PRP Records

Probable Primes Top 10000

(301668 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 ?
27512^629036+1874011189359Enzo Doria06/2016
27522^628930+80779189327Enzo Doria07/2016
2753(134*10^189309-11)/3189311Robert Price01/2022
27549*10^189306-11189307Mischa Rodermond04/2023
27553^396740-396740^3189294Henri Lifchitz07/2024
27562^628582+1179439189223Enzo Doria06/2016
2757(44*10^188999-503)/9189000Robert Price12/2018
2758(16*10^188823+167)/3188824Robert Price06/2019
2759(10^188796+7)/4967/71933188788Alfred Reich08/2021
27602^627037-2785843188757Enzo Doria10/2015
2761(10^188566+7)/311640753181661188552Alfred Reich04/2022
2762(16*10^188457+161)/3188458Robert Price02/2019
2763L(901657)188436Renaud Lifchitz11/2008
2764(19*10^188375+137)/3188376Robert Price03/2022
27652^625651+74213188340Enzo Doria04/2016
27662^625584-460919188320Enzo Doria06/2015
2767(8*10^188308-71)/9188308Serge Batalov11/2022
27685^269399-3^269399-1188302Jon Grantham08/2023
2769(14*10^188218+139)/9188219Robert Price11/2021
277040760^40821-40821^40760188195Norbert Schneider07/2024
2771(10^188164+359)/9188164Serge Batalov12/2014
27722^624481-113611187988Enzo Doria08/2014
2773(2^624389+125582)/2187960Stefano Morozzi09/2019
2774(2^624389+166982)/2187960Stefano Morozzi09/2019
2775(2^624389+179886)/2187960Stefano Morozzi09/2019
2776(2^624387+64466)/2187959Stefano Morozzi09/2019
2777(2^624378+112990)/2187957Stefano Morozzi09/2019
2778(2^624380+161986)/2187957Stefano Morozzi09/2019
2780(2^624376+55762)/2187956Stefano Morozzi09/2019
2779(2^624377+169506)/2187956Stefano Morozzi09/2019
2781(2^624355+80178)/2187950Stefano Morozzi09/2019
2782(2^624351+61350)/2187949Stefano Morozzi09/2019
2783(2^624341+63462)/2187946Stefano Morozzi09/2019
2784(2^624344+135990)/2187946Stefano Morozzi09/2019
2785(2^624344+183898)/2187946Stefano Morozzi09/2019
2787(2^624340+126982)/2187945Stefano Morozzi09/2019
2786(2^624338+196110)/2187945Stefano Morozzi09/2019
2788(2^624337+105162)/2187944Stefano Morozzi09/2019
2789(2^624333+44594)/2187943Stefano Morozzi09/2019
2790(2^624321+88742)/2187940Stefano Morozzi09/2019
2791(2^624324+135178)/2187940Stefano Morozzi09/2019
2792(2^624317+14186)/2187938Stefano Morozzi09/2019
2793(2^624313+24450)/2187937Stefano Morozzi09/2019
2794(2^624309+184590)/2187936Stefano Morozzi09/2019
2796(2^624307+152658)/2187935Stefano Morozzi09/2019
2795(2^624307+185978)/2187935Stefano Morozzi09/2019
2797(2^624303+40814)/2187934Stefano Morozzi09/2019
2798(2^624304+99238)/2187934Stefano Morozzi09/2019
27992^624077-112723187866Enzo Doria07/2014
28002^624008+1874941187846Enzo Doria06/2016
28012^623870+78679187804Enzo Doria05/2016
28022^623714-114035187757Enzo Doria11/2014
28032^623651-1834251187738Enzo Doria07/2015
2804(7*10^187645+53)/3187646Robert Price05/2018
280521650^43269+43269^21650187591Norbert Schneider02/2023
28062^623146+1879609187586Enzo Doria09/2016
2807(401*10^187512+13)/9187514Robert Price09/2021
2808(5*10^187471+91)/3187472Robert Price04/2018
28092^622500+81931187392Enzo Doria08/2016
2810(13*10^187382-157)/9187383Robert Price05/2021
