PRP Records

Probable Primes Top 10000

(295149 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 ?
3001(861^54181-1)/860159019Jinyuan Wang11/2023
30022^528000-23307158944Enzo Doria08/2013
3003(29*10^158909+61)/9158910Robert Price08/2018
30042^527817+1876817158889Enzo Doria07/2016
30052^527774-49451158876Enzo Doria10/2015
30062^527745-291553158868Enzo Doria07/2015
3007(91*10^158862+11)/3158864Robert Price02/2020
30082^527644-1856999158837Enzo Doria10/2015
3009(37200^37199-37198^37199)/(2^37199)158822Henri Lifchitz06/2013
3010(17*10^158819+7)/3158820Robert Price06/2023
30112^527573-1863253158816Enzo Doria12/2015
30122^527553-23401158810Enzo Doria08/2013
3013(49*10^158783+437)/9158784Robert Price09/2021
301410^158755+310207158756Patrick De Geest08/2021
301510^158755-50001158755Robert Price08/2020
3016(61*10^158748-619)/9158749Robert Price03/2022
301711^152420-210158730Enzo Doria09/2012
3018(13*10^158694+401)/9158695Robert Price01/2018
30192^527052-69059158659Enzo Doria11/2015
30202^526849-113233158598Enzo Doria07/2014
302124286^36161+36161^24286158579Norbert Schneider08/2023
3022(2^526763-lucasV(1,2,526763)+1)/2158572Mike Oakes11/2016
3023(299*10^158544-17)/3158546Robert Price04/2020
30242^526658-3551158540Yves Minet03/2017
30257*10^158465-11158466Robert Price06/2019
3026(7^187507-3^187507)/4158462Jon Grantham08/2023
30272^526375-23115158455Enzo Doria08/2013
3028(77*10^158407-293)/9158408Robert Price09/2019
302931209^35242-35242^31209158388Frank Doornink01/2024
303032071^35144-35144^32071158363Frank Doornink01/2024
30312^526028-112793158351Enzo Doria07/2014
3032(229*10^158339-1)/3158341Robert Price07/2020
303332042^35123-35123^32042158255Frank Doornink01/2024
30342^525690-9221158249Lelio R Paula01/2013
30352*10^158242-7158243Robert Price10/2015
30362^525667-525667^2158242Henri Lifchitz12/2017
3037(56*10^158230+187)/9158231Robert Price10/2021
303810^158209-7000000001158209Robert Price12/2021
303931050^35207-35207^31050158153Frank Doornink01/2024
30402^525186-1857431158097Enzo Doria10/2015
304131527^35108-35108^31527157940Frank Doornink01/2024
30422^524515-23245157895Enzo Doria08/2013
30432^524499-109087157890Enzo Doria04/2014
30442^524384-219533157856Enzo Doria03/2024
30462^18067*(2^506221+1)-1157827Makoto Morimoto05/2014
30472^524288+189093157827Makoto Morimoto01/2016
30452^524288-164073157827Matthias Baur03/2020
3048(2^(2^19)-9333)/(19*23*463*1213*31973)157814Makoto Morimoto09/2017
3049(10^157792+359)/9157792Serge Batalov12/2014
30502^524154+25157787Stefano Morozzi04/2021
30512^523924+1876591157717Enzo Doria07/2016
3052(17*10^157705+67)/3157706Robert Price01/2019
3053(46^94841+1)/47157696Robert Price01/2014
30542^523774+77839157672Enzo Doria05/2016
30552^523587+2799143157616Enzo Doria04/2016
30562^523496+220141157588Enzo Doria03/2024
30572^523371+1872113157551Enzo Doria05/2016
30588*10^157477+27157478Robert Price09/2021
305932268^34909-34909^32268157397Frank Doornink02/2024
3060(8*10^157368+49)/3157369Robert Price05/2020
3061(82*10^157319+449)/9157320Robert Price11/2019
