PRP Records

Probable Primes Top 10000

(294613 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 ?
2751(10^164643+83)/3164643Robert Price08/2021
27522^546398-59201164483Enzo Doria10/2015
27532^546332-114893164463Enzo Doria05/2015
275432003^36504-36504^32003164458Frank Doornink01/2024
2755(65*10^164427+277)/9164428Robert Price08/2021
27562^545958+1876189164350Enzo Doria07/2016
27572^545878-49841164326Enzo Doria10/2015
2758(10^164284+77)/3164284Robert Price01/2018
27592^545668-4019164263Yves Minet04/2017
276010^164216+780639164217Patrick De Geest08/2021
276210^164216-50000000001164216Robert Price12/2020
276110^164216-891051164216Patrick De Geest08/2021
2763(13*53^238539*617^9)/10^247183164151Hans Havermann07/2017
2764(16*10^164122+197)/3164123Robert Price04/2019
27652^545185+76757164118Enzo Doria05/2016
27662^545076-114329164085Enzo Doria01/2015
2767(2*10^164043-143)/3164043Robert Price03/2018
2768(33085^36481-1)/(33085^191-1)164018Ryan Propper11/2023
2769(29^112153+1)/30164011Lelio R Paula03/2017
27702^544757+1874777163989Enzo Doria06/2016
27712^544723+211193163978Enzo Doria08/2023
27722^544444-457199163894Enzo Doria01/2015
2773(32804^36481-1)/(32804^191-1)163883Ryan Propper11/2023
27742^544264-343529163840Enzo Doria07/2015
27757*10^163780+9163781Robert Price09/2015
27762^543989+2793047163758Enzo Doria02/2016
2777(28*10^163709+113)/3163710Robert Price03/2020
2778(2013^49729-1)/(2013^223-1)163561Ryan Propper11/2023
2779(23*10^163523+301)/9163524Robert Price06/2021
2780(68*10^163521-329)/9163522Robert Price03/2021
278135820^35899+35899^35820163489Norbert Schneider11/2021
27822^542870-69551163421Enzo Doria12/2015
27832^542502+24799163310Enzo Doria10/2023
27842^542395+72533163278Enzo Doria04/2016
27852^542258+216949163236Enzo Doria12/2023
27862^542072-3683163180Yves Minet03/2017
2787fibonacci(780566)-4163129Jon Grantham08/2023
2788(682*10^163106-7)/9163108Robert Price08/2021
27892^541779-1867357163092Enzo Doria04/2016
2790(29*10^163056+313)/9163057Robert Price04/2021
27912^541476+214743163001Enzo Doria11/2023
27928*10^162924+9162925Robert Price12/2015
27932^540905+81557162829Enzo Doria08/2016
27942^540628-2939162746Yves Minet09/2014
2795919^54919-918^54919162743Jean-Louis Charton01/2013
2796(203*10^162689+1)/3162691Robert Price03/2020
27973*10^162620-59162621Robert Price09/2018
27982^540180+26791162611Enzo Doria12/2023
27993^340694-112960162553Enzo Doria07/2014
28002^539807-114081162499Enzo Doria12/2014
2801414^62093+62093^414162498Norbert Schneider03/2022
28022^539654-114893162453Enzo Doria05/2015
28039*10^162449-71162450Robert Price11/2020
28042^539617-1851583162441Enzo Doria08/2015
2805(509*10^162422+31)/9162424Robert Price08/2022
2806(91*10^162410+11)/3162412Robert Price02/2020
28072^539346+81049162360Enzo Doria07/2016
28082^539220-115499162322Enzo Doria07/2015
28092^539217-113713162321Enzo Doria09/2014
28109^170099-8^170099162316Jean-Louis Charton05/2005
28114*10^162263-39162264Robert Price09/2020
281231243^36098-36098^31243162252Frank Doornink01/2024
281331987^36000-36000^31987162180Frank Doornink01/2024
2814(115*10^162153-1)/3162155Serge Batalov12/2014
2815(10^162138+11)/3162138Serge Batalov07/2015
2816(61*10^162100-403)/9162101Robert Price10/2021
28172^538473-112723162097Enzo Doria06/2014
28182^538157+79337162002Enzo Doria06/2016
28192^538136-114749161996Enzo Doria05/2015
28202^538104+1531161986Lelio R Paula01/2013
2821(9*29^110727-1199)/14161927Curtis Bright05/2015
2822((2^179294-1)^3+2)/11161918Serge Batalov03/2023
282331198^36027-36027^31198161910Frank Doornink01/2024
28242^537815-22737161899Enzo Doria07/2013
28252^537804-39839161896Enzo Doria09/2015
2826(754*10^161816-7)/9161818Robert Price05/2020
28272^537458-59201161791Enzo Doria10/2015
28282*10^161766+51161767Robert Price05/2018
2829(7*10^161760+131)/3161761Robert Price06/2020
28302^537209-49849161717Enzo Doria10/2015
2831(58*10^161691+329)/9161692Robert Price05/2019
283223*10^161668-3161670Robert Price10/2021
28332^536937+1879397161635Enzo Doria09/2016
28343*2^536868-5161614Jon Grantham07/2023
