PRP Records

Probable Primes Top 10000

(295158 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 ?
2501(101*10^176815-17)/3176817Robert Price02/2020
2502(25*10^176715-37)/3176716Robert Price10/2019
25035^252763-12862176674Enzo Doria05/2014
250438442^38531+38531^38442176658Norbert Schneider09/2022
25052^586829+23961176654Enzo Doria10/2023
25062^586804+81721176646Enzo Doria08/2016
2507(10^176584+77)/3176584Robert Price01/2018
25082^586570+1874419176576Enzo Doria06/2016
2509(157*10^176482-1)/3176484Robert Price01/2022
25105*2^586202+3176466Jon Grantham07/2023
251127122^39799-39799^27122176442Frank Doornink01/2024
25122^585994-3311176402Yves Minet12/2014
25138*10^176383-81176384Robert Price02/2021
2514(23*10^176357+61)/3176358Robert Price01/2022
25152^585832-112799176354Enzo Doria07/2014
2516fibonacci(843383)+4176257Jon Grantham08/2023
2517(29*10^176240+49)/3176241Robert Price09/2021
2518(2^585387-11)/3176219Stefano Morozzi08/2022
25192^585336-461039176204Enzo Doria06/2015
2520(25*10^176164+143)/3176165Robert Price08/2020
25212^585095-1848127176132Enzo Doria08/2015
2522(5*10^176101-311)/9176101Robert Price12/2021
25236*10^176092+77176093Robert Price06/2020
25242^584950-115451176088Enzo Doria07/2015
2525(646*10^176044+11)/9176046Robert Price10/2021
2526(7^208283-5^208283)/2176020Jon Grantham08/2023
25272^584671-3697176004Yves Minet03/2017
2528(13*10^175965-37)/3175966Robert Price01/2019
252931728^39089-39089^31728175957Frank Doornink01/2024
25302*10^175860-87175861Robert Price04/2018
253127009^39670-39670^27009175798Frank Doornink01/2024
2532(86*10^175774-221)/9175775Robert Price09/2019
25332^583614+216037175686Enzo Doria11/2023
25349*10^175654+47175655Robert Price01/2022
253525430^39869-39869^25430175637Frank Doornink01/2024
253610^175608+2971175609Mike Oakes05/2010
253710^175608-55829175608Patrick De Geest09/2013
25382^583051+1879793175516Enzo Doria09/2016
2539(76*10^175514+491)/9175515Robert Price10/2021
25402^582860-23829175459Enzo Doria08/2013
2541(8*10^175428-53)/9175428Serge Batalov11/2022
2542(28*10^175417-67)/3175418Robert Price10/2020
25432^582670-23913175402Enzo Doria08/2013
25442^582573-29563175372Enzo Doria08/2015
25452^582435-1862767175331Enzo Doria12/2015
254610^175295-40000001175295Robert Price07/2022
254731093^39018-39018^31093175295Frank Doornink01/2024
2548(11*10^175250-149)/3175251Robert Price09/2018
2549(29*10^175236+31)/3175237Robert Price04/2021
25502^582072-1848599175222Enzo Doria08/2015
2551(404267#+465)/(3^4*5^2*31)175208Makoto Morimoto06/2019
2552Phi(262767,10)/259613797175168Makoto Kamada12/2022
2553(2^581871-15)/7175160Stefano Morozzi08/2022
2554(5*10^175117-311)/9175117Robert Price12/2021
255531193^38966-38966^31193175116Frank Doornink01/2024
255610^175093-89175093Riley Fisher10/2023
2557(220221^32768+1)/2175075Serge Batalov03/2018
25582^581560+1874911175068Enzo Doria06/2016
2559(25*10^174987-97)/9174988Robert Price01/2022
2560(75^93307-1)/74174955Paul Bourdelais09/2017
256126446^39555-39555^26446174927Frank Doornink03/2024
