PRP Records

Probable Primes Top 10000

(294687 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 ?
27512^549663+212543165466Enzo Doria08/2023
2752(529*10^165394-7)/9165396Robert Price08/2021
2753-tau(103^14938)165374Nik Lygeros / Olivier Rozier10/2013
2754(28*10^165358-1)/9165359Serge Batalov10/2014
27552^549278+1879669165350Enzo Doria09/2016
2756(7*10^165350-439)/9165350Robert Price02/2018
27572^549252-351269165342Enzo Doria06/2015
275867*10^165327-9165329Robert Price03/2021
2760(14*10^165282+73)/3165283Robert Price12/2018
2759(8*10^165283-629)/9165283Robert Price01/2022
27612^549049+2797607165281Enzo Doria04/2016
2762(218*10^165258+7)/9165260Robert Price06/2022
2763(7*10^165239+107)/3165240Robert Price02/2018
27642^548880+23961165230Enzo Doria10/2023
27655*2^548778+3165200Jon Grantham07/2023
2766(44^100511-1)/43165184Paul Bourdelais11/2017
2767(7*10^165134+107)/3165135Robert Price02/2018
2768(301*10^165082+23)/9165084Robert Price06/2021
2769(23*10^165060-83)/3165061Robert Price08/2019
27707*10^165023-27165024Robert Price11/2022
2771(76*10^164984+77)/9164985Robert Price10/2019
277231058^36715-36715^31058164931Frank Doornink01/2024
2773(4*10^164929-211)/9164929Robert Price03/2022
277410^164878-500001164878Robert Price03/2022
27759*10^164791-89164792Robert Price04/2020
27762^547178-1856501164717Enzo Doria10/2015
277711^158160-60164707Enzo Doria07/2012
2778(26*10^164643-167)/3164644Robert Price10/2019
2779(10^164643+83)/3164643Robert Price08/2021
27802^546398-59201164483Enzo Doria10/2015
27812^546332-114893164463Enzo Doria05/2015
278232003^36504-36504^32003164458Frank Doornink01/2024
2783(65*10^164427+277)/9164428Robert Price08/2021
27842^545958+1876189164350Enzo Doria07/2016
27852^545878-49841164326Enzo Doria10/2015
2786(10^164284+77)/3164284Robert Price01/2018
27872^545668-4019164263Yves Minet04/2017
278810^164216+780639164217Patrick De Geest08/2021
279010^164216-50000000001164216Robert Price12/2020
278910^164216-891051164216Patrick De Geest08/2021
2791(13*53^238539*617^9)/10^247183164151Hans Havermann07/2017
2792(16*10^164122+197)/3164123Robert Price04/2019
27932^545185+76757164118Enzo Doria05/2016
27942^545076-114329164085Enzo Doria01/2015
2795(2*10^164043-143)/3164043Robert Price03/2018
2796(33085^36481-1)/(33085^191-1)164018Ryan Propper11/2023
2797(29^112153+1)/30164011Lelio R Paula03/2017
27982^544757+1874777163989Enzo Doria06/2016
27992^544723+211193163978Enzo Doria08/2023
28002^544444-457199163894Enzo Doria01/2015
2801(32804^36481-1)/(32804^191-1)163883Ryan Propper11/2023
28022^544264-343529163840Enzo Doria07/2015
28037*10^163780+9163781Robert Price09/2015
28042^543989+2793047163758Enzo Doria02/2016
2805(28*10^163709+113)/3163710Robert Price03/2020
2806(2013^49729-1)/(2013^223-1)163561Ryan Propper11/2023
2807(23*10^163523+301)/9163524Robert Price06/2021
2808(68*10^163521-329)/9163522Robert Price03/2021
280935820^35899+35899^35820163489Norbert Schneider11/2021
28102^542870-69551163421Enzo Doria12/2015
28112^542502+24799163310Enzo Doria10/2023
28122^542395+72533163278Enzo Doria04/2016
28132^542258+216949163236Enzo Doria12/2023
28142^542072-3683163180Yves Minet03/2017
2815fibonacci(780566)-4163129Jon Grantham08/2023
2816(682*10^163106-7)/9163108Robert Price08/2021
28172^541779-1867357163092Enzo Doria04/2016
2818(29*10^163056+313)/9163057Robert Price04/2021
28192^541476+214743163001Enzo Doria11/2023
28208*10^162924+9162925Robert Price12/2015
28212^540905+81557162829Enzo Doria08/2016
28222^540628-2939162746Yves Minet09/2014
2823919^54919-918^54919162743Jean-Louis Charton01/2013
2824(203*10^162689+1)/3162691Robert Price03/2020
28253*10^162620-59162621Robert Price09/2018
28262^540180+26791162611Enzo Doria12/2023
28273^340694-112960162553Enzo Doria07/2014
28282^539807-114081162499Enzo Doria12/2014
2829414^62093+62093^414162498Norbert Schneider03/2022
28302^539654-114893162453Enzo Doria05/2015
28319*10^162449-71162450Robert Price11/2020
28322^539617-1851583162441Enzo Doria08/2015
2833(509*10^162422+31)/9162424Robert Price08/2022
