PRP Records

Probable Primes Top 10000

(300940 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 ?
3251(68*10^163521-329)/9163522Robert Price03/2021
325235820^35899+35899^35820163489Norbert Schneider11/2021
32532^542870-69551163421Enzo Doria12/2015
32542^542502+24799163310Enzo Doria10/2023
32552^542395+72533163278Enzo Doria04/2016
32562^542258+216949163236Enzo Doria12/2023
32572^542072-3683163180Yves Minet03/2017
3258fibonacci(780566)-4163129Jon Grantham08/2023
3259(682*10^163106-7)/9163108Robert Price08/2021
32602^541779-1867357163092Enzo Doria04/2016
3261(29*10^163056+313)/9163057Robert Price04/2021
32622^541476+214743163001Enzo Doria11/2023
326313^142159+14^142159-2162933Harsh Aggarwal05/2024
32648*10^162924+9162925Robert Price12/2015
32652^540905+81557162829Enzo Doria08/2016
32662^540628-2939162746Yves Minet09/2014
3267919^54919-918^54919162743Jean-Louis Charton01/2013
3268(203*10^162689+1)/3162691Robert Price03/2020
32693*10^162620-59162621Robert Price09/2018
32702^540180+26791162611Enzo Doria12/2023
32713^340694-112960162553Enzo Doria07/2014
32722^539925+81162534Henri Lifchitz11/2024
32732^539807-114081162499Enzo Doria12/2014
3274414^62093+62093^414162498Norbert Schneider03/2022
32752^539654-114893162453Enzo Doria05/2015
32769*10^162449-71162450Robert Price11/2020
32772^539617-1851583162441Enzo Doria08/2015
3278(509*10^162422+31)/9162424Robert Price08/2022
3279(91*10^162410+11)/3162412Robert Price02/2020
32802^539346+81049162360Enzo Doria07/2016
32812^539220-115499162322Enzo Doria07/2015
32822^539217-113713162321Enzo Doria09/2014
32839^170099-8^170099162316Jean-Louis Charton05/2005
32844*10^162263-39162264Robert Price09/2020
328531243^36098-36098^31243162252Frank Doornink01/2024
328631987^36000-36000^31987162180Frank Doornink01/2024
3287(115*10^162153-1)/3162155Serge Batalov12/2014
3288(10^162138+11)/3162138Serge Batalov07/2015
3289(61*10^162100-403)/9162101Robert Price10/2021
32902^538473-112723162097Enzo Doria06/2014
32912^538157+79337162002Enzo Doria06/2016
32922^538136-114749161996Enzo Doria05/2015
32932^538104+1531161986Lelio R Paula01/2013
3294(9*29^110727-1199)/14161927Curtis Bright05/2015
3295((2^179294-1)^3+2)/11161918Serge Batalov03/2023
329631198^36027-36027^31198161910Frank Doornink01/2024
32972^537815-22737161899Enzo Doria07/2013
32982^537804-39839161896Enzo Doria09/2015
3299(754*10^161816-7)/9161818Robert Price05/2020
33002^537461+29867161792Enzo Doria03/2024
33012^537458-59201161791Enzo Doria10/2015
33022*10^161766+51161767Robert Price05/2018
3303(7*10^161760+131)/3161761Robert Price06/2020
33042^537209-49849161717Enzo Doria10/2015
3305(58*10^161691+329)/9161692Robert Price05/2019
330623*10^161668-3161670Robert Price10/2021
33072^536937+1879397161635Enzo Doria09/2016
33083*2^536868-5161614Jon Grantham07/2023
330934*10^161593-9161595Robert Price06/2020
3310(31*10^161582-1)/3161584Robert Price02/2020
331124494^36813+36813^24494161575Norbert Schneider11/2023
33122^536569-22881161524Enzo Doria07/2013
3313(46*10^161505+593)/9161506Robert Price04/2022
331410^161253+573493161254Patrick De Geest07/2018
331510^161253-8001161253Robert Price03/2018
331697*10^161247-3161249Robert Price05/2020
33177*10^161192-9161193Robert Price10/2015
33182^535415-19161176Stefano Morozzi07/2022
33192^535269-113803161133Enzo Doria09/2014
33202^535205-23295161113Enzo Doria08/2013
3321(49*10^161105+437)/9161106Robert Price09/2021
33222^534961+6561161040Henri Lifchitz11/2024
3323(89^82609+1)/90161036Paul Bourdelais10/2017
332435385^35385-17692^17692160960Henri Lifchitz10/2024
33252^534429-19160880Stefano Morozzi07/2022
33262^534359-23229160859Enzo Doria08/2013
332710^160836-1001160836Robert Price10/2022
3328457^60454+60454^457160803Norbert Schneider07/2021
33298*10^160782+53160783Robert Price08/2020
333067^88037-66^88037160763Robert Price10/2013
3331(88*10^160761-637)/9160762Robert Price11/2020
33322^533981+81160745Henri Lifchitz11/2024
33332^533948-1852559160735Enzo Doria08/2015
33342^533665-23335160650Enzo Doria08/2013
33352^533600+217981160630Enzo Doria01/2024