30622^522535-351457157299Enzo Doria07/2015
306325401^35704-35704^25401157271Frank Doornink01/2024
30642^522226+2799079157206Enzo Doria04/2016
3065(134*10^157191-11)/3157193Robert Price01/2022
30662^522134-1849451157178Enzo Doria08/2015
30679*10^157152+71157153Robert Price08/2020
30684*10^157150+93157151Robert Price08/2018
306931227^34952-34952^31227157093Frank Doornink01/2024
3070(32^104347+5^104347)/37157057Anonymous12/2023
3071fibonacci(751442)-2157042Jon Grantham08/2023
30722^521401-29593156958Enzo Doria08/2015
30737*10^156956+87156957Robert Price07/2019
30742^521348-23397156942Enzo Doria08/2013
307510^156902+34509156903Patrick De Geest08/2021
307710^156902-80000001156902Robert Price04/2021
307610^156902-69789156902Patrick De Geest08/2021
3078(98^78797+1)/99156901Paul Bourdelais12/2017
307965^86522+64156857Lelio R Paula04/2016
30808^173687-7^173687156855Jean-Louis Charton09/2004
30812^520977-1858183156830Enzo Doria10/2015
3082(8*10^156718-101)/3156719Robert Price08/2018
3083(10^156640+7)/53156639Alfred Reich07/2021
30842^520314-1849481156631Enzo Doria08/2015
3085(16*10^156563-637)/9156564Robert Price09/2022
3086(13*10^156522+89)/3156523Robert Price09/2018
3088(2^(6*86654+1)-5)/3156513Kevin Acres12/2013
3087(2^519925-5)/3156513Stefano Morozzi08/2022
3089(4*10^156501+119)/3156502Robert Price12/2021
3090(83*10^156476-101)/9156477Robert Price08/2021
30913*10^156435-97156436Robert Price07/2018
3092(8*10^156371-77)/3156372Robert Price07/2018
309353^90679-52^90679156356Robert Price01/2013
309431267^34782-34782^31267156349Frank Doornink01/2024
3095(418*10^156309-31)/9156311Robert Price05/2022
30962^519106-59141156267Enzo Doria10/2015
309725929^35404-35404^25929156266Frank Doornink03/2024
30982^519053+6077156251Enzo Doria02/2016
309931199^34764-34764^31199156235Frank Doornink01/2024
31002^518968-1860989156225Enzo Doria11/2015
3101(25*10^156221-7)/9156222Robert Price05/2018
31022^518931-2782297156214Enzo Doria09/2015
31032^518608-2939156117Yves Minet09/2014
310410*27^109005+697156027Curtis Bright05/2015
3105(49*10^155933-319)/9155934Robert Price10/2021
31062^517967-113485155924Enzo Doria08/2014
3107(103*10^155904+17)/3155906Robert Price08/2020
3108(8*10^155887-719)/9155887Robert Price03/2021
31092^517789+29231155871Enzo Doria02/2024
31104*10^155853-39155854Robert Price09/2020
31112^517698+4429155843Lelio R Paula01/2013
311232015^34584-34584^32015155814Frank Doornink01/2024
31132^517543-113257155796Enzo Doria07/2014
3114(14*10^155740-143)/3155741Robert Price11/2018
311531959^34564-34564^31959155697Frank Doornink01/2024
311631^104309-30^104309155563Henri Lifchitz08/2013
31172^516742-39851155555Enzo Doria09/2015
3118(22*10^155543+47)/3155544Robert Price06/2021
3119(19*10^155504+131)/3155505Robert Price06/2020
31207*10^155496+61155497Robert Price08/2019
31212^516440+1878421155464Enzo Doria08/2016
312226012^35173-35173^26012155295Frank Doornink03/2024
31232^515863-1867237155291Enzo Doria03/2016
31242^515786-461861155268Enzo Doria07/2015
31252^515644-113247155225Enzo Doria07/2014
3126(7*10^155203+107)/3155204Robert Price02/2018