2834(91*10^162410+11)/3162412Robert Price02/2020
28352^539346+81049162360Enzo Doria07/2016
28362^539220-115499162322Enzo Doria07/2015
28372^539217-113713162321Enzo Doria09/2014
28389^170099-8^170099162316Jean-Louis Charton05/2005
28394*10^162263-39162264Robert Price09/2020
284031243^36098-36098^31243162252Frank Doornink01/2024
284131987^36000-36000^31987162180Frank Doornink01/2024
2842(115*10^162153-1)/3162155Serge Batalov12/2014
2843(10^162138+11)/3162138Serge Batalov07/2015
2844(61*10^162100-403)/9162101Robert Price10/2021
28452^538473-112723162097Enzo Doria06/2014
28462^538157+79337162002Enzo Doria06/2016
28472^538136-114749161996Enzo Doria05/2015
28482^538104+1531161986Lelio R Paula01/2013
2849(9*29^110727-1199)/14161927Curtis Bright05/2015
2850((2^179294-1)^3+2)/11161918Serge Batalov03/2023
285131198^36027-36027^31198161910Frank Doornink01/2024
28522^537815-22737161899Enzo Doria07/2013
28532^537804-39839161896Enzo Doria09/2015
2854(754*10^161816-7)/9161818Robert Price05/2020
28552^537461+29867161792Enzo Doria03/2024
28562^537458-59201161791Enzo Doria10/2015
28572*10^161766+51161767Robert Price05/2018
2858(7*10^161760+131)/3161761Robert Price06/2020
28592^537209-49849161717Enzo Doria10/2015
2860(58*10^161691+329)/9161692Robert Price05/2019
286123*10^161668-3161670Robert Price10/2021
28622^536937+1879397161635Enzo Doria09/2016
28633*2^536868-5161614Jon Grantham07/2023
286434*10^161593-9161595Robert Price06/2020
2865(31*10^161582-1)/3161584Robert Price02/2020
286624494^36813+36813^24494161575Norbert Schneider11/2023
28672^536569-22881161524Enzo Doria07/2013
2868(46*10^161505+593)/9161506Robert Price04/2022
286910^161253+573493161254Patrick De Geest07/2018
287010^161253-8001161253Robert Price03/2018
287197*10^161247-3161249Robert Price05/2020
28727*10^161192-9161193Robert Price10/2015
28732^535415-19161176Stefano Morozzi07/2022
28742^535269-113803161133Enzo Doria09/2014
28752^535205-23295161113Enzo Doria08/2013
2876(49*10^161105+437)/9161106Robert Price09/2021
2877(89^82609+1)/90161036Paul Bourdelais10/2017
28782^534429-19160880Stefano Morozzi07/2022
28792^534359-23229160859Enzo Doria08/2013
288010^160836-1001160836Robert Price10/2022
2881457^60454+60454^457160803Norbert Schneider07/2021
28828*10^160782+53160783Robert Price08/2020
288367^88037-66^88037160763Robert Price10/2013
2884(88*10^160761-637)/9160762Robert Price11/2020
28852^533948-1852559160735Enzo Doria08/2015
28862^533665-23335160650Enzo Doria08/2013
28872^533600+217981160630Enzo Doria01/2024
2888(19*10^160619+77)/3160620Robert Price05/2019
28892^533350-5160555Stefano Morozzi07/2022
2890(38*10^160508+151)/9160509Robert Price03/2022
28913^336353-2^336353160482Mike Oakes10/2007
28922*10^160339-63160340Robert Price01/2022
289324419^36532+36532^24419160293Norbert Schneider10/2023
2894(91*10^160249+11)/3160251Robert Price02/2020
2895(772*10^160239-7)/9160241Robert Price06/2022
2896(2*10^160226+187)/9160226Robert Price06/2022
28972^532253+1868417160225Enzo Doria04/2016
28982^532108-291989160181Enzo Doria07/2015
2899(28*10^160171-79)/3160172Robert Price02/2021
2900(26*10^160166-131)/3160167Robert Price10/2019
290155*10^160145+9160147Robert Price03/2022
2902(17*10^160143+67)/3160144Robert Price01/2019
2903(394^61637-1)/393159977Jinyuan Wang04/2023
2904(19*10^159921-49)/3159922Robert Price05/2019
29052^531110-1853771159881Enzo Doria09/2015
2906(275^65536+53^65536)/2159864Kellen Shenton11/2020
29072^530992-1845299159845Enzo Doria07/2015
29082^530810+25159790Stefano Morozzi04/2021
290925590^36241-36241^25590159753Frank Doornink02/2024
2910(136*10^159736-1)/9159738Serge Batalov12/2014
29112^530417-113833159672Enzo Doria09/2014
29122^530406-69701159669Enzo Doria02/2016
29135*10^159656+41159657Robert Price03/2019
29148*10^159614+29159615Robert Price11/2021
29157^188858-188858^7159604Norbert Schneider05/2018
291628^110278+27159590Alfred Reich02/2024
29177*10^159553-27159554Robert Price11/2022
29183^334409-5*2^334409159554Jon Grantham08/2023
2919(24^115597-1)/23159547Paul Bourdelais09/2017