256231522^38883-38883^31522174920Frank Doornink01/2024
2563(27398^39601-1)/(27398^199-1)174855Ryan Propper11/2023
2564(861^59557-1)/860174798Jinyuan Wang11/2023
256531492^38859-38859^31492174796Frank Doornink01/2024
2566(47*10^174790+493)/9174791Robert Price03/2019
25672^580528-114035174757Enzo Doria11/2014
2568(19*10^174754+737)/9174755Robert Price07/2018
2569(35*10^174704-377)/9174705Robert Price07/2018
2571(49*10^174681+293)/9174682Robert Price03/2021
25706*10^174681+11174682Robert Price07/2022
25723*10^174665-97174666Robert Price07/2018
25732^580046-459161174612Enzo Doria05/2015
25742^579992-39779174595Enzo Doria09/2015
257525613^39582-39582^25613174496Frank Doornink02/2024
2576(29*10^174481-149)/3174482Robert Price08/2022
2577(4*10^174423+101)/3174424Robert Price11/2021
2578(2^579371-17)/3174408Stefano Morozzi08/2022
2579(2*10^174301-71)/3174301Robert Price12/2017
258014^152048+3174267Paul Bourdelais12/2020
2581(2^578696+1)/257174203Lelio R Paula09/2015
25822^578656-1851809174193Enzo Doria08/2015
25832^578583-113917174171Enzo Doria10/2014
25842^578434-83174126Yves Minet07/2017
258515^148048-2174118Robert Price06/2015
25865*10^174101+81174102Robert Price03/2019
25872^578346+2794249174100Enzo Doria03/2016
258810^173947+1372429173948Patrick De Geest08/2021
259010^173947-500000001173947Robert Price12/2020
258910^173947-286391173947Patrick De Geest08/2021
25915*10^173904-13173905Robert Price01/2019
2592(8*10^173862-59)/3173863Robert Price08/2021
2593(71*10^173854-287)/9173855Robert Price09/2019
2594(43*10^173826+101)/9173827Robert Price11/2018
25952*10^173809-87173810Robert Price04/2018
2596(2^577372-23)/7173806Stefano Morozzi08/2022
2597(L!41532)/2173772Serge Batalov07/2017
25982^577146-49877173739Enzo Doria10/2015
25992^576889+49727173661Enzo Doria09/2016
2600(167*10^173571-17)/3173573Robert Price03/2020
260137803^37916+37916^37803173562Norbert Schneider06/2022
26025*10^173534+29173535Robert Price12/2020
2603(2^576551-1)/4612409/64758208321/242584327930759173528Dario Alpern06/2014
26044*10^173509+99173510Robert Price12/2020
2605(13*10^173467-37)/3173468Robert Price01/2019
26062^576016-113919173399Enzo Doria11/2014
26072^575911-1849387173367Enzo Doria08/2015
26082^575879+215843173357Enzo Doria11/2023
26092^575871+28733173355Enzo Doria01/2024
2610515^63898+63898^515173280Norbert Schneider12/2022
26112^575614+9173278Stefano Morozzi04/2021
26122^575606-219533173275Enzo Doria03/2024
2613(16*10^173251+107)/3173252Robert Price03/2019
261426618^39149-39149^26618173242Frank Doornink03/2024
26152^575196-114053173152Enzo Doria11/2014
26167*10^173135-53173136Robert Price06/2020
2617(301*10^173047+23)/9173049Robert Price06/2021
26182^574591-115387172970Enzo Doria07/2015
261925210^39297-39297^25210172969Frank Doornink12/2023
2620(202*10^172940-13)/9172942Robert Price01/2020
262145^104608+104608^45172940Norbert Schneider06/2021
26222^574328+81121172890Enzo Doria07/2016
2623(115*10^172862-1)/3172864Serge Batalov12/2014
26243*10^172812+13172813Robert Price07/2018
26254*5^247217-9172798Lelio R Paula10/2015
