PRP Records

Probable Primes Top 10000

(295036 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(76*10^175514+491)/9175515Robert Price10/2021
25022^582860-23829175459Enzo Doria08/2013
2503(8*10^175428-53)/9175428Serge Batalov11/2022
2504(28*10^175417-67)/3175418Robert Price10/2020
25052^582670-23913175402Enzo Doria08/2013
25062^582573-29563175372Enzo Doria08/2015
25072^582435-1862767175331Enzo Doria12/2015
250810^175295-40000001175295Robert Price07/2022
250931093^39018-39018^31093175295Frank Doornink01/2024
2510(11*10^175250-149)/3175251Robert Price09/2018
2511(29*10^175236+31)/3175237Robert Price04/2021
25122^582072-1848599175222Enzo Doria08/2015
2513(404267#+465)/(3^4*5^2*31)175208Makoto Morimoto06/2019
2514Phi(262767,10)/259613797175168Makoto Kamada12/2022
2515(2^581871-15)/7175160Stefano Morozzi08/2022
2516(5*10^175117-311)/9175117Robert Price12/2021
251731193^38966-38966^31193175116Frank Doornink01/2024
251810^175093-89175093Riley Fisher10/2023
2519(220221^32768+1)/2175075Serge Batalov03/2018
25202^581560+1874911175068Enzo Doria06/2016
2521(25*10^174987-97)/9174988Robert Price01/2022
2522(75^93307-1)/74174955Paul Bourdelais09/2017
252326446^39555-39555^26446174927Frank Doornink03/2024
252431522^38883-38883^31522174920Frank Doornink01/2024
2525(27398^39601-1)/(27398^199-1)174855Ryan Propper11/2023
2526(861^59557-1)/860174798Jinyuan Wang11/2023
252731492^38859-38859^31492174796Frank Doornink01/2024
2528(47*10^174790+493)/9174791Robert Price03/2019
25292^580528-114035174757Enzo Doria11/2014
2530(19*10^174754+737)/9174755Robert Price07/2018
2531(35*10^174704-377)/9174705Robert Price07/2018
2533(49*10^174681+293)/9174682Robert Price03/2021
25326*10^174681+11174682Robert Price07/2022
25343*10^174665-97174666Robert Price07/2018
25352^580046-459161174612Enzo Doria05/2015
25362^579992-39779174595Enzo Doria09/2015
253725613^39582-39582^25613174496Frank Doornink02/2024
2538(29*10^174481-149)/3174482Robert Price08/2022
2539(4*10^174423+101)/3174424Robert Price11/2021
2540(2^579371-17)/3174408Stefano Morozzi08/2022
2541(2*10^174301-71)/3174301Robert Price12/2017
254214^152048+3174267Paul Bourdelais12/2020
2543(2^578696+1)/257174203Lelio R Paula09/2015
25442^578656-1851809174193Enzo Doria08/2015
25452^578583-113917174171Enzo Doria10/2014
25462^578434-83174126Yves Minet07/2017
254715^148048-2174118Robert Price06/2015
25485*10^174101+81174102Robert Price03/2019
25492^578346+2794249174100Enzo Doria03/2016
255010^173947+1372429173948Patrick De Geest08/2021
255210^173947-500000001173947Robert Price12/2020
255110^173947-286391173947Patrick De Geest08/2021
25535*10^173904-13173905Robert Price01/2019
2554(8*10^173862-59)/3173863Robert Price08/2021
2555(71*10^173854-287)/9173855Robert Price09/2019
2556(43*10^173826+101)/9173827Robert Price11/2018
25572*10^173809-87173810Robert Price04/2018
2558(2^577372-23)/7173806Stefano Morozzi08/2022
2559(L!41532)/2173772Serge Batalov07/2017
25602^577146-49877173739Enzo Doria10/2015
25612^576889+49727173661Enzo Doria09/2016
2562(167*10^173571-17)/3173573Robert Price03/2020
256337803^37916+37916^37803173562Norbert Schneider06/2022
25645*10^173534+29173535Robert Price12/2020
2565(2^576551-1)/4612409/64758208321/242584327930759173528Dario Alpern06/2014
25664*10^173509+99173510Robert Price12/2020
2567(13*10^173467-37)/3173468Robert Price01/2019
25682^576016-113919173399Enzo Doria11/2014
25692^575911-1849387173367Enzo Doria08/2015
25702^575879+215843173357Enzo Doria11/2023
25712^575871+28733173355Enzo Doria01/2024
2572515^63898+63898^515173280Norbert Schneider12/2022
25732^575614+9173278Stefano Morozzi04/2021
25742^575606-219533173275Enzo Doria03/2024
2575(16*10^173251+107)/3173252Robert Price03/2019
257626618^39149-39149^26618173242Frank Doornink03/2024
25772^575196-114053173152Enzo Doria11/2014
25787*10^173135-53173136Robert Price06/2020
2579(301*10^173047+23)/9173049Robert Price06/2021
25802^574591-115387172970Enzo Doria07/2015
258125210^39297-39297^25210172969Frank Doornink12/2023
2582(202*10^172940-13)/9172942Robert Price01/2020