3336(19*10^160619+77)/3160620Robert Price05/2019
33372^533350-5160555Stefano Morozzi07/2022
3338(38*10^160508+151)/9160509Robert Price03/2022
33393^336353-2^336353160482Mike Oakes10/2007
334026134^36315-36315^26134160411Frank Doornink03/2024
334125821^36358-36358^25821160411Frank Doornink03/2024
33422*10^160339-63160340Robert Price01/2022
334324419^36532+36532^24419160293Norbert Schneider10/2023
3344(91*10^160249+11)/3160251Robert Price02/2020
3345(772*10^160239-7)/9160241Robert Price06/2022
3346(2*10^160226+187)/9160226Robert Price06/2022
33472^532253+1868417160225Enzo Doria04/2016
33482^532108-291989160181Enzo Doria07/2015
3349(28*10^160171-79)/3160172Robert Price02/2021
3350(26*10^160166-131)/3160167Robert Price10/2019
335155*10^160145+9160147Robert Price03/2022
3352(17*10^160143+67)/3160144Robert Price01/2019
3353(394^61637-1)/393159977Jinyuan Wang04/2023
3354(19*10^159921-49)/3159922Robert Price05/2019
33552^531110-1853771159881Enzo Doria09/2015
3356(275^65536+53^65536)/2159864Kellen Shenton11/2020
33572^530992-1845299159845Enzo Doria07/2015
33582^530810+25159790Stefano Morozzi04/2021
335925590^36241-36241^25590159753Frank Doornink02/2024
3360(136*10^159736-1)/9159738Serge Batalov12/2014
33612^530417-113833159672Enzo Doria09/2014
33622^530406-69701159669Enzo Doria02/2016
33635*10^159656+41159657Robert Price03/2019
33648*10^159614+29159615Robert Price11/2021
33657^188858-188858^7159604Norbert Schneider05/2018
336628^110278+27159590Alfred Reich02/2024
3367(45^96517-2^96517)/43159562Robert Price11/2024
33687*10^159553-27159554Robert Price11/2022
33693^334409-5*2^334409159554Jon Grantham08/2023
3370(24^115597-1)/23159547Paul Bourdelais09/2017
337125472^36209-36209^25472159540Frank Doornink01/2024
3372(17*10^159438-377)/9159439Robert Price03/2018
3373(203*10^159381+1)/3159383Robert Price03/2020
337432282^35343-35343^32282159361Frank Doornink02/2024
33752^529215+219383159310Enzo Doria02/2024
337689*10^159258-9159260Robert Price05/2020
33772^528944-461315159229Enzo Doria07/2015
3378(13*10^159147+161)/3159148Robert Price11/2018
33792^528620-113879159131Enzo Doria10/2014
338032125^35306-35306^32125159119Frank Doornink02/2024
3381(47*10^159083+259)/9159084Robert Price03/2022
3382(861^54181-1)/860159019Jinyuan Wang11/2023
33832^528000-23307158944Enzo Doria08/2013
3384(29*10^158909+61)/9158910Robert Price08/2018
33852^527817+1876817158889Enzo Doria07/2016
33862^527774-49451158876Enzo Doria10/2015
33872^527745-291553158868Enzo Doria07/2015
3388(91*10^158862+11)/3158864Robert Price02/2020
33892^527644-1856999158837Enzo Doria10/2015
3390(37200^37199-37198^37199)/(2^37199)158822Henri Lifchitz06/2013
3391(17*10^158819+7)/3158820Robert Price06/2023
33922^527573-1863253158816Enzo Doria12/2015
33932^527553-23401158810Enzo Doria08/2013
3394(49*10^158783+437)/9158784Robert Price09/2021
339510^158755+310207158756Patrick De Geest08/2021
339610^158755-50001158755Robert Price08/2020
3397(61*10^158748-619)/9158749Robert Price03/2022
339811^152420-210158730Enzo Doria09/2012
3399(13*10^158694+401)/9158695Robert Price01/2018
34002^527052-69059158659Enzo Doria11/2015
34012^526849-113233158598Enzo Doria07/2014
340224286^36161+36161^24286158579Norbert Schneider08/2023
3403(2^526763-lucasV(1,2,526763)+1)/2158572Mike Oakes11/2016
3404(299*10^158544-17)/3158546Robert Price04/2020
34052^526658-3551158540Yves Minet03/2017
34067*10^158465-11158466Robert Price06/2019
3407(7^187507-3^187507)/4158462Jon Grantham08/2023
34082^526375-23115158455Enzo Doria08/2013
3409(77*10^158407-293)/9158408Robert Price09/2019
341031209^35242-35242^31209158388Frank Doornink01/2024
341132071^35144-35144^32071158363Frank Doornink01/2024
34122^526028-112793158351Enzo Doria07/2014
3413(229*10^158339-1)/3158341Robert Price07/2020
341432042^35123-35123^32042158255Frank Doornink01/2024
34152^525690-9221158249Lelio R Paula01/2013
34162*10^158242-7158243Robert Price10/2015
34172^525667-525667^2158242Henri Lifchitz12/2017
3418(56*10^158230+187)/9158231Robert Price10/2021