26266*10^172772-31172773Robert Price07/2020
262769061#+(467617#)/(69061#)172766Makoto Morimoto10/2017
2628(34*10^172693-547)/9172694Robert Price03/2021
26295*10^172692+57172693Robert Price12/2018
26302^573668-2782319172692Enzo Doria09/2015
26312^573444-1855109172624Enzo Doria09/2015
263225500^39173-39173^25500172618Frank Doornink02/2024
263327180^38917-38917^27180172568Frank Doornink01/2024
2634(14*10^172532-29)/3172533Robert Price09/2021
26353^361608+2172531Robert Price08/2014
2636(54^99563+1)/55172481Paul Bourdelais11/2017
26372^572592-114893172368Enzo Doria05/2015
26384*10^172354-39172355Robert Price09/2020
263937535^37674+37674^37535172338Norbert Schneider05/2022
2640(11*10^172322-119)/9172323Robert Price11/2021
26415^246497-4^246497172295Jean-Louis Charton11/2008
2642(38^109037-1)/37172254Paul Bourdelais10/2017
2643(4*10^172241+89)/3172242Robert Price08/2021
26443*10^172219+73172220Robert Price08/2018
26452^571810+28549172132Enzo Doria01/2024
2646A352736(15)172032Kellen Shenton05/2022
264732298^38149-38149^32298172021Frank Doornink02/2024
26482^571300+25861171979Enzo Doria11/2023
2649(36^110503+1)/37171975Lelio R Paula04/2017
26508*10^171934+71171935Robert Price05/2022
2651(11*10^171933+601)/9171934Robert Price02/2022
2652(22*10^171929-73)/3171930Robert Price04/2019
2653(49*10^171892-319)/9171893Robert Price10/2021
26544*10^171891-63171892Robert Price10/2018
265567*10^171882-9171884Robert Price03/2021
26562^570980-2782289171883Enzo Doria09/2015
2657(25*10^171849-37)/3171850Robert Price10/2019
265810^171832+387909171833Patrick De Geest08/2021
265910^171832-10001171832Robert Price02/2021
2661(2^(12*47563+13)-9)/7171818Kevin Acres11/2013
2660(2^570769-9)/7171818Stefano Morozzi08/2022
2662(74*10^171651-29)/9171652Robert Price06/2022
2663(536*10^171601-23)/9171603Robert Price02/2020
26647*10^171535-99171536Robert Price06/2019
2665(28*10^171534+101)/3171535Robert Price09/2020
26662^569563-1854607171456Enzo Doria09/2015
266732133^38042-38042^32133171454Frank Doornink02/2024
26683*10^171391+59171392Robert Price08/2018
2669(13*10^171306-37)/3171307Robert Price01/2019
26708*10^171296+87171297Robert Price10/2019
2671(55^98419-1)/54171284Paul Bourdelais12/2017
2672(29*10^171275+67)/3171276Robert Price12/2019
2673(457*10^171248-7)/9171250Robert Price09/2022
2674(194*10^171193+1)/3171195Robert Price01/2022
26752^568642+1876129171179Enzo Doria07/2016
26764*10^171146-47171147Robert Price10/2021
2677(19*10^170970+131)/3170971Robert Price06/2020
2678(46*10^170932+143)/9170933Robert Price01/2019
2679(79*10^170901-1)/3170903Robert Price02/2020
2680(58*10^170842+221)/9170843Robert Price02/2017
2681(29*10^170830+583)/9170831Robert Price06/2021
26823*10^170800+73170801Robert Price08/2018
2683(29*10^170799-119)/9170800Robert Price12/2021
268411^164009-270170798Enzo Doria10/2012
26852*10^170767+41170768Robert Price05/2018
26863^357706-112358170670Enzo Doria07/2014
2687TheodorusPrime(170657)170657Eric W. Weisstein08/2013
26882^566871+1876163170646Enzo Doria07/2016