292025472^36209-36209^25472159540Frank Doornink01/2024
2921(17*10^159438-377)/9159439Robert Price03/2018
2922(203*10^159381+1)/3159383Robert Price03/2020
292332282^35343-35343^32282159361Frank Doornink02/2024
29242^529215+219383159310Enzo Doria02/2024
292589*10^159258-9159260Robert Price05/2020
29262^528944-461315159229Enzo Doria07/2015
2927(13*10^159147+161)/3159148Robert Price11/2018
29282^528620-113879159131Enzo Doria10/2014
292932125^35306-35306^32125159119Frank Doornink02/2024
2930(47*10^159083+259)/9159084Robert Price03/2022
2931(861^54181-1)/860159019Jinyuan Wang11/2023
29322^528000-23307158944Enzo Doria08/2013
2933(29*10^158909+61)/9158910Robert Price08/2018
29342^527817+1876817158889Enzo Doria07/2016
29352^527774-49451158876Enzo Doria10/2015
29362^527745-291553158868Enzo Doria07/2015
2937(91*10^158862+11)/3158864Robert Price02/2020
29382^527644-1856999158837Enzo Doria10/2015
2939(37200^37199-37198^37199)/(2^37199)158822Henri Lifchitz06/2013
2940(17*10^158819+7)/3158820Robert Price06/2023
29412^527573-1863253158816Enzo Doria12/2015
29422^527553-23401158810Enzo Doria08/2013
2943(49*10^158783+437)/9158784Robert Price09/2021
294410^158755+310207158756Patrick De Geest08/2021
294510^158755-50001158755Robert Price08/2020
2946(61*10^158748-619)/9158749Robert Price03/2022
294711^152420-210158730Enzo Doria09/2012
2948(13*10^158694+401)/9158695Robert Price01/2018
29492^527052-69059158659Enzo Doria11/2015
29502^526849-113233158598Enzo Doria07/2014
295124286^36161+36161^24286158579Norbert Schneider08/2023
2952(2^526763-lucasV(1,2,526763)+1)/2158572Mike Oakes11/2016
2953(299*10^158544-17)/3158546Robert Price04/2020
29542^526658-3551158540Yves Minet03/2017
29557*10^158465-11158466Robert Price06/2019
2956(7^187507-3^187507)/4158462Jon Grantham08/2023
29572^526375-23115158455Enzo Doria08/2013
2958(77*10^158407-293)/9158408Robert Price09/2019
295931209^35242-35242^31209158388Frank Doornink01/2024
296032071^35144-35144^32071158363Frank Doornink01/2024
29612^526028-112793158351Enzo Doria07/2014
2962(229*10^158339-1)/3158341Robert Price07/2020
296332042^35123-35123^32042158255Frank Doornink01/2024
29642^525690-9221158249Lelio R Paula01/2013
29652*10^158242-7158243Robert Price10/2015
29662^525667-525667^2158242Henri Lifchitz12/2017
2967(56*10^158230+187)/9158231Robert Price10/2021
296810^158209-7000000001158209Robert Price12/2021
296931050^35207-35207^31050158153Frank Doornink01/2024
29702^525186-1857431158097Enzo Doria10/2015
297131527^35108-35108^31527157940Frank Doornink01/2024
29722^524515-23245157895Enzo Doria08/2013
29732^524499-109087157890Enzo Doria04/2014
29742^524384-219533157856Enzo Doria03/2024
29762^18067*(2^506221+1)-1157827Makoto Morimoto05/2014
29772^524288+189093157827Makoto Morimoto01/2016
29752^524288-164073157827Matthias Baur03/2020
2978(2^(2^19)-9333)/(19*23*463*1213*31973)157814Makoto Morimoto09/2017
2979(10^157792+359)/9157792Serge Batalov12/2014
29802^524154+25157787Stefano Morozzi04/2021
29812^523924+1876591157717Enzo Doria07/2016
2982(17*10^157705+67)/3157706Robert Price01/2019
2983(46^94841+1)/47157696Robert Price01/2014
29842^523774+77839157672Enzo Doria05/2016
29852^523587+2799143157616Enzo Doria04/2016
29862^523496+220141157588Enzo Doria03/2024
29872^523371+1872113157551Enzo Doria05/2016
29888*10^157477+27157478Robert Price09/2021
298932268^34909-34909^32268157397Frank Doornink02/2024
2990(8*10^157368+49)/3157369Robert Price05/2020
2991(82*10^157319+449)/9157320Robert Price11/2019
29922^522535-351457157299Enzo Doria07/2015
299325401^35704-35704^25401157271Frank Doornink01/2024
29942^522226+2799079157206Enzo Doria04/2016
2995(134*10^157191-11)/3157193Robert Price01/2022
29962^522134-1849451157178Enzo Doria08/2015
29979*10^157152+71157153Robert Price08/2020
29984*10^157150+93157151Robert Price08/2018
299931227^34952-34952^31227157093Frank Doornink01/2024
3000(32^104347+5^104347)/37157057Anonymous12/2023


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 27 2024 11:51 (Time in France)

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