PRP Records

Probable Primes Top 10000

(295158 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 ?
30012^529215+219383159310Enzo Doria02/2024
300289*10^159258-9159260Robert Price05/2020
30032^528944-461315159229Enzo Doria07/2015
3004(13*10^159147+161)/3159148Robert Price11/2018
30052^528620-113879159131Enzo Doria10/2014
300632125^35306-35306^32125159119Frank Doornink02/2024
3007(47*10^159083+259)/9159084Robert Price03/2022
3008(861^54181-1)/860159019Jinyuan Wang11/2023
30092^528000-23307158944Enzo Doria08/2013
3010(29*10^158909+61)/9158910Robert Price08/2018
30112^527817+1876817158889Enzo Doria07/2016
30122^527774-49451158876Enzo Doria10/2015
30132^527745-291553158868Enzo Doria07/2015
3014(91*10^158862+11)/3158864Robert Price02/2020
30152^527644-1856999158837Enzo Doria10/2015
3016(37200^37199-37198^37199)/(2^37199)158822Henri Lifchitz06/2013
3017(17*10^158819+7)/3158820Robert Price06/2023
30182^527573-1863253158816Enzo Doria12/2015
30192^527553-23401158810Enzo Doria08/2013
3020(49*10^158783+437)/9158784Robert Price09/2021
302110^158755+310207158756Patrick De Geest08/2021
302210^158755-50001158755Robert Price08/2020
3023(61*10^158748-619)/9158749Robert Price03/2022
302411^152420-210158730Enzo Doria09/2012
3025(13*10^158694+401)/9158695Robert Price01/2018
30262^527052-69059158659Enzo Doria11/2015
30272^526849-113233158598Enzo Doria07/2014
302824286^36161+36161^24286158579Norbert Schneider08/2023
3029(2^526763-lucasV(1,2,526763)+1)/2158572Mike Oakes11/2016
3030(299*10^158544-17)/3158546Robert Price04/2020
30312^526658-3551158540Yves Minet03/2017
30327*10^158465-11158466Robert Price06/2019
3033(7^187507-3^187507)/4158462Jon Grantham08/2023
30342^526375-23115158455Enzo Doria08/2013
3035(77*10^158407-293)/9158408Robert Price09/2019
303631209^35242-35242^31209158388Frank Doornink01/2024
303732071^35144-35144^32071158363Frank Doornink01/2024
30382^526028-112793158351Enzo Doria07/2014
3039(229*10^158339-1)/3158341Robert Price07/2020
304032042^35123-35123^32042158255Frank Doornink01/2024
30412^525690-9221158249Lelio R Paula01/2013
30422*10^158242-7158243Robert Price10/2015
30432^525667-525667^2158242Henri Lifchitz12/2017
3044(56*10^158230+187)/9158231Robert Price10/2021
304510^158209-7000000001158209Robert Price12/2021
304631050^35207-35207^31050158153Frank Doornink01/2024
30472^525186-1857431158097Enzo Doria10/2015
304831527^35108-35108^31527157940Frank Doornink01/2024
30492^524515-23245157895Enzo Doria08/2013
30502^524499-109087157890Enzo Doria04/2014
30512^524384-219533157856Enzo Doria03/2024
30532^18067*(2^506221+1)-1157827Makoto Morimoto05/2014
30542^524288+189093157827Makoto Morimoto01/2016
30522^524288-164073157827Matthias Baur03/2020
3055(2^(2^19)-9333)/(19*23*463*1213*31973)157814Makoto Morimoto09/2017
3056(10^157792+359)/9157792Serge Batalov12/2014
30572^524154+25157787Stefano Morozzi04/2021
30582^523924+1876591157717Enzo Doria07/2016
3059(17*10^157705+67)/3157706Robert Price01/2019
3060(46^94841+1)/47157696Robert Price01/2014
30612^523774+77839157672Enzo Doria05/2016