2689(10657#+(404267#)/(10657#))/(1675379)170624Makoto Morimoto10/2017
26902^566496+7170533Donovan Johnson07/2006
2691(7^201653+1)/8170416Paul Bourdelais02/2010
269232150^37807-37807^32150170403Frank Doornink02/2024
26937*10^170348+33170349Robert Price06/2020
26942^565799+216011170323Enzo Doria12/2023
26952^565183-352021170138Enzo Doria07/2015
26962^565143-114457170125Enzo Doria02/2015
26973*2^565024-5170090Jon Grantham07/2023
26982^564976-49869170075Enzo Doria10/2015
2699(7*10^169944+23)/3169945Robert Price06/2020
2700(37*10^169943+251)/9169944Robert Price09/2021
27012^564526-351401169940Enzo Doria07/2015
27024*10^169759+19169760Robert Price10/2018
2703(2^563903-13)/5169752Stefano Morozzi08/2022
270421^128327-20^128327169677Jean-Louis Charton11/2014
27052^563583+89169656Stefano Morozzi04/2021
27062^563311+215813169574Enzo Doria11/2023
2707(4*10^169559+83)/3169560Robert Price02/2018
2708(194*10^169461-17)/3169463Robert Price09/2020
27092^562749+2793047169405Enzo Doria02/2016
2710(154*10^169337-1)/9169339Serge Batalov12/2014
2711(109*10^169337+11)/3169339Robert Price06/2022
2712(56*10^169311+691)/9169312Robert Price05/2019
27132^562369-29503169290Enzo Doria08/2015
2714(17*10^169283+19)/9169284Robert Price03/2021
271510^169074-5000000001169074Robert Price09/2022
27168*10^169071+59169072Robert Price11/2021
2717(10^169044+173)/3169044Robert Price05/2021
2718(22*10^169019+383)/9169020Robert Price05/2018
2719(64*10^168935+143)/9168936Robert Price05/2021
2720(22*10^168906+47)/3168907Robert Price06/2021
27215*10^168807+87168808Robert Price02/2019
2722(77*10^168803-149)/9168804Robert Price03/2022
27234*10^168788-47168789Robert Price10/2021
2724(154*10^168781+17)/9168783Robert Price06/2022
2725(418*10^168751-31)/9168753Robert Price05/2022
2726(29*10^168711+691)/9168712Robert Price08/2021
27272^560405-39943168699Enzo Doria09/2015
2728(397*10^168634+17)/9168636Robert Price03/2022
272989*10^168614-7168616Robert Price04/2020
2730(23*10^168608-83)/3168609Robert Price08/2019
2731(94*10^168541+11)/3168543Robert Price04/2020
27322^559686-350471168483Enzo Doria06/2015
27332^559672-1855889168479Enzo Doria09/2015
2734(5*10^168379-473)/9168379Robert Price01/2018
27352024^50920+3168353Martin Hopf01/2024
27362^559000-59939168276Enzo Doria11/2015
27372^558830+25009168225Enzo Doria11/2023
2738(16*10^168181+41)/3168182Robert Price03/2019
2739(19*10^168173+77)/3168174Robert Price05/2019
2740(74*10^168170+529)/9168171Robert Price02/2022
27412^558640-114149168168Enzo Doria12/2014
27422^558498-1849277168125Enzo Doria08/2015
27432^558476-1850249168119Enzo Doria08/2015
2744(7*10^168067+71)/3168068Robert Price05/2018
27452^558150-1852211168020Enzo Doria08/2015
27462^558125-113661168013Enzo Doria09/2014
2747393^64747-392^64747167980Jean-Louis Charton08/2012
2748(8*10^167965-11)/3167966Robert Price07/2023
27492^557916+216151167950Enzo Doria12/2023
2750(13*10^167911+179)/3167912Robert Price11/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 27 2024 13:30 (Time in France)

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