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) !!!


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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(2^(6*86654+1)-5)/3156513Kevin Acres12/2013
3002(4*10^156501+119)/3156502Robert Price12/2021
3003(83*10^156476-101)/9156477Robert Price08/2021
30043*10^156435-97156436Robert Price07/2018
3005(8*10^156371-77)/3156372Robert Price07/2018
300653^90679-52^90679156356Robert Price01/2013
300731267^34782-34782^31267156349Frank Doornink01/2024
3008(418*10^156309-31)/9156311Robert Price05/2022
30092^519106-59141156267Enzo Doria10/2015
30102^519053+6077156251Enzo Doria02/2016
301131199^34764-34764^31199156235Frank Doornink01/2024
30122^518968-1860989156225Enzo Doria11/2015
3013(25*10^156221-7)/9156222Robert Price05/2018
30142^518931-2782297156214Enzo Doria09/2015
30152^518608-2939156117Yves Minet09/2014
301610*27^109005+697156027Curtis Bright05/2015
3017(49*10^155933-319)/9155934Robert Price10/2021
30182^517967-113485155924Enzo Doria08/2014
3019(103*10^155904+17)/3155906Robert Price08/2020
3020(8*10^155887-719)/9155887Robert Price03/2021
30212^517789+29231155871Enzo Doria02/2024
30224*10^155853-39155854Robert Price09/2020
30232^517698+4429155843Lelio R Paula01/2013
302432015^34584-34584^32015155814Frank Doornink01/2024
30252^517543-113257155796Enzo Doria07/2014
3026(14*10^155740-143)/3155741Robert Price11/2018
302731959^34564-34564^31959155697Frank Doornink01/2024
302831^104309-30^104309155563Henri Lifchitz08/2013
30292^516742-39851155555Enzo Doria09/2015
3030(22*10^155543+47)/3155544Robert Price06/2021
3031(19*10^155504+131)/3155505Robert Price06/2020
30327*10^155496+61155497Robert Price08/2019
30332^516440+1878421155464Enzo Doria08/2016
30342^515863-1867237155291Enzo Doria03/2016
30352^515786-461861155268Enzo Doria07/2015
30362^515644-113247155225Enzo Doria07/2014
3037(7*10^155203+107)/3155204Robert Price02/2018
303810^155163+206871155164Patrick De Geest05/2021
303910^155163-40001155163Robert Price01/2021
3040(17*10^155133-89)/9155134Robert Price07/2018
30412^515249+214457155106Enzo Doria10/2023
30422^515227-114997155099Enzo Doria06/2015
3044EPrime(155025)155025Eric W. Weisstein10/2010
3043(14*10^155024-221)/9155025Robert Price04/2018
3045(4*10^155022+173)/3155023Robert Price02/2018
3046(266*10^154897+1)/3154899Robert Price04/2020
3047(115*10^154869-1)/3154871Serge Batalov12/2014
3048(86*10^154853-221)/9154854Robert Price09/2019
30492^514361+78167154839Enzo Doria05/2016
30502^514281-115033154815Enzo Doria06/2015
305125701^35104-35104^25701154807Frank Doornink02/2024
30522^514194-3311154788Yves Minet12/2014
3053(14*10^154773+37)/3154774Robert Price12/2018
3054(16*10^154748+131)/3154749Robert Price03/2022
30556*10^154742-31154743Robert Price07/2020
3056(14*10^154645+139)/9154646Robert Price11/2021
30572^513690+216949154637Enzo Doria12/2023
30585*10^154618-79154619Robert Price03/2021
3059(167*10^154595+1)/3154597Robert Price04/2021
30602^513437+1879337154560Enzo Doria09/2016
30612^513306-113201154521Enzo Doria07/2014
3062(10^154494-13)/3154494Robert Price12/2017
