PRP Records

Probable Primes Top 10000

(294627 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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(301*10^165082+23)/9165084Robert Price06/2021
2752(23*10^165060-83)/3165061Robert Price08/2019
27537*10^165023-27165024Robert Price11/2022
2754(76*10^164984+77)/9164985Robert Price10/2019
275531058^36715-36715^31058164931Frank Doornink01/2024
2756(4*10^164929-211)/9164929Robert Price03/2022
275710^164878-500001164878Robert Price03/2022
27589*10^164791-89164792Robert Price04/2020
27592^547178-1856501164717Enzo Doria10/2015
276011^158160-60164707Enzo Doria07/2012
2761(26*10^164643-167)/3164644Robert Price10/2019
2762(10^164643+83)/3164643Robert Price08/2021
27632^546398-59201164483Enzo Doria10/2015
27642^546332-114893164463Enzo Doria05/2015
276532003^36504-36504^32003164458Frank Doornink01/2024
2766(65*10^164427+277)/9164428Robert Price08/2021
27672^545958+1876189164350Enzo Doria07/2016
27682^545878-49841164326Enzo Doria10/2015
2769(10^164284+77)/3164284Robert Price01/2018
27702^545668-4019164263Yves Minet04/2017
277110^164216+780639164217Patrick De Geest08/2021
277310^164216-50000000001164216Robert Price12/2020
277210^164216-891051164216Patrick De Geest08/2021
2774(13*53^238539*617^9)/10^247183164151Hans Havermann07/2017
2775(16*10^164122+197)/3164123Robert Price04/2019
27762^545185+76757164118Enzo Doria05/2016
27772^545076-114329164085Enzo Doria01/2015
2778(2*10^164043-143)/3164043Robert Price03/2018
2779(33085^36481-1)/(33085^191-1)164018Ryan Propper11/2023
2780(29^112153+1)/30164011Lelio R Paula03/2017
27812^544757+1874777163989Enzo Doria06/2016
27822^544723+211193163978Enzo Doria08/2023
27832^544444-457199163894Enzo Doria01/2015
2784(32804^36481-1)/(32804^191-1)163883Ryan Propper11/2023
27852^544264-343529163840Enzo Doria07/2015
27867*10^163780+9163781Robert Price09/2015
27872^543989+2793047163758Enzo Doria02/2016
2788(28*10^163709+113)/3163710Robert Price03/2020
2789(2013^49729-1)/(2013^223-1)163561Ryan Propper11/2023
2790(23*10^163523+301)/9163524Robert Price06/2021
2791(68*10^163521-329)/9163522Robert Price03/2021
279235820^35899+35899^35820163489Norbert Schneider11/2021
27932^542870-69551163421Enzo Doria12/2015
27942^542502+24799163310Enzo Doria10/2023
27952^542395+72533163278Enzo Doria04/2016
27962^542258+216949163236Enzo Doria12/2023
27972^542072-3683163180Yves Minet03/2017
2798fibonacci(780566)-4163129Jon Grantham08/2023
2799(682*10^163106-7)/9163108Robert Price08/2021
28002^541779-1867357163092Enzo Doria04/2016
2801(29*10^163056+313)/9163057Robert Price04/2021
28022^541476+214743163001Enzo Doria11/2023
28038*10^162924+9162925Robert Price12/2015
28042^540905+81557162829Enzo Doria08/2016
28052^540628-2939162746Yves Minet09/2014
2806919^54919-918^54919162743Jean-Louis Charton01/2013
2807(203*10^162689+1)/3162691Robert Price03/2020
28083*10^162620-59162621Robert Price09/2018
28092^540180+26791162611Enzo Doria12/2023
28103^340694-112960162553Enzo Doria07/2014
28112^539807-114081162499Enzo Doria12/2014
2812414^62093+62093^414162498Norbert Schneider03/2022
28132^539654-114893162453Enzo Doria05/2015
28149*10^162449-71162450Robert Price11/2020
28152^539617-1851583162441Enzo Doria08/2015
2816(509*10^162422+31)/9162424Robert Price08/2022
2817(91*10^162410+11)/3162412Robert Price02/2020
28182^539346+81049162360Enzo Doria07/2016
28192^539220-115499162322Enzo Doria07/2015
28202^539217-113713162321Enzo Doria09/2014
28219^170099-8^170099162316Jean-Louis Charton05/2005
28224*10^162263-39162264Robert Price09/2020
282331243^36098-36098^31243162252Frank Doornink01/2024
282431987^36000-36000^31987162180Frank Doornink01/2024
2825(115*10^162153-1)/3162155Serge Batalov12/2014
2826(10^162138+11)/3162138Serge Batalov07/2015
2827(61*10^162100-403)/9162101Robert Price10/2021
28282^538473-112723162097Enzo Doria06/2014
28292^538157+79337162002Enzo Doria06/2016
28302^538136-114749161996Enzo Doria05/2015
28312^538104+1531161986Lelio R Paula01/2013
2832(9*29^110727-1199)/14161927Curtis Bright05/2015