28112^622300-1861739187331Enzo Doria12/2015
2812(22*10^187317-91)/3187318Robert Price02/2022
2813(38*10^187281+349)/9187282Robert Price10/2018
28142^622052+76771187257Enzo Doria05/2016
28152^622005-24091187243Enzo Doria08/2013
28167*10^187205-57187206Robert Price06/2020
28172^621879-351787187205Enzo Doria07/2015
2818(5*10^187168-53)/3187169Robert Price09/2020
2819(23*10^187164-143)/3187165Robert Price12/2019
28202^621700+79411187151Enzo Doria06/2016
28212^621597+39187120Jon Grantham08/2023
2822(7*10^187101+131)/3187102Robert Price06/2020
2823(2*10^187062-71)/3187062Robert Price12/2017
2824V(1118570)187013Serge Batalov07/2024
28252^620929-113203186919Enzo Doria07/2014
282610^186842+168223186843Patrick De Geest07/2018
282710^186842-8001186842Robert Price03/2018
2828V(1117640)/13411681/26823361/575709775681/989889277441186814Serge Batalov07/2024
28292^620347-1777186744Lelio R Paula07/2013
2830(11*10^186659+133)/9186660Robert Price04/2022
283111^179143-4170186559Enzo Doria12/2012
2832(13^186535)%(10^186535)186535Henri Lifchitz05/2025
2833(5^266863+1)/6186529Paul Bourdelais07/2010
28342*10^186517+33186518Robert Price11/2021
28352^619297-2792353186427Enzo Doria02/2016
2836(49*10^186409+383)/9186410Robert Price04/2019
28372^618940-460139186320Enzo Doria06/2015
28382^618046+74179186051Enzo Doria04/2016
28393*10^186019+11186020Robert Price07/2018
2840(16*10^185978-19)/3185979Robert Price02/2019
2841(22*10^185950-7)/3185951Robert Price12/2022
28422*10^185930-3185931Robert Price07/2015
2843(82^97151+1)/83185928Paul Bourdelais10/2017
28444*10^185905+91185906Robert Price08/2018
2845(34*10^185902-601)/9185903Robert Price07/2022
2846(19*10^185873+131)/3185874Robert Price06/2020
2847(37*10^185811+377)/9185812Robert Price11/2018
28482^617250+9385185811Lelio R Paula07/2013
28492^617130+9185775Stefano Morozzi05/2021
285039^116749+2185756Robert Price04/2015
28512^616924-39719185713Enzo Doria09/2015
28522^616712+1867621185649Enzo Doria04/2016
2853(3^388897+2^388897)/5185551Jean-Louis Charton09/2011
28548*10^185529-67185530Robert Price08/2019
2855(5*10^185520-11)/3185521Tyler Busby02/2023
28565*2^616124+3185473Jon Grantham07/2023
28572^615916+26791185410Enzo Doria12/2023
28584*10^185355+9185356Robert Price05/2015
2859(16*10^185347+89)/3185348Robert Price03/2021
286040247^40247-56^56185327Henri Lifchitz08/2024
28612^615622+76639185321Enzo Doria05/2016
28622^615591+1879223185312Enzo Doria08/2016
28632^615587+217013185311Enzo Doria12/2023
28642^615503+1876643185285Enzo Doria07/2016
28655^265007-4^265007185232Jean-Louis Charton02/2013
2866(4*10^185221-91)/3185222Robert Price03/2018
2867(7*10^185221+131)/3185222Robert Price06/2020
2868(62*10^185216-413)/9185217Robert Price09/2021
2869(232*10^185180+17)/3185182Robert Price04/2021
287056*10^185139-3185141Robert Price03/2020
2871(28*10^185105+47)/3185106Robert Price02/2021
28722^614783-2790097185069Enzo Doria12/2015
28732^614745-29323185057Enzo Doria07/2015
2874(((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840185052Serge Batalov07/2013