306323462^35343+35343^23462154462Norbert Schneider04/2023
30642^513042-113787154442Enzo Doria09/2014
3065(151*10^154434-7)/9154436Robert Price01/2020
3066(118*10^154428+11)/3154430Robert Price03/2022
30672^512987+29153154425Enzo Doria02/2024
3068(14*10^154413+139)/9154414Robert Price11/2021
3069(77*10^154389-149)/9154390Robert Price03/2022
307032184^34247-34247^32184154374Frank Doornink02/2024
307110^154359+49154360Robert Price02/2023
30722^512628-114053154317Enzo Doria11/2014
30732^512529-49783154287Enzo Doria10/2015
3074(355573#+6991)/(6991*2031599)154285Makoto Morimoto06/2019
30752^512315-115297154223Enzo Doria06/2015
3076(47*10^154221+241)/9154222Robert Price06/2022
3077(7*10^154211+173)/9154211Robert Price01/2022
30782^512243+22703154201Enzo Doria09/2023
30792^512168+79561154178Enzo Doria06/2016
3080(77*10^154175+67)/9154176Robert Price12/2021
3081(59*19^120562-5)/18154170Anonymous12/2023
3082(5*10^154158-311)/9154158Robert Price12/2021
308327169^34758-34758^27169154120Frank Doornink01/2024
3084(89*10^154103-737)/9154104Robert Price01/2022
30852^511857+23327154085Enzo Doria10/2023
30864*10^154078-57154079Robert Price10/2018
3087(355049#+1859)/(11*13*10148891*62587751)154051Makoto Morimoto06/2019
30887*10^154038-57154039Robert Price06/2020
30892^511658-114371154025Enzo Doria02/2015
3090(57^87719+1)/58154022Paul Bourdelais11/2017
30912^511580-1846679154001Enzo Doria07/2015
3092(259*10^153998-1)/3154000Robert Price12/2020
30932^511541-113713153990Enzo Doria09/2014
309449958^32768+49957^32768153965Kellen Shenton11/2020
309510^153935+970801153936Patrick De Geest05/2021
309610^153935-1000001153935Robert Price08/2020
3097(16*10^153868-73)/3153869Robert Price07/2020
30989*10^153851-67153852Robert Price11/2020
30992^511077-112723153850Enzo Doria06/2014
310069^83653-68^83653153826Robert Price12/2013
31012^510963-113707153816Enzo Doria09/2014
3102(154*10^153810-1)/9153812Serge Batalov12/2014
3103(181*25^109991-75077)/8153763Curtis Bright05/2015
31042*10^153746-3153747Robert Price07/2015
31052^510626+1179379153714Enzo Doria05/2016
3106(7*10^153664+113)/3153665Robert Price02/2018
31072^510448+24991153661Enzo Doria11/2023
31082^510420+81121153652Enzo Doria07/2016
3109(197*7^181761-1)/2153608Karsten Bonath05/2017
31102^509894-459161153494Enzo Doria05/2015
3111(74*10^153489+673)/9153490Robert Price02/2022
3112(49*10^153484-211)/9153485Robert Price06/2022
31132^509841+71657153478Enzo Doria04/2016
31149*10^153446+41153447Robert Price08/2020
31152^509533-1846723153385Enzo Doria07/2015
31162^509468-39989153366Enzo Doria09/2015
311770^83117-69^83117153360Robert Price01/2014
3118(209246*34^99997-81)/11153148Eric Chen08/2023
3119(7*10^153116-1)/3153117Robert Price08/2022
3120(112*10^153025-1)/3153027Serge Batalov12/2014
312131912^33975-33975^31912153022Frank Doornink01/2024
3122(19*10^153010+131)/3153011Robert Price06/2020
31232^508174-1855151152976Enzo Doria09/2015
3124181^67757-2152974Lelio R Paula12/2017
31252^508160-1864829152972Enzo Doria01/2016
312610^152960+412563152961Patrick De Geest05/2021