2833((2^179294-1)^3+2)/11161918Serge Batalov03/2023
283431198^36027-36027^31198161910Frank Doornink01/2024
28352^537815-22737161899Enzo Doria07/2013
28362^537804-39839161896Enzo Doria09/2015
2837(754*10^161816-7)/9161818Robert Price05/2020
28382^537461+29867161792Enzo Doria03/2024
28392^537458-59201161791Enzo Doria10/2015
28402*10^161766+51161767Robert Price05/2018
2841(7*10^161760+131)/3161761Robert Price06/2020
28422^537209-49849161717Enzo Doria10/2015
2843(58*10^161691+329)/9161692Robert Price05/2019
284423*10^161668-3161670Robert Price10/2021
28452^536937+1879397161635Enzo Doria09/2016
28463*2^536868-5161614Jon Grantham07/2023
284734*10^161593-9161595Robert Price06/2020
2848(31*10^161582-1)/3161584Robert Price02/2020
284924494^36813+36813^24494161575Norbert Schneider11/2023
28502^536569-22881161524Enzo Doria07/2013
2851(46*10^161505+593)/9161506Robert Price04/2022
285210^161253+573493161254Patrick De Geest07/2018
285310^161253-8001161253Robert Price03/2018
285497*10^161247-3161249Robert Price05/2020
28557*10^161192-9161193Robert Price10/2015
28562^535415-19161176Stefano Morozzi07/2022
28572^535269-113803161133Enzo Doria09/2014
28582^535205-23295161113Enzo Doria08/2013
2859(49*10^161105+437)/9161106Robert Price09/2021
2860(89^82609+1)/90161036Paul Bourdelais10/2017
28612^534429-19160880Stefano Morozzi07/2022
28622^534359-23229160859Enzo Doria08/2013
286310^160836-1001160836Robert Price10/2022
2864457^60454+60454^457160803Norbert Schneider07/2021
28658*10^160782+53160783Robert Price08/2020
286667^88037-66^88037160763Robert Price10/2013
2867(88*10^160761-637)/9160762Robert Price11/2020
28682^533948-1852559160735Enzo Doria08/2015
28692^533665-23335160650Enzo Doria08/2013
28702^533600+217981160630Enzo Doria01/2024
2871(19*10^160619+77)/3160620Robert Price05/2019
28722^533350-5160555Stefano Morozzi07/2022
2873(38*10^160508+151)/9160509Robert Price03/2022
28743^336353-2^336353160482Mike Oakes10/2007
28752*10^160339-63160340Robert Price01/2022
287624419^36532+36532^24419160293Norbert Schneider10/2023
2877(91*10^160249+11)/3160251Robert Price02/2020
2878(772*10^160239-7)/9160241Robert Price06/2022
2879(2*10^160226+187)/9160226Robert Price06/2022
28802^532253+1868417160225Enzo Doria04/2016
28812^532108-291989160181Enzo Doria07/2015
2882(28*10^160171-79)/3160172Robert Price02/2021
2883(26*10^160166-131)/3160167Robert Price10/2019
288455*10^160145+9160147Robert Price03/2022
2885(17*10^160143+67)/3160144Robert Price01/2019
2886(394^61637-1)/393159977Jinyuan Wang04/2023
2887(19*10^159921-49)/3159922Robert Price05/2019
28882^531110-1853771159881Enzo Doria09/2015
2889(275^65536+53^65536)/2159864Kellen Shenton11/2020
28902^530992-1845299159845Enzo Doria07/2015
28912^530810+25159790Stefano Morozzi04/2021
289225590^36241-36241^25590159753Frank Doornink02/2024
2893(136*10^159736-1)/9159738Serge Batalov12/2014
28942^530417-113833159672Enzo Doria09/2014
28952^530406-69701159669Enzo Doria02/2016
28965*10^159656+41159657Robert Price03/2019
28978*10^159614+29159615Robert Price11/2021
28987^188858-188858^7159604Norbert Schneider05/2018
289928^110278+27159590Alfred Reich02/2024
29007*10^159553-27159554Robert Price11/2022
29013^334409-5*2^334409159554Jon Grantham08/2023
2902(24^115597-1)/23159547Paul Bourdelais09/2017
290325472^36209-36209^25472159540Frank Doornink01/2024
2904(17*10^159438-377)/9159439Robert Price03/2018
2905(203*10^159381+1)/3159383Robert Price03/2020
290632282^35343-35343^32282159361Frank Doornink02/2024
29072^529215+219383159310Enzo Doria02/2024
290889*10^159258-9159260Robert Price05/2020
29092^528944-461315159229Enzo Doria07/2015
2910(13*10^159147+161)/3159148Robert Price11/2018
29112^528620-113879159131Enzo Doria10/2014
291232125^35306-35306^32125159119Frank Doornink02/2024
2913(47*10^159083+259)/9159084Robert Price03/2022
2914(861^54181-1)/860159019Jinyuan Wang11/2023
29152^528000-23307158944Enzo Doria08/2013
2916(29*10^158909+61)/9158910Robert Price08/2018
29172^527817+1876817158889Enzo Doria07/2016
29182^527774-49451158876Enzo Doria10/2015
29192^527745-291553158868Enzo Doria07/2015