312710^155163+206871155164Patrick De Geest05/2021
312810^155163-40001155163Robert Price01/2021
3129(17*10^155133-89)/9155134Robert Price07/2018
313026024^35131-35131^26024155117Frank Doornink03/2024
31312^515249+214457155106Enzo Doria10/2023
31322^515227-114997155099Enzo Doria06/2015
313326510^35061-35061^26510155090Frank Doornink03/2024
3135EPrime(155025)155025Eric W. Weisstein10/2010
3134(14*10^155024-221)/9155025Robert Price04/2018
3136(4*10^155022+173)/3155023Robert Price02/2018
3137(266*10^154897+1)/3154899Robert Price04/2020
3138(115*10^154869-1)/3154871Serge Batalov12/2014
3139(86*10^154853-221)/9154854Robert Price09/2019
31402^514361+78167154839Enzo Doria05/2016
31412^514281-115033154815Enzo Doria06/2015
314225701^35104-35104^25701154807Frank Doornink02/2024
31432^514194-3311154788Yves Minet12/2014
314425930^35067-35067^25930154779Frank Doornink03/2024
3145(14*10^154773+37)/3154774Robert Price12/2018
3146(16*10^154748+131)/3154749Robert Price03/2022
31476*10^154742-31154743Robert Price07/2020
3148(14*10^154645+139)/9154646Robert Price11/2021
31492^513690+216949154637Enzo Doria12/2023
31505*10^154618-79154619Robert Price03/2021
3151(167*10^154595+1)/3154597Robert Price04/2021
31522^513437+1879337154560Enzo Doria09/2016
31532^513306-113201154521Enzo Doria07/2014
315426415^34942-34942^26415154509Frank Doornink03/2024
315518^120818+19^120818-2154497Harsh Aggarwal05/2024
3156(10^154494-13)/3154494Robert Price12/2017
315723462^35343+35343^23462154462Norbert Schneider04/2023
31582^513042-113787154442Enzo Doria09/2014
3159(151*10^154434-7)/9154436Robert Price01/2020
3160(118*10^154428+11)/3154430Robert Price03/2022
31612^512987+29153154425Enzo Doria02/2024
3162(14*10^154413+139)/9154414Robert Price11/2021
3163(77*10^154389-149)/9154390Robert Price03/2022
316432184^34247-34247^32184154374Frank Doornink02/2024
316510^154359+49154360Robert Price02/2023
31662^512628-114053154317Enzo Doria11/2014
31672^512529-49783154287Enzo Doria10/2015
3168(355573#+6991)/(6991*2031599)154285Makoto Morimoto06/2019
31692^512315-115297154223Enzo Doria06/2015
3170(47*10^154221+241)/9154222Robert Price06/2022
3171(7*10^154211+173)/9154211Robert Price01/2022
31722^512243+22703154201Enzo Doria09/2023
31732^512168+79561154178Enzo Doria06/2016
3174(77*10^154175+67)/9154176Robert Price12/2021
3175(59*19^120562-5)/18154170Anonymous12/2023
3176(5*10^154158-311)/9154158Robert Price12/2021
317727169^34758-34758^27169154120Frank Doornink01/2024
3178(89*10^154103-737)/9154104Robert Price01/2022
31792^511857+23327154085Enzo Doria10/2023
31804*10^154078-57154079Robert Price10/2018
318126242^34863-34863^26242154060Frank Doornink03/2024
3182(355049#+1859)/(11*13*10148891*62587751)154051Makoto Morimoto06/2019
31837*10^154038-57154039Robert Price06/2020
31842^511658-114371154025Enzo Doria02/2015
3185(57^87719+1)/58154022Paul Bourdelais11/2017
31862^511580-1846679154001Enzo Doria07/2015
3187(259*10^153998-1)/3154000Robert Price12/2020
31882^511541-113713153990Enzo Doria09/2014
318949958^32768+49957^32768153965Kellen Shenton11/2020