312710^152960-50000000001152960Robert Price12/2020
312810^152960-423749152960Patrick De Geest05/2021
3129(71*10^152933-143)/9152934Robert Price10/2021
313032109^33932-33932^32109152919Frank Doornink02/2024
31312^507857-1848199152881Enzo Doria07/2015
31322^507638-115361152815Enzo Doria07/2015
31332^507551-114025152789Enzo Doria11/2014
3134(6^196337+1)/7152780Paul Bourdelais02/2010
3135(22*10^152670-13)/9152671Robert Price06/2018
31362^507085+28517152648Enzo Doria01/2024
31372^506917+28847152598Enzo Doria02/2024
31382^506451-22339152457Enzo Doria07/2013
313931898^33837-33837^31898152394Frank Doornink01/2024
31402^505995-113185152320Enzo Doria07/2014
3141(8*10^152260-17)/9152260Serge Batalov11/2022
3142(4*10^152253+149)/9152253Robert Price04/2018
3143578^55117-577^55117152230Jean-Louis Charton08/2012
31442^505431-505431152150Henri Lifchitz04/2005
3145(203*10^152143+1)/3152145Robert Price03/2020
314631730^33787-33787^31730152092Frank Doornink01/2024
31472^505089+217787152047Enzo Doria01/2024
31482^505053+73097152037Enzo Doria04/2016
314922*10^151998+3152000Robert Price01/2020
3150(238*10^151979-1)/3151981Robert Price04/2020
3151(2^504793-7)/46765151954Lelio R Paula12/2017
3152350377#+797581151937Nicolas PALAU08/2017
3153(79*10^151906-529)/9151907Robert Price01/2022
31542^504618-343991151906Enzo Doria07/2015
31552^504259+211193151798Enzo Doria08/2023
31562^504212-461939151783Enzo Doria07/2015
31577*10^151772-41151773Robert Price08/2021
31582^504054-2231151736Yves Minet10/2011
315925237^34458-34458^25237151686Frank Doornink11/2023
3160(28*10^151682+191)/3151683Robert Price02/2020
31612^503817+23961151665Enzo Doria10/2023
31622^503475-933075151562Paul Bourdelais06/2021
31632^503371+26289151530Enzo Doria12/2023
31642^503361-39883151527Enzo Doria09/2015
31652^503225+382667151486Enzo Doria10/2016
3166(206*10^151483-11)/3151485Robert Price02/2022
3167(844*10^151396-7)/9151398Robert Price05/2021
3168(26*10^151391-503)/9151392Robert Price07/2018
31692^502769+1877567151349Enzo Doria08/2016
31702^502576-4019151291Yves Minet10/2011
31715*10^151257+41151258Robert Price03/2019
31722^502290-2792501151205Enzo Doria02/2016
31732^502181+1868417151172Enzo Doria04/2016
31742^502055+22583151134Enzo Doria09/2023
3175(3*23^110967+41)/22151106Anonymous12/2023
31766*10^151063-77151064Robert Price09/2021
31772^501781-1850503151052Enzo Doria08/2015
3178(5*10^151007+37)/3151008Robert Price03/2018
31793^316494+5*2^316494151007Jon Grantham08/2023
31802^501627-991151005Yves Minet02/2014
31812^501577-115333150990Enzo Doria07/2015
318225239^34298-34298^25239150983Frank Doornink12/2023
3183(19*10^150977-7)/3150978Robert Price12/2023
31848*10^150975+3150976Robert Price08/2015
31852^501512-113669150971Enzo Doria09/2014
3186(83*10^150908+493)/9150909Robert Price12/2021
31872*10^150818+83150819Robert Price12/2021
3188(12^139739+1)/13150803Paul Bourdelais09/2011
3189(31^101111-1)/30150792Alexander Zhirkov11/2010
31902^500899-500899150786Henri Lifchitz04/2005
31912^500832+1876801150766Enzo Doria07/2016
3192(23*10^150763-59)/9150764Robert Price05/2018
