2015
312821554^40005-40005^21554173363Norbert Schneider04/2025
31292^575879+215843173357Enzo Doria11/2023
31302^575871+28733173355Enzo Doria01/2024
3131515^63898+63898^515173280Norbert Schneider12/2022
31322^575614+9173278Stefano Morozzi04/2021
31332^575606-219533173275Enzo Doria03/2024
3134(16*10^173251+107)/3173252Robert Price03/2019
313526618^39149-39149^26618173242Frank Doornink03/2024
31362^575196-114053173152Enzo Doria11/2014
31377*10^173135-53173136Robert Price06/2020
3138(301*10^173047+23)/9173049Robert Price06/2021
31392^574591-115387172970Enzo Doria07/2015
314025210^39297-39297^25210172969Frank Doornink12/2023
3141(202*10^172940-13)/9172942Robert Price01/2020
314245^104608+104608^45172940Norbert Schneider06/2021
31432^574328+81121172890Enzo Doria07/2016
3144(115*10^172862-1)/3172864Serge Batalov12/2014
31453*10^172812+13172813Robert Price07/2018
31464*5^247217-9172798Lelio R Paula10/2015
31476*10^172772-31172773Robert Price07/2020
314869061#+(467617#)/(69061#)172766Makoto Morimoto10/2017
3149(34*10^172693-547)/9172694Robert Price03/2021
31505*10^172692+57172693Robert Price12/2018
31512^573668-2782319172692Enzo Doria09/2015
31522^573444-1855109172624Enzo Doria09/2015
315325500^39173-39173^25500172618Frank Doornink02/2024
315427180^38917-38917^27180172568Frank Doornink01/2024
3155(14*10^172532-29)/3172533Robert Price09/2021
31563^361608+2172531Robert Price08/2014
3157(54^99563+1)/55172481Paul Bourdelais11/2017
31582^572592-114893172368Enzo Doria05/2015
31594*10^172354-39172355Robert Price09/2020
316037535^37674+37674^37535172338Norbert Schneider05/2022
3161(11*10^172322-119)/9172323Robert Price11/2021
31625^246497-4^246497172295Jean-Louis Charton11/2008
3163(38^109037-1)/37172254Paul Bourdelais10/2017
3164(4*10^172241+89)/3172242Robert Price08/2021
31653*10^172219+73172220Robert Price08/2018
31662^571810+28549172132Enzo Doria01/2024
3167A352736(15)172032Kellen Shenton05/2022
316832298^38149-38149^32298172021Frank Doornink02/2024
31692^571300+25861171979Enzo Doria11/2023
3170(36^110503+1)/37171975Lelio R Paula04/2017
31718*10^171934+71171935Robert Price05/2022
3172(11*10^171933+601)/9171934Robert Price02/2022
3173(22*10^171929-73)/3171930Robert Price04/2019
3174(49*10^171892-319)/9171893Robert Price10/2021
31754*10^171891-63171892Robert Price10/2018
317667*10^171882-9171884Robert Price03/2021
31772^570980-2782289171883Enzo Doria09/2015
3178(25*10^171849-37)/3171850Robert Price10/2019
317910^171832+387909171833Patrick De Geest08/2021
318010^171832-10001171832Robert Price02/2021
3182(2^(12*47563+13)-9)/7171818Kevin Acres11/2013
3181(2^570769-9)/7171818Stefano Morozzi08/2022
31832^570545+11025171752Henri Lifchitz01/2025
318424^124375-124375^24171664Henri Lifchitz08/2024
3185(74*10^171651-29)/9171652Robert Price06/2022
3186(536*10^171601-23)/9171603Robert Price02/2020
31877*10^171535-99171536Robert Price06/2019
3188(28*10^171534+101)/3171535Robert Price09/2020
31892^569563-1854607171456Enzo Doria09/2015
319032133^38042-38042^32133171454Frank Doornink02/2024
31913*10^171391+59171392Robert Price08/2018
3192(13*10^171306-37)/3171307Robert Price01/2019
31938*10^171296+87171297Robert Price10/2019
3194(55^98419-1)/54171284Paul Bourdelais12/2017
3195(29*10^171275+67)/3171276Robert Price12/2019
3196(457*10^171248-7)/9171250Robert Price09/2022
3197(194*10^171193+1)/3171195Robert Price01/2022
31982^568642+1876129171179Enzo Doria07/2016
31994*10^171146-47171147Robert Price10/2021
3200(19*10^170970+131)/3170971Robert Price06/2020
3201(46*10^170932+143)/9170933Robert Price01/2019
3202(79*10^170901-1)/3170903Robert Price02/2020
3203(58*10^170842+221)/9170843Robert Price02/2017
3204(29*10^170830+583)/9170831Robert Price06/2021
32053*10^170800+73170801Robert Price08/2018
3206(29*10^170799-119)/9170800Robert Price12/2021
320711^164009-270170798Enzo Doria10/2012
32082*10^170767+41170768Robert Price05/2018
32093^357706-112358170670Enzo Doria07/2014
3210TheodorusPrime(170657)170657Eric W. Weisstein08/2013
32112^566871+1876163170646Enzo Doria07/2016
3212(10657#+(404267#)/(10657#))/(1675379)170624Makoto Morimoto10/2017
32132^566496+7170533Donovan Johnson07/2006
3214(7^201653+1)/8170416Paul Bourdelais02/2010
321532150^37807-37807^32150170403Frank Doornink02/2024
32167*10^170348+33170349Robert Price06/2020
32172^565799+216011170323Enzo Doria12/2023
32182^565183-352021170138Enzo Doria07/2015
32192^565143-114457170125Enzo Doria02/2015
32203*2^565024-5170090Jon Grantham07/2023
32212^564976-49869170075Enzo Doria10/2015
32222^564561+225169950Henri Lifchitz11/2024
3223(7*10^169944+23)/3169945Robert Price06/2020
3224(37*10^169943+251)/9169944Robert Price09/2021
32252^564526-351401169940Enzo Doria07/2015
32263^355902+4169809Aurel Gibier10/2024
32274*10^169759+19169760Robert Price10/2018
3228(2^563903-13)/5169752Stefano Morozzi08/2022
322921^128327-20^128327169677Jean-Louis Charton11/2014
32302^563583+89169656Stefano Morozzi04/2021
32312^563311+215813169574Enzo Doria11/2023
3232(4*10^169559+83)/3169560Robert Price02/2018
3233(194*10^169461-17)/3169463Robert Price09/2020
32342^562749+2793047169405Enzo Doria02/2016
3235(154*10^169337-1)/9169339Serge Batalov12/2014
3236(109*10^169337+11)/3169339Robert Price06/2022
3237(56*10^169311+691)/9169312Robert Price05/2019
32382^562369-29503169290Enzo Doria08/2015
3239(17*10^169283+19)/9169284Robert Price03/2021
3240390151#-2322911169082Hayden Chesnut07/2024
324110^169074-5000000001169074Robert Price09/2022
32428*10^169071+59169072Robert Price11/2021
3243(10^169044+173)/3169044Robert Price05/2021
3244(22*10^169019+383)/9169020Robert Price05/2018
3245(64*10^168935+143)/9168936Robert Price05/2021
3246(22*10^168906+47)/3168907Robert Price06/2021
32475*10^168807+87168808Robert Price02/2019
3248(77*10^168803-149)/9168804Robert Price03/2022
32494*10^168788-47168789Robert Price10/2021
3250(154*10^168781+17)/9168783Robert Price06/2022


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 21 2025 13:33 (Time in France)

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