319010^153935+970801153936Patrick De Geest05/2021
319110^153935-1000001153935Robert Price08/2020
3192(16*10^153868-73)/3153869Robert Price07/2020
31939*10^153851-67153852Robert Price11/2020
31942^511077-112723153850Enzo Doria06/2014
319569^83653-68^83653153826Robert Price12/2013
31962^510963-113707153816Enzo Doria09/2014
3197(154*10^153810-1)/9153812Serge Batalov12/2014
3198(181*25^109991-75077)/8153763Curtis Bright05/2015
31992*10^153746-3153747Robert Price07/2015
32002^510626+1179379153714Enzo Doria05/2016
3201(7*10^153664+113)/3153665Robert Price02/2018
32022^510448+24991153661Enzo Doria11/2023
32032^510420+81121153652Enzo Doria07/2016
3204(197*7^181761-1)/2153608Karsten Bonath05/2017
32052^509894-459161153494Enzo Doria05/2015
3206(74*10^153489+673)/9153490Robert Price02/2022
3207(49*10^153484-211)/9153485Robert Price06/2022
32082^509841+71657153478Enzo Doria04/2016
32099*10^153446+41153447Robert Price08/2020
32102^509533-1846723153385Enzo Doria07/2015
32112^509468-39989153366Enzo Doria09/2015
321270^83117-69^83117153360Robert Price01/2014
3213(209246*34^99997-81)/11153148Eric Chen08/2023
3214(7*10^153116-1)/3153117Robert Price08/2022
3215(112*10^153025-1)/3153027Serge Batalov12/2014
321631912^33975-33975^31912153022Frank Doornink01/2024
3217(19*10^153010+131)/3153011Robert Price06/2020
32182^508174-1855151152976Enzo Doria09/2015
3219181^67757-2152974Lelio R Paula12/2017
32202^508160-1864829152972Enzo Doria01/2016
322110^152960+412563152961Patrick De Geest05/2021
322210^152960-50000000001152960Robert Price12/2020
322310^152960-423749152960Patrick De Geest05/2021
3224(71*10^152933-143)/9152934Robert Price10/2021
322532109^33932-33932^32109152919Frank Doornink02/2024
32262^507857-1848199152881Enzo Doria07/2015
32272^507638-115361152815Enzo Doria07/2015
32282^507551-114025152789Enzo Doria11/2014
3229(6^196337+1)/7152780Paul Bourdelais02/2010
3230(22*10^152670-13)/9152671Robert Price06/2018
32312^507085+28517152648Enzo Doria01/2024
32322^506917+28847152598Enzo Doria02/2024
32332^506451-22339152457Enzo Doria07/2013
323426463^34460-34460^26463152405Frank Doornink03/2024
323531898^33837-33837^31898152394Frank Doornink01/2024
32362^505995-113185152320Enzo Doria07/2014
3237(8*10^152260-17)/9152260Serge Batalov11/2022
3238(4*10^152253+149)/9152253Robert Price04/2018
323933530^33643-33643^33530152250Norbert Schneider04/2024
3240578^55117-577^55117152230Jean-Louis Charton08/2012
32412^505431-505431152150Henri Lifchitz04/2005
3242(203*10^152143+1)/3152145Robert Price03/2020
324331730^33787-33787^31730152092Frank Doornink01/2024
32442^505089+217787152047Enzo Doria01/2024
324533565^33594-33594^33565152043Norbert Schneider04/2024
32462^505053+73097152037Enzo Doria04/2016
324722*10^151998+3152000Robert Price01/2020
3248(238*10^151979-1)/3151981Robert Price04/2020
3249(2^504793-7)/46765151954Lelio R Paula12/2017
3250350377#+797581151937Nicolas PALAU08/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 22 2024 21:19 (Time in France)

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