2875(49*10^184993-67)/9184994Robert Price03/2019
2876(5*10^184954-191)/3184955Robert Price05/2021
2877(14*10^184950+211)/9184951Robert Price04/2018
28782^614360+215221184941Enzo Doria11/2023
28792^614315+81353184928Enzo Doria08/2016
28802^614294-1849961184921Enzo Doria08/2015
28812^614266+1877809184913Enzo Doria08/2016
2882(185*10^184878-11)/3184880Robert Price10/2020
288391*10^184867-9184869Robert Price06/2021
288439803^40170-40170^39803184779Norbert Schneider05/2024
2885(14789^44521-1)/(14789^211-1)184770Ryan Propper11/2023
2886(85*10^184768+77)/9184769Robert Price07/2022
28872^613715-1860727184747Enzo Doria11/2015
2888(4*10^184730+89)/3184731Robert Price08/2021
28892*10^184723+41184724Robert Price05/2018
2890(49*10^184703+293)/9184704Robert Price03/2021
28912^613487-349987184678Enzo Doria07/2015
2892(95^93377+1)/96184672Paul Bourdelais11/2017
289314^161089-161089^14184629Serge Batalov05/2016
289440008^40109-40109^40008184588Norbert Schneider05/2024
28952^613033-114621184542Enzo Doria05/2015
28963*2^612759+5184460Jon Grantham07/2023
28972^612587+213413184408Enzo Doria09/2023
2898(9^193247+1)/10184404Paul Bourdelais02/2010
28992^612424+212341184358Enzo Doria08/2023
29002^612341-1604809184334Enzo Doria05/2015
2901(11*10^184308-161)/3184309Robert Price11/2021
2902(2^611999-1)/18464214225958267477777390354183184199Dario Alpern06/2017
2903(14*10^184150+37)/3184151Robert Price12/2018
29042^611731-4837184150Yves Minet08/2018
29053*10^184124-7184125Robert Price08/2015
29062^611644+29371184124Enzo Doria02/2024
29079*10^184122-11184123Mischa Rodermond04/2023
29082^611628-24537184119Enzo Doria08/2013
29093*10^184110+13184111Robert Price07/2018
2910(14280^44521-1)/(14280^211-1)184097Ryan Propper11/2023
2911(194*10^184093+1)/3184095Robert Price01/2022
29122^611460+71881184068Enzo Doria04/2016
29134*10^184004-63184005Robert Price10/2018
29142^611111+84083183963Boyan Hu05/2024
29152^610982-1867301183924Enzo Doria03/2016
2916(10^183917+1)/11/9952852373183906Alfred Reich02/2024
29173*10^183872-49183873Robert Price07/2018
29182^610597+1178897183809Enzo Doria05/2016
2919(8*10^183773-269)/9183773Robert Price09/2021
2920(65*10^183768-29)/9183769Robert Price01/2021
2921(17*10^183764+31)/3183765Robert Price01/2019
2922(28*10^183760-1)/9183761Serge Batalov10/2014
29232^610401+1277183750Lelio R Paula07/2013
29242^610356-1849019183736Enzo Doria08/2015
2925(63^102103+1)/64183717Paul Bourdelais10/2017
292623*10^183710-7183712Robert Price02/2020
2927(2^610289+1)/(3*528882550291)183704Gord Palameta08/2018
2928(4*10^183659+149)/9183659Robert Price04/2018
2929(4*10^183657+41)/9183657Serge Batalov11/2022
2930(11^176327-1)/31738870183619Paul Vanderveen05/2025
29317*10^183596+39183597Robert Price01/2023
29322^609846-1834251183582Enzo Doria07/2015
293310^183546+1547323183547Patrick De Geest02/2021
293510^183546-800000001183546Robert Price09/2020
293410^183546-584297183546Patrick De Geest02/2021
29367*10^183511+39183512Robert Price01/2023
2937(23*10^183477-71)/3183478Robert Price07/2020
293811^176176-240183469Enzo Doria11/2012