319332001^33458-33458^32001150734Frank Doornink01/2024
31942^500699+1884953150726Enzo Doria02/2017
3195(13*10^150675-37)/3150676Robert Price01/2019
3196(2^500527+lucasV(1,2,500527)+1)/4150674Mike Oakes11/2016
31972^500337-71101150617Enzo Doria04/2016
3198(74*10^150616+133)/9150617Robert Price06/2019
3199(2*10^150612-17)/3150612Serge Batalov11/2022
32004*10^150577+91150578Robert Price08/2018
32012^500160+80071150564Enzo Doria06/2016
3202(2^500120+5)/9150551Lelio R Paula12/2017
3204(43*10^150515-421)/9150516Robert Price01/2019
32034695^40994+40994^4695150516Norbert Schneider11/2023
32052^499999+15981150515Norman Luhn08/2023
3206(10^150551-1)/9/385207015049/57498437921/7808738631274081150512Maksym Voznyy08/2014
3207(10^150551-1)/1556587827131683185788921941743157225041150512Robert Price07/2016
32082^499861-29503150474Enzo Doria08/2015
32092^499653-113533150411Enzo Doria08/2014
3210(14*10^150391-191)/3150392Robert Price10/2020
321129033^33696+33696^29033150382Norbert Schneider10/2023
32122^499534-221150375Yves Minet06/2012
321330110^33567+33567^30110150337Norbert Schneider10/2023
3214(28*10^150294+41)/3150295Robert Price07/2021
32152^499225+49727150282Enzo Doria09/2016
3216(695*10^150274+7)/9150276Robert Price12/2021
32172^499054-29261150231Enzo Doria07/2015
321818580^35187+35187^18580150215Norbert Schneider10/2023
3219(844*10^150196-7)/9150198Robert Price05/2021
32202^498907-933075150186Paul Bourdelais06/2021
3221(2^498898-7)/9150183Lelio R Paula10/2015
32223*10^150182+17150183Robert Price07/2018
32235*10^150175+63150176Robert Price09/2020
322432363^33292+33292^32363150149Norbert Schneider07/2022
3225(77*10^150128+67)/9150129Robert Price12/2021
3226(7*10^(2*75062+1)-9*10^75062-7)/9150125Robert Price12/2023
32272^498623+1866983150101Enzo Doria03/2016
3228(25*10^150050-403)/9150051Robert Price12/2020
3229numbpart(18140942830)150033Serge Batalov04/2017
323010^150029+4381150030Patrick De Geest05/2016
323110^150029-41150029Serge Batalov12/2014
32329*34^97952+529150013Eric Chen08/2023
323310^150000+1158603150001Patrick De Geest09/2018
323410^150000-245703150000Patrick De Geest09/2018
3235(38*10^149999+691)/9150000Robert Price10/2018
32362043563126843649194^8192+2043563126843649185^8192150000Youcef Lemsafer01/2023
3237(2043563126843649232^8192+2043563126843649201^8192)/147457149994Youcef Lemsafer01/2023
32382^498238-53149985Lelio R Paula12/2017
323945728^1905+1905^45728149984Hans Havermann10/2020
3240(211^65024+1)/(211^512+1)149945Martin Hopf12/2023
32415*10^149907+23149908Robert Price03/2019
324232^99585-829149891Eric Chen11/2023
324339347^6442+6442^39347149874Hans Havermann09/2020
32442^497850+81049149868Enzo Doria07/2016
324537228^10575+10575^37228149816Hans Havermann10/2020
3246(5*2^497673+1)/2743149812Lelio R Paula10/2015
3247(5*2^497671+1)/373703149810Lelio R Paula10/2015
3248(2*10^149803-143)/3149803Robert Price03/2018
324933845^26604+26604^33845149763Hans Havermann09/2020
32502^497434-2784191149743Enzo Doria10/2015


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

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