30622^523587+2799143157616Enzo Doria04/2016
30632^523496+220141157588Enzo Doria03/2024
30642^523371+1872113157551Enzo Doria05/2016
30658*10^157477+27157478Robert Price09/2021
306632268^34909-34909^32268157397Frank Doornink02/2024
3067(8*10^157368+49)/3157369Robert Price05/2020
3068(82*10^157319+449)/9157320Robert Price11/2019
30692^522535-351457157299Enzo Doria07/2015
307025401^35704-35704^25401157271Frank Doornink01/2024
30712^522226+2799079157206Enzo Doria04/2016
3072(134*10^157191-11)/3157193Robert Price01/2022
30732^522134-1849451157178Enzo Doria08/2015
30749*10^157152+71157153Robert Price08/2020
30754*10^157150+93157151Robert Price08/2018
307631227^34952-34952^31227157093Frank Doornink01/2024
3077(32^104347+5^104347)/37157057Anonymous12/2023
3078fibonacci(751442)-2157042Jon Grantham08/2023
30792^521401-29593156958Enzo Doria08/2015
30807*10^156956+87156957Robert Price07/2019
30812^521348-23397156942Enzo Doria08/2013
308210^156902+34509156903Patrick De Geest08/2021
308410^156902-80000001156902Robert Price04/2021
308310^156902-69789156902Patrick De Geest08/2021
3085(98^78797+1)/99156901Paul Bourdelais12/2017
308665^86522+64156857Lelio R Paula04/2016
30878^173687-7^173687156855Jean-Louis Charton09/2004
30882^520977-1858183156830Enzo Doria10/2015
3089(8*10^156718-101)/3156719Robert Price08/2018
3090(10^156640+7)/53156639Alfred Reich07/2021
30912^520314-1849481156631Enzo Doria08/2015
3092(16*10^156563-637)/9156564Robert Price09/2022
3093(13*10^156522+89)/3156523Robert Price09/2018
3095(2^(6*86654+1)-5)/3156513Kevin Acres12/2013
3094(2^519925-5)/3156513Stefano Morozzi08/2022
3096(4*10^156501+119)/3156502Robert Price12/2021
3097(83*10^156476-101)/9156477Robert Price08/2021
30983*10^156435-97156436Robert Price07/2018
3099(8*10^156371-77)/3156372Robert Price07/2018
310053^90679-52^90679156356Robert Price01/2013
310131267^34782-34782^31267156349Frank Doornink01/2024
3102(418*10^156309-31)/9156311Robert Price05/2022
31032^519106-59141156267Enzo Doria10/2015
310425929^35404-35404^25929156266Frank Doornink03/2024
31052^519053+6077156251Enzo Doria02/2016
310631199^34764-34764^31199156235Frank Doornink01/2024
31072^518968-1860989156225Enzo Doria11/2015
3108(25*10^156221-7)/9156222Robert Price05/2018
31092^518931-2782297156214Enzo Doria09/2015
31102^518608-2939156117Yves Minet09/2014
311110*27^109005+697156027Curtis Bright05/2015
3112(49*10^155933-319)/9155934Robert Price10/2021
31132^517967-113485155924Enzo Doria08/2014
3114(103*10^155904+17)/3155906Robert Price08/2020
3115(8*10^155887-719)/9155887Robert Price03/2021
31162^517789+29231155871Enzo Doria02/2024
31174*10^155853-39155854Robert Price09/2020
31182^517698+4429155843Lelio R Paula01/2013
311932015^34584-34584^32015155814Frank Doornink01/2024
31202^517543-113257155796Enzo Doria07/2014
3121(14*10^155740-143)/3155741Robert Price11/2018
312231959^34564-34564^31959155697Frank Doornink01/2024
312331^104309-30^104309155563Henri Lifchitz08/2013
31242^516742-39851155555Enzo Doria09/2015
3125(22*10^155543+47)/3155544Robert Price06/2021
3126(19*10^155504+131)/3155505Robert Price06/2020