283534*10^161593-9161595Robert Price06/2020
2836(31*10^161582-1)/3161584Robert Price02/2020
283724494^36813+36813^24494161575Norbert Schneider11/2023
28382^536569-22881161524Enzo Doria07/2013
2839(46*10^161505+593)/9161506Robert Price04/2022
284010^161253+573493161254Patrick De Geest07/2018
284110^161253-8001161253Robert Price03/2018
284297*10^161247-3161249Robert Price05/2020
28437*10^161192-9161193Robert Price10/2015
28442^535415-19161176Stefano Morozzi07/2022
28452^535269-113803161133Enzo Doria09/2014
28462^535205-23295161113Enzo Doria08/2013
2847(49*10^161105+437)/9161106Robert Price09/2021
2848(89^82609+1)/90161036Paul Bourdelais10/2017
28492^534429-19160880Stefano Morozzi07/2022
28502^534359-23229160859Enzo Doria08/2013
285110^160836-1001160836Robert Price10/2022
2852457^60454+60454^457160803Norbert Schneider07/2021
28538*10^160782+53160783Robert Price08/2020
285467^88037-66^88037160763Robert Price10/2013
2855(88*10^160761-637)/9160762Robert Price11/2020
28562^533948-1852559160735Enzo Doria08/2015
28572^533665-23335160650Enzo Doria08/2013
28582^533600+217981160630Enzo Doria01/2024
2859(19*10^160619+77)/3160620Robert Price05/2019
28602^533350-5160555Stefano Morozzi07/2022
2861(38*10^160508+151)/9160509Robert Price03/2022
28623^336353-2^336353160482Mike Oakes10/2007
28632*10^160339-63160340Robert Price01/2022
286424419^36532+36532^24419160293Norbert Schneider10/2023
2865(91*10^160249+11)/3160251Robert Price02/2020
2866(772*10^160239-7)/9160241Robert Price06/2022
2867(2*10^160226+187)/9160226Robert Price06/2022
28682^532253+1868417160225Enzo Doria04/2016
28692^532108-291989160181Enzo Doria07/2015
2870(28*10^160171-79)/3160172Robert Price02/2021
2871(26*10^160166-131)/3160167Robert Price10/2019
287255*10^160145+9160147Robert Price03/2022
2873(17*10^160143+67)/3160144Robert Price01/2019
2874(394^61637-1)/393159977Jinyuan Wang04/2023
2875(19*10^159921-49)/3159922Robert Price05/2019
28762^531110-1853771159881Enzo Doria09/2015
2877(275^65536+53^65536)/2159864Kellen Shenton11/2020
28782^530992-1845299159845Enzo Doria07/2015
28792^530810+25159790Stefano Morozzi04/2021
288025590^36241-36241^25590159753Frank Doornink02/2024
2881(136*10^159736-1)/9159738Serge Batalov12/2014
28822^530417-113833159672Enzo Doria09/2014
28832^530406-69701159669Enzo Doria02/2016
28845*10^159656+41159657Robert Price03/2019
28858*10^159614+29159615Robert Price11/2021
28867^188858-188858^7159604Norbert Schneider05/2018
288728^110278+27159590Alfred Reich02/2024
28887*10^159553-27159554Robert Price11/2022
28893^334409-5*2^334409159554Jon Grantham08/2023
2890(24^115597-1)/23159547Paul Bourdelais09/2017
289125472^36209-36209^25472159540Frank Doornink01/2024
2892(17*10^159438-377)/9159439Robert Price03/2018
2893(203*10^159381+1)/3159383Robert Price03/2020
289432282^35343-35343^32282159361Frank Doornink02/2024
28952^529215+219383159310Enzo Doria02/2024
289689*10^159258-9159260Robert Price05/2020
28972^528944-461315159229Enzo Doria07/2015
2898(13*10^159147+161)/3159148Robert Price11/2018
28992^528620-113879159131Enzo Doria10/2014
290032125^35306-35306^32125159119Frank Doornink02/2024
2901(47*10^159083+259)/9159084Robert Price03/2022
2902(861^54181-1)/860159019Jinyuan Wang11/2023
29032^528000-23307158944Enzo Doria08/2013
2904(29*10^158909+61)/9158910Robert Price08/2018
29052^527817+1876817158889Enzo Doria07/2016
29062^527774-49451158876Enzo Doria10/2015
29072^527745-291553158868Enzo Doria07/2015
2908(91*10^158862+11)/3158864Robert Price02/2020
29092^527644-1856999158837Enzo Doria10/2015
2910(37200^37199-37198^37199)/(2^37199)158822Henri Lifchitz06/2013
2911(17*10^158819+7)/3158820Robert Price06/2023
29122^527573-1863253158816Enzo Doria12/2015
29132^527553-23401158810Enzo Doria08/2013
2914(49*10^158783+437)/9158784Robert Price09/2021
291510^158755+310207158756Patrick De Geest08/2021
291610^158755-50001158755Robert Price08/2020
2917(61*10^158748-619)/9158749Robert Price03/2022
291811^152420-210158730Enzo Doria09/2012
2919(13*10^158694+401)/9158695Robert Price01/2018