2920(91*10^158862+11)/3158864Robert Price02/2020
29212^527644-1856999158837Enzo Doria10/2015
2922(37200^37199-37198^37199)/(2^37199)158822Henri Lifchitz06/2013
2923(17*10^158819+7)/3158820Robert Price06/2023
29242^527573-1863253158816Enzo Doria12/2015
29252^527553-23401158810Enzo Doria08/2013
2926(49*10^158783+437)/9158784Robert Price09/2021
292710^158755+310207158756Patrick De Geest08/2021
292810^158755-50001158755Robert Price08/2020
2929(61*10^158748-619)/9158749Robert Price03/2022
293011^152420-210158730Enzo Doria09/2012
2931(13*10^158694+401)/9158695Robert Price01/2018
29322^527052-69059158659Enzo Doria11/2015
29332^526849-113233158598Enzo Doria07/2014
293424286^36161+36161^24286158579Norbert Schneider08/2023
2935(2^526763-lucasV(1,2,526763)+1)/2158572Mike Oakes11/2016
2936(299*10^158544-17)/3158546Robert Price04/2020
29372^526658-3551158540Yves Minet03/2017
29387*10^158465-11158466Robert Price06/2019
2939(7^187507-3^187507)/4158462Jon Grantham08/2023
29402^526375-23115158455Enzo Doria08/2013
2941(77*10^158407-293)/9158408Robert Price09/2019
294231209^35242-35242^31209158388Frank Doornink01/2024
294332071^35144-35144^32071158363Frank Doornink01/2024
29442^526028-112793158351Enzo Doria07/2014
2945(229*10^158339-1)/3158341Robert Price07/2020
294632042^35123-35123^32042158255Frank Doornink01/2024
29472^525690-9221158249Lelio R Paula01/2013
29482*10^158242-7158243Robert Price10/2015
29492^525667-525667^2158242Henri Lifchitz12/2017
2950(56*10^158230+187)/9158231Robert Price10/2021
295110^158209-7000000001158209Robert Price12/2021
295231050^35207-35207^31050158153Frank Doornink01/2024
29532^525186-1857431158097Enzo Doria10/2015
295431527^35108-35108^31527157940Frank Doornink01/2024
29552^524515-23245157895Enzo Doria08/2013
29562^524499-109087157890Enzo Doria04/2014
29572^524384-219533157856Enzo Doria03/2024
29592^18067*(2^506221+1)-1157827Makoto Morimoto05/2014
29602^524288+189093157827Makoto Morimoto01/2016
29582^524288-164073157827Matthias Baur03/2020
2961(2^(2^19)-9333)/(19*23*463*1213*31973)157814Makoto Morimoto09/2017
2962(10^157792+359)/9157792Serge Batalov12/2014
29632^524154+25157787Stefano Morozzi04/2021
29642^523924+1876591157717Enzo Doria07/2016
2965(17*10^157705+67)/3157706Robert Price01/2019
2966(46^94841+1)/47157696Robert Price01/2014
29672^523774+77839157672Enzo Doria05/2016
29682^523587+2799143157616Enzo Doria04/2016
29692^523496+220141157588Enzo Doria03/2024
29702^523371+1872113157551Enzo Doria05/2016
29718*10^157477+27157478Robert Price09/2021
297232268^34909-34909^32268157397Frank Doornink02/2024
2973(8*10^157368+49)/3157369Robert Price05/2020
2974(82*10^157319+449)/9157320Robert Price11/2019
29752^522535-351457157299Enzo Doria07/2015
297625401^35704-35704^25401157271Frank Doornink01/2024
29772^522226+2799079157206Enzo Doria04/2016
2978(134*10^157191-11)/3157193Robert Price01/2022
29792^522134-1849451157178Enzo Doria08/2015
29809*10^157152+71157153Robert Price08/2020
29814*10^157150+93157151Robert Price08/2018
298231227^34952-34952^31227157093Frank Doornink01/2024
2983(32^104347+5^104347)/37157057Anonymous12/2023
2984fibonacci(751442)-2157042Jon Grantham08/2023
29852^521401-29593156958Enzo Doria08/2015
29867*10^156956+87156957Robert Price07/2019
29872^521348-23397156942Enzo Doria08/2013
298810^156902+34509156903Patrick De Geest08/2021
299010^156902-80000001156902Robert Price04/2021
298910^156902-69789156902Patrick De Geest08/2021
2991(98^78797+1)/99156901Paul Bourdelais12/2017
299265^86522+64156857Lelio R Paula04/2016
29938^173687-7^173687156855Jean-Louis Charton09/2004
29942^520977-1858183156830Enzo Doria10/2015
2995(8*10^156718-101)/3156719Robert Price08/2018
2996(10^156640+7)/53156639Alfred Reich07/2021
29972^520314-1849481156631Enzo Doria08/2015
2998(16*10^156563-637)/9156564Robert Price09/2022
2999(13*10^156522+89)/3156523Robert Price09/2018
3000(2^519925-5)/3156513Stefano Morozzi08/2022


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 12 2024 13:37 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!