31277*10^155496+61155497Robert Price08/2019
31282^516440+1878421155464Enzo Doria08/2016
312926012^35173-35173^26012155295Frank Doornink03/2024
31302^515863-1867237155291Enzo Doria03/2016
31312^515786-461861155268Enzo Doria07/2015
31322^515644-113247155225Enzo Doria07/2014
3133(7*10^155203+107)/3155204Robert Price02/2018
313410^155163+206871155164Patrick De Geest05/2021
313510^155163-40001155163Robert Price01/2021
3136(17*10^155133-89)/9155134Robert Price07/2018
313726024^35131-35131^26024155117Frank Doornink03/2024
31382^515249+214457155106Enzo Doria10/2023
31392^515227-114997155099Enzo Doria06/2015
314026510^35061-35061^26510155090Frank Doornink03/2024
3142EPrime(155025)155025Eric W. Weisstein10/2010
3141(14*10^155024-221)/9155025Robert Price04/2018
3143(4*10^155022+173)/3155023Robert Price02/2018
3144(266*10^154897+1)/3154899Robert Price04/2020
3145(115*10^154869-1)/3154871Serge Batalov12/2014
3146(86*10^154853-221)/9154854Robert Price09/2019
31472^514361+78167154839Enzo Doria05/2016
31482^514281-115033154815Enzo Doria06/2015
314925701^35104-35104^25701154807Frank Doornink02/2024
31502^514194-3311154788Yves Minet12/2014
315125930^35067-35067^25930154779Frank Doornink03/2024
3152(14*10^154773+37)/3154774Robert Price12/2018
3153(16*10^154748+131)/3154749Robert Price03/2022
31546*10^154742-31154743Robert Price07/2020
3155(14*10^154645+139)/9154646Robert Price11/2021
31562^513690+216949154637Enzo Doria12/2023
31575*10^154618-79154619Robert Price03/2021
3158(167*10^154595+1)/3154597Robert Price04/2021
31592^513437+1879337154560Enzo Doria09/2016
31602^513306-113201154521Enzo Doria07/2014
316126415^34942-34942^26415154509Frank Doornink03/2024
316218^120818+19^120818-2154497Harsh Aggarwal05/2024
3163(10^154494-13)/3154494Robert Price12/2017
316423462^35343+35343^23462154462Norbert Schneider04/2023
31652^513042-113787154442Enzo Doria09/2014
3166(151*10^154434-7)/9154436Robert Price01/2020
3167(118*10^154428+11)/3154430Robert Price03/2022
31682^512987+29153154425Enzo Doria02/2024
3169(14*10^154413+139)/9154414Robert Price11/2021
3170(77*10^154389-149)/9154390Robert Price03/2022
317132184^34247-34247^32184154374Frank Doornink02/2024
317210^154359+49154360Robert Price02/2023
31732^512628-114053154317Enzo Doria11/2014
31742^512529-49783154287Enzo Doria10/2015
3175(355573#+6991)/(6991*2031599)154285Makoto Morimoto06/2019
31762^512315-115297154223Enzo Doria06/2015
3177(47*10^154221+241)/9154222Robert Price06/2022
3178(7*10^154211+173)/9154211Robert Price01/2022
31792^512243+22703154201Enzo Doria09/2023
31802^512168+79561154178Enzo Doria06/2016
3181(77*10^154175+67)/9154176Robert Price12/2021
3182(59*19^120562-5)/18154170Anonymous12/2023
3183(5*10^154158-311)/9154158Robert Price12/2021
318427169^34758-34758^27169154120Frank Doornink01/2024
3185(89*10^154103-737)/9154104Robert Price01/2022
31862^511857+23327154085Enzo Doria10/2023
31874*10^154078-57154079Robert Price10/2018
318826242^34863-34863^26242154060Frank Doornink03/2024
3189(355049#+1859)/(11*13*10148891*62587751)154051Makoto Morimoto06/2019