29202^527052-69059158659Enzo Doria11/2015
29212^526849-113233158598Enzo Doria07/2014
292224286^36161+36161^24286158579Norbert Schneider08/2023
2923(2^526763-lucasV(1,2,526763)+1)/2158572Mike Oakes11/2016
2924(299*10^158544-17)/3158546Robert Price04/2020
29252^526658-3551158540Yves Minet03/2017
29267*10^158465-11158466Robert Price06/2019
2927(7^187507-3^187507)/4158462Jon Grantham08/2023
29282^526375-23115158455Enzo Doria08/2013
2929(77*10^158407-293)/9158408Robert Price09/2019
293031209^35242-35242^31209158388Frank Doornink01/2024
293132071^35144-35144^32071158363Frank Doornink01/2024
29322^526028-112793158351Enzo Doria07/2014
2933(229*10^158339-1)/3158341Robert Price07/2020
293432042^35123-35123^32042158255Frank Doornink01/2024
29352^525690-9221158249Lelio R Paula01/2013
29362*10^158242-7158243Robert Price10/2015
29372^525667-525667^2158242Henri Lifchitz12/2017
2938(56*10^158230+187)/9158231Robert Price10/2021
293910^158209-7000000001158209Robert Price12/2021
294031050^35207-35207^31050158153Frank Doornink01/2024
29412^525186-1857431158097Enzo Doria10/2015
294231527^35108-35108^31527157940Frank Doornink01/2024
29432^524515-23245157895Enzo Doria08/2013
29442^524499-109087157890Enzo Doria04/2014
29452^524384-219533157856Enzo Doria03/2024
29472^18067*(2^506221+1)-1157827Makoto Morimoto05/2014
29482^524288+189093157827Makoto Morimoto01/2016
29462^524288-164073157827Matthias Baur03/2020
2949(2^(2^19)-9333)/(19*23*463*1213*31973)157814Makoto Morimoto09/2017
2950(10^157792+359)/9157792Serge Batalov12/2014
29512^524154+25157787Stefano Morozzi04/2021
29522^523924+1876591157717Enzo Doria07/2016
2953(17*10^157705+67)/3157706Robert Price01/2019
2954(46^94841+1)/47157696Robert Price01/2014
29552^523774+77839157672Enzo Doria05/2016
29562^523587+2799143157616Enzo Doria04/2016
29572^523371+1872113157551Enzo Doria05/2016
29588*10^157477+27157478Robert Price09/2021
295932268^34909-34909^32268157397Frank Doornink02/2024
2960(8*10^157368+49)/3157369Robert Price05/2020
2961(82*10^157319+449)/9157320Robert Price11/2019
29622^522535-351457157299Enzo Doria07/2015
296325401^35704-35704^25401157271Frank Doornink01/2024
29642^522226+2799079157206Enzo Doria04/2016
2965(134*10^157191-11)/3157193Robert Price01/2022
29662^522134-1849451157178Enzo Doria08/2015
29679*10^157152+71157153Robert Price08/2020
29684*10^157150+93157151Robert Price08/2018
296931227^34952-34952^31227157093Frank Doornink01/2024
2970(32^104347+5^104347)/37157057Anonymous12/2023
2971fibonacci(751442)-2157042Jon Grantham08/2023
29722^521401-29593156958Enzo Doria08/2015
29737*10^156956+87156957Robert Price07/2019
29742^521348-23397156942Enzo Doria08/2013
297510^156902+34509156903Patrick De Geest08/2021
297710^156902-80000001156902Robert Price04/2021
297610^156902-69789156902Patrick De Geest08/2021
2978(98^78797+1)/99156901Paul Bourdelais12/2017
297965^86522+64156857Lelio R Paula04/2016
29808^173687-7^173687156855Jean-Louis Charton09/2004
29812^520977-1858183156830Enzo Doria10/2015
2982(8*10^156718-101)/3156719Robert Price08/2018
2983(10^156640+7)/53156639Alfred Reich07/2021
29842^520314-1849481156631Enzo Doria08/2015
2985(16*10^156563-637)/9156564Robert Price09/2022
2986(13*10^156522+89)/3156523Robert Price09/2018
2988(2^(6*86654+1)-5)/3156513Kevin Acres12/2013
2987(2^519925-5)/3156513Stefano Morozzi08/2022
2989(4*10^156501+119)/3156502Robert Price12/2021
2990(83*10^156476-101)/9156477Robert Price08/2021
29913*10^156435-97156436Robert Price07/2018
2992(8*10^156371-77)/3156372Robert Price07/2018
299353^90679-52^90679156356Robert Price01/2013
299431267^34782-34782^31267156349Frank Doornink01/2024
2995(418*10^156309-31)/9156311Robert Price05/2022
29962^519106-59141156267Enzo Doria10/2015
29972^519053+6077156251Enzo Doria02/2016
299831199^34764-34764^31199156235Frank Doornink01/2024
29992^518968-1860989156225Enzo Doria11/2015
3000(25*10^156221-7)/9156222Robert Price05/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 04 2024 15:31 (Time in France)

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