2939(41^113749+1)/42183451Paul Bourdelais11/2017
29406*10^183429+53183430Robert Price05/2020
2941(28*10^183403+191)/3183404Robert Price02/2020
2942U(1096855)183383Serge Batalov07/2024
2943(5^262337-1)/363486427756606700767551233751524443601036183325Paul Vanderveen05/2025
2944(101^91463+1)/102183320Paul Bourdelais11/2017
29452^608965-113989183317Enzo Doria10/2014
2946A005165(43592)183312Serge Batalov07/2017
2947(61*10^183294+119)/9183295Robert Price05/2019
29482^608814-461261183272Enzo Doria06/2015
2949(163*10^183227-1)/9183229Serge Batalov12/2014
29502^608541-608541^2183190Henri Lifchitz02/2018
29512^608293+143807183115Enzo Doria10/2016
29522^608164-462419183076Enzo Doria08/2015
29532^607950-1862303183012Enzo Doria12/2015
29545*3^383376+2^383376182918Jon Grantham08/2023
2955(46*10^182896+683)/9182897Robert Price03/2019
2956(2*10^182787+73)/3182787Robert Price09/2020
29572^607101+1871987182756Enzo Doria05/2016
29582^606869-69175182686Enzo Doria11/2015
29598*10^182671+71182672Robert Price05/2022
2960(23*10^182666-71)/3182667Robert Price07/2020
29613*10^182614-11182615Robert Price07/2018
29622^606560-357182593Enzo Doria05/2014
296366*10^182420+7182422Robert Price07/2020
29642^605687+1866983182330Enzo Doria03/2016
29652^605655-114445182321Enzo Doria02/2015
296694*10^182291-3182293Robert Price05/2020
2967(20^140053+1)/21182212Paul Bourdelais04/2010
2968(14*10^182177-221)/9182178Robert Price04/2018
29692^605174-112751182176Enzo Doria06/2014
2970(905^61609-1)/904182154Anonymous05/2024
29712^604761+1874507182052Enzo Doria06/2016
29722^604705+1871957182035Enzo Doria05/2016
2973(14*10^182000+229)/9182001Robert Price03/2018
2974(10^181996+41)/3181996Robert Price12/2017
2975(17*10^181979+91)/9181980Robert Price02/2022
2976(10^181960+3)/7181960Jinyuan Wang11/2024
2977(5*10^181950-101)/3181951Robert Price04/2018
29782^603915+75233181797Enzo Doria04/2016
297939470^39537+39537^39470181723Norbert Schneider12/2022
2980(10^181710+7)/563747/2019847181698Alfred Reich08/2021
29817*10^181594-57181595Robert Price06/2020
29828*10^181580+29181581Robert Price11/2021
2983(83*10^181544+61)/9181545Serge Batalov01/2023
2984(2*10^181457+7)/9181457Rytis Slatkevicius01/2023
29853*10^181445+23181446Robert Price03/2022
2986(194*10^181369-11)/3181371Robert Price09/2020
298711^174145-360181354Enzo Doria10/2012
29882^602351-396765181326Enzo Doria08/2013
29896*10^181306+17181307Robert Price04/2019
2990(353^71143-1)/352181254Anonymous04/2024
2991(286*10^181220-1)/3181222Robert Price11/2020
29922^601957-113833181208Enzo Doria09/2014
299366^99581-65^99581181193Robert Price09/2013
299410^181182+383973181183Patrick De Geest04/2016
299510^181182-21181182Serge Batalov12/2014
2996(797*10^181171-41)/9181173Robert Price04/2022
29972^601722+74209181137Enzo Doria08/2023
2998(5*10^181127-29)/3181128Robert Price03/2018
29992^601521-29143181076Enzo Doria07/2015
30002^601442-2797811181053Enzo Doria04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 20 2025 15:18 (Time in France)

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