31907*10^154038-57154039Robert Price06/2020
31912^511658-114371154025Enzo Doria02/2015
3192(57^87719+1)/58154022Paul Bourdelais11/2017
31932^511580-1846679154001Enzo Doria07/2015
3194(259*10^153998-1)/3154000Robert Price12/2020
31952^511541-113713153990Enzo Doria09/2014
319649958^32768+49957^32768153965Kellen Shenton11/2020
319710^153935+970801153936Patrick De Geest05/2021
319810^153935-1000001153935Robert Price08/2020
3199(16*10^153868-73)/3153869Robert Price07/2020
32009*10^153851-67153852Robert Price11/2020
32012^511077-112723153850Enzo Doria06/2014
320269^83653-68^83653153826Robert Price12/2013
32032^510963-113707153816Enzo Doria09/2014
3204(154*10^153810-1)/9153812Serge Batalov12/2014
3205(181*25^109991-75077)/8153763Curtis Bright05/2015
32062*10^153746-3153747Robert Price07/2015
32072^510626+1179379153714Enzo Doria05/2016
3208(7*10^153664+113)/3153665Robert Price02/2018
32092^510448+24991153661Enzo Doria11/2023
32102^510420+81121153652Enzo Doria07/2016
3211(197*7^181761-1)/2153608Karsten Bonath05/2017
32122^509894-459161153494Enzo Doria05/2015
3213(74*10^153489+673)/9153490Robert Price02/2022
3214(49*10^153484-211)/9153485Robert Price06/2022
32152^509841+71657153478Enzo Doria04/2016
32169*10^153446+41153447Robert Price08/2020
32172^509533-1846723153385Enzo Doria07/2015
32182^509468-39989153366Enzo Doria09/2015
321970^83117-69^83117153360Robert Price01/2014
3220(209246*34^99997-81)/11153148Eric Chen08/2023
3221(7*10^153116-1)/3153117Robert Price08/2022
3222(112*10^153025-1)/3153027Serge Batalov12/2014
322331912^33975-33975^31912153022Frank Doornink01/2024
3224(19*10^153010+131)/3153011Robert Price06/2020
32252^508174-1855151152976Enzo Doria09/2015
3226181^67757-2152974Lelio R Paula12/2017
32272^508160-1864829152972Enzo Doria01/2016
322810^152960+412563152961Patrick De Geest05/2021
322910^152960-50000000001152960Robert Price12/2020
323010^152960-423749152960Patrick De Geest05/2021
3231(71*10^152933-143)/9152934Robert Price10/2021
323232109^33932-33932^32109152919Frank Doornink02/2024
32332^507857-1848199152881Enzo Doria07/2015
32342^507638-115361152815Enzo Doria07/2015
32352^507551-114025152789Enzo Doria11/2014
3236(6^196337+1)/7152780Paul Bourdelais02/2010
3237(22*10^152670-13)/9152671Robert Price06/2018
32382^507085+28517152648Enzo Doria01/2024
32392^506917+28847152598Enzo Doria02/2024
32402^506451-22339152457Enzo Doria07/2013
324126463^34460-34460^26463152405Frank Doornink03/2024
324231898^33837-33837^31898152394Frank Doornink01/2024
32432^505995-113185152320Enzo Doria07/2014
3244(8*10^152260-17)/9152260Serge Batalov11/2022
3245(4*10^152253+149)/9152253Robert Price04/2018
324633530^33643-33643^33530152250Norbert Schneider04/2024
3247578^55117-577^55117152230Jean-Louis Charton08/2012
32482^505431-505431152150Henri Lifchitz04/2005
3249(203*10^152143+1)/3152145Robert Price03/2020
325031730^33787-33787^31730152092Frank Doornink01/2024


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 27 2024 13:30 (Time in France)

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