341910^158209-7000000001158209Robert Price12/2021
342031050^35207-35207^31050158153Frank Doornink01/2024
34212^525186-1857431158097Enzo Doria10/2015
342231527^35108-35108^31527157940Frank Doornink01/2024
34232^524515-23245157895Enzo Doria08/2013
34242^524499-109087157890Enzo Doria04/2014
34252^524384-219533157856Enzo Doria03/2024
34272^18067*(2^506221+1)-1157827Makoto Morimoto05/2014
34282^524288+189093157827Makoto Morimoto01/2016
34262^524288-164073157827Matthias Baur03/2020
3429(2^(2^19)-9333)/(19*23*463*1213*31973)157814Makoto Morimoto09/2017
3430(10^157792+359)/9157792Serge Batalov12/2014
34312^524154+25157787Stefano Morozzi04/2021
34322^523924+1876591157717Enzo Doria07/2016
3433(17*10^157705+67)/3157706Robert Price01/2019
3434(46^94841+1)/47157696Robert Price01/2014
34352^523774+77839157672Enzo Doria05/2016
34362^523587+2799143157616Enzo Doria04/2016
34372^523496+220141157588Enzo Doria03/2024
34382^523371+1872113157551Enzo Doria05/2016
34398*10^157477+27157478Robert Price09/2021
3440p(30987)#-p(30987+1)157417Henri Lifchitz11/2024
344132268^34909-34909^32268157397Frank Doornink02/2024
3442(8*10^157368+49)/3157369Robert Price05/2020
3443(82*10^157319+449)/9157320Robert Price11/2019
34442^522535-351457157299Enzo Doria07/2015
344525401^35704-35704^25401157271Frank Doornink01/2024
34462^522226+2799079157206Enzo Doria04/2016
3447(134*10^157191-11)/3157193Robert Price01/2022
34482^522134-1849451157178Enzo Doria08/2015
34499*10^157152+71157153Robert Price08/2020
34504*10^157150+93157151Robert Price08/2018
345131227^34952-34952^31227157093Frank Doornink01/2024
3452(32^104347+5^104347)/37157057Anonymous12/2023
3453fibonacci(751442)-2157042Jon Grantham08/2023
34542^521401-29593156958Enzo Doria08/2015
34557*10^156956+87156957Robert Price07/2019
34562^521348-23397156942Enzo Doria08/2013
345710^156902+34509156903Patrick De Geest08/2021
345910^156902-80000001156902Robert Price04/2021
345810^156902-69789156902Patrick De Geest08/2021
3460(98^78797+1)/99156901Paul Bourdelais12/2017
346165^86522+64156857Lelio R Paula04/2016
34628^173687-7^173687156855Jean-Louis Charton09/2004
34632^520977-1858183156830Enzo Doria10/2015
3464(8*10^156718-101)/3156719Robert Price08/2018
3465(10^156640+7)/53156639Alfred Reich07/2021
34662^520314-1849481156631Enzo Doria08/2015
3467(16*10^156563-637)/9156564Robert Price09/2022
3468(13*10^156522+89)/3156523Robert Price09/2018
3470(2^(6*86654+1)-5)/3156513Kevin Acres12/2013
3469(2^519925-5)/3156513Stefano Morozzi08/2022
3471(4*10^156501+119)/3156502Robert Price12/2021
3472(83*10^156476-101)/9156477Robert Price08/2021
34733*10^156435-97156436Robert Price07/2018
347410^156428+111156429Boyan Hu10/2024
3475(8*10^156371-77)/3156372Robert Price07/2018
347653^90679-52^90679156356Robert Price01/2013
347731267^34782-34782^31267156349Frank Doornink01/2024
3478(418*10^156309-31)/9156311Robert Price05/2022
34792^519106-59141156267Enzo Doria10/2015
348025929^35404-35404^25929156266Frank Doornink03/2024
34812^519053+6077156251Enzo Doria02/2016
348231199^34764-34764^31199156235Frank Doornink01/2024
34832^518968-1860989156225Enzo Doria11/2015
3484(25*10^156221-7)/9156222Robert Price05/2018
34852^518931-2782297156214Enzo Doria09/2015
34862^518608-2939156117Yves Minet09/2014
348710*27^109005+697156027Curtis Bright05/2015
3488(49*10^155933-319)/9155934Robert Price10/2021
34892^517967-113485155924Enzo Doria08/2014
3490(103*10^155904+17)/3155906Robert Price08/2020
3491(8*10^155887-719)/9155887Robert Price03/2021
34922^517789+29231155871Enzo Doria02/2024
34934*10^155853-39155854Robert Price09/2020
34942^517698+4429155843Lelio R Paula01/2013
349532015^34584-34584^32015155814Frank Doornink01/2024
34962^517543-113257155796Enzo Doria07/2014
3497(14*10^155740-143)/3155741Robert Price11/2018
349831959^34564-34564^31959155697Frank Doornink01/2024
349931^104309-30^104309155563Henri Lifchitz08/2013
35002^516742-39851155555Enzo Doria09/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 10 2025 11:16 (Time in France)

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