258345^104608+104608^45172940Norbert Schneider06/2021
25842^574328+81121172890Enzo Doria07/2016
2585(115*10^172862-1)/3172864Serge Batalov12/2014
25863*10^172812+13172813Robert Price07/2018
25874*5^247217-9172798Lelio R Paula10/2015
25886*10^172772-31172773Robert Price07/2020
258969061#+(467617#)/(69061#)172766Makoto Morimoto10/2017
2590(34*10^172693-547)/9172694Robert Price03/2021
25915*10^172692+57172693Robert Price12/2018
25922^573668-2782319172692Enzo Doria09/2015
25932^573444-1855109172624Enzo Doria09/2015
259425500^39173-39173^25500172618Frank Doornink02/2024
259527180^38917-38917^27180172568Frank Doornink01/2024
2596(14*10^172532-29)/3172533Robert Price09/2021
25973^361608+2172531Robert Price08/2014
2598(54^99563+1)/55172481Paul Bourdelais11/2017
25992^572592-114893172368Enzo Doria05/2015
26004*10^172354-39172355Robert Price09/2020
260137535^37674+37674^37535172338Norbert Schneider05/2022
2602(11*10^172322-119)/9172323Robert Price11/2021
26035^246497-4^246497172295Jean-Louis Charton11/2008
2604(38^109037-1)/37172254Paul Bourdelais10/2017
2605(4*10^172241+89)/3172242Robert Price08/2021
26063*10^172219+73172220Robert Price08/2018
26072^571810+28549172132Enzo Doria01/2024
2608A352736(15)172032Kellen Shenton05/2022
260932298^38149-38149^32298172021Frank Doornink02/2024
26102^571300+25861171979Enzo Doria11/2023
2611(36^110503+1)/37171975Lelio R Paula04/2017
26128*10^171934+71171935Robert Price05/2022
2613(11*10^171933+601)/9171934Robert Price02/2022
2614(22*10^171929-73)/3171930Robert Price04/2019
2615(49*10^171892-319)/9171893Robert Price10/2021
26164*10^171891-63171892Robert Price10/2018
261767*10^171882-9171884Robert Price03/2021
26182^570980-2782289171883Enzo Doria09/2015
2619(25*10^171849-37)/3171850Robert Price10/2019
262010^171832+387909171833Patrick De Geest08/2021
262110^171832-10001171832Robert Price02/2021
2623(2^(12*47563+13)-9)/7171818Kevin Acres11/2013
2622(2^570769-9)/7171818Stefano Morozzi08/2022
2624(74*10^171651-29)/9171652Robert Price06/2022
2625(536*10^171601-23)/9171603Robert Price02/2020
26267*10^171535-99171536Robert Price06/2019
2627(28*10^171534+101)/3171535Robert Price09/2020
26282^569563-1854607171456Enzo Doria09/2015
262932133^38042-38042^32133171454Frank Doornink02/2024
26303*10^171391+59171392Robert Price08/2018
2631(13*10^171306-37)/3171307Robert Price01/2019
26328*10^171296+87171297Robert Price10/2019
2633(55^98419-1)/54171284Paul Bourdelais12/2017
2634(29*10^171275+67)/3171276Robert Price12/2019
2635(457*10^171248-7)/9171250Robert Price09/2022
2636(194*10^171193+1)/3171195Robert Price01/2022
26372^568642+1876129171179Enzo Doria07/2016
26384*10^171146-47171147Robert Price10/2021
2639(19*10^170970+131)/3170971Robert Price06/2020
2640(46*10^170932+143)/9170933Robert Price01/2019
2641(79*10^170901-1)/3170903Robert Price02/2020
2642(58*10^170842+221)/9170843Robert Price02/2017
2643(29*10^170830+583)/9170831Robert Price06/2021
26443*10^170800+73170801Robert Price08/2018
2645(29*10^170799-119)/9170800Robert Price12/2021
264611^164009-270170798Enzo Doria10/2012
26472*10^170767+41170768Robert Price05/2018
26483^357706-112358170670Enzo Doria07/2014
2649TheodorusPrime(170657)170657Eric W. Weisstein08/2013
26502^566871+1876163170646Enzo Doria07/2016
2651(10657#+(404267#)/(10657#))/(1675379)170624Makoto Morimoto10/2017
26522^566496+7170533Donovan Johnson07/2006
2653(7^201653+1)/8170416Paul Bourdelais02/2010
265432150^37807-37807^32150170403Frank Doornink02/2024
26557*10^170348+33170349Robert Price06/2020
26562^565799+216011170323Enzo Doria12/2023
26572^565183-352021170138Enzo Doria07/2015
26582^565143-114457170125Enzo Doria02/2015
26593*2^565024-5170090Jon Grantham07/2023
26602^564976-49869170075Enzo Doria10/2015
2661(7*10^169944+23)/3169945Robert Price06/2020
2662(37*10^169943+251)/9169944Robert Price09/2021
26632^564526-351401169940Enzo Doria07/2015
26644*10^169759+19169760Robert Price10/2018
2665(2^563903-13)/5169752Stefano Morozzi08/2022
266621^128327-20^128327169677Jean-Louis Charton11/2014
26672^563583+89169656Stefano Morozzi04/2021
26682^563311+215813169574Enzo Doria11/2023
2669(4*10^169559+83)/3169560Robert Price02/2018
2670(194*10^169461-17)/3169463Robert Price09/2020
26712^562749+2793047169405Enzo Doria02/2016
2672(154*10^169337-1)/9169339Serge Batalov12/2014
2673(109*10^169337+11)/3169339Robert Price06/2022
2674(56*10^169311+691)/9169312Robert Price05/2019
26752^562369-29503169290Enzo Doria08/2015
2676(17*10^169283+19)/9169284Robert Price03/2021
267710^169074-5000000001169074Robert Price09/2022
26788*10^169071+59169072Robert Price11/2021
2679(10^169044+173)/3169044Robert Price05/2021
2680(22*10^169019+383)/9169020Robert Price05/2018
2681(64*10^168935+143)/9168936Robert Price05/2021
2682(22*10^168906+47)/3168907Robert Price06/2021
26835*10^168807+87168808Robert Price02/2019
2684(77*10^168803-149)/9168804Robert Price03/2022
26854*10^168788-47168789Robert Price10/2021
2686(154*10^168781+17)/9168783Robert Price06/2022
2687(418*10^168751-31)/9168753Robert Price05/2022
2688(29*10^168711+691)/9168712Robert Price08/2021
26892^560405-39943168699Enzo Doria09/2015
2690(397*10^168634+17)/9168636Robert Price03/2022
269189*10^168614-7168616Robert Price04/2020
2692(23*10^168608-83)/3168609Robert Price08/2019
2693(94*10^168541+11)/3168543Robert Price04/2020
26942^559686-350471168483Enzo Doria06/2015
26952^559672-1855889168479Enzo Doria09/2015
2696(5*10^168379-473)/9168379Robert Price01/2018
26972024^50920+3168353Martin Hopf01/2024
26982^559000-59939168276Enzo Doria11/2015
26992^558830+25009168225Enzo Doria11/2023
2700(16*10^168181+41)/3168182Robert Price03/2019
2701(19*10^168173+77)/3168174Robert Price05/2019
2702(74*10^168170+529)/9168171Robert Price02/2022
27032^558640-114149168168Enzo Doria12/2014
27042^558498-1849277168125Enzo Doria08/2015
27052^558476-1850249168119Enzo Doria08/2015
2706(7*10^168067+71)/3168068Robert Price05/2018
27072^558150-1852211168020Enzo Doria08/2015
27082^558125-113661168013Enzo Doria09/2014
2709393^64747-392^64747167980Jean-Louis Charton08/2012
2710(8*10^167965-11)/3167966Robert Price07/2023
27112^557916+216151167950Enzo Doria12/2023
2712(13*10^167911+179)/3167912Robert Price11/2018
2713(26*10^167861-167)/3167862Robert Price10/2019
271436^107827-107827167812Kellen Shenton06/2023
271532027^37242-37242^32027167795Frank Doornink01/2024
271639^105456+2167788Robert Price04/2015
27172^557322+217519167771Enzo Doria01/2024
2718(28^115877-1)/27167691Paul Bourdelais12/2017
27196*10^167662-13167663Robert Price07/2022
272010^167639+121911167640Patrick De Geest07/2018
272110^167639-8001167639Robert Price03/2018
27222^556504-462059167525Enzo Doria07/2015
2723(88*10^167522-637)/9167523Robert Price11/2020
27245*10^167510+9167511Robert Price08/2015
27257*10^167437-93167438Robert Price08/2020
272625455^37978-37978^25455167323Frank Doornink01/2024
272711^160663+6167314Paul Bourdelais02/2021
2728(7*10^167308-493)/9167308Robert Price04/2021
27292^555759+74333167301Enzo Doria07/2023
273026084^37871-37871^26084167253Frank Doornink03/2024
27312^555343+1874333167175Enzo Doria06/2016
27322^555210-461261167135Enzo Doria07/2015
27339*10^166996+59166997Robert Price01/2020
2734(68*10^166976-329)/9166977Robert Price03/2021
2735(64*10^166901+683)/9166902Robert Price06/2022
27362^554372+1880527166883Enzo Doria11/2016
27372^554299+72173166861Enzo Doria04/2016
2738(185*10^166837+7)/3166839Robert Price03/2020
2739(14*10^166813+139)/9166814Robert Price11/2021
274026084^37767-37767^26084166794Frank Doornink03/2024
27412^554037-2797063166782Enzo Doria03/2016
274231861^37028-37028^31861166747Frank Doornink01/2024
2743(49*10^166721-139)/9166722Robert Price03/2019
27442*10^166646+69166647Robert Price06/2020
27452^553484-29819166616Enzo Doria08/2015
2746(188*10^166611+7)/3166613Robert Price03/2020
27472^553383-2784217166585Enzo Doria10/2015
27482^553069+76427166491Enzo Doria05/2016
274925218^37819-37819^25218166469Frank Doornink12/2023
27502*10^166458+51166459Robert Price05/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 23 2024 10:10 (Time in France)

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