PRP Records

Probable Primes Top 10000

(288949 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 ?
300132303^13914+13914^32303133846Hans Havermann04/2021
300230739^22458+22458^30739133757Hans Havermann04/2021
300334942^6721+6721^34942133739Hans Havermann04/2021
300434792^6935+6935^34792133638Hans Havermann04/2021
3005(266*10^133603+1)/3133605Robert Price04/2020
300632261^13842+13842^32261133600Hans Havermann04/2021
3007(89*10^133580+1)/9133581Serge Batalov05/2010
3008(134*10^133573-11)/3133575Robert Price01/2022
300962^74521-61^74521133571Robert Price05/2013
3010(182*10^133543+1)/3133545Robert Price02/2020
3011(103*10^133535+11)/3133537Robert Price01/2021
301232589^12520+12520^32589133537Hans Havermann03/2021
301334516^7373+7373^34516133496Hans Havermann04/2021
301430135^26882+26882^30135133482Hans Havermann04/2021
30152^443198-1867301133416Enzo Doria03/2016
3016(19*10^133390+101)/3133391Robert Price09/2019
3017(71^72043-1)/70133369Paul Bourdelais09/2017
301836117^4910+4910^36117133311Hans Havermann04/2021
30192^442799+1874633133296Enzo Doria06/2016
3020L(637751)133283Henri Lifchitz09/2008
3021109^65410-2133269Lelio R Paula10/2017
30222^442688-113489133263Enzo Doria08/2014
3023(7*2^442640-1)/783133246Lelio R Paula07/2015
3024(9*2^442463+1)/17441133192Lelio R Paula07/2015
30252^442437-1849993133187Enzo Doria08/2015
30262^442430-2791721133185Enzo Doria03/2016
3027(13*2^442428-1)/309133183Lelio R Paula07/2015
302829959^27870+27870^29959133172Hans Havermann03/2021
3029(25*2^442379-1)/71133169Lelio R Paula07/2015
303034240^7737+7737^34240133145Hans Havermann03/2021
3031452^50145+50145^452133142Norbert Schneider09/2020
303230659^21796+21796^30659133011Hans Havermann04/2021
303333276^9935+9935^33276133010Hans Havermann04/2021
303430111^26122+26122^30111133001Hans Havermann04/2021
303530790^20869+20869^30790132998Hans Havermann04/2021
3037(2^441799+78557)/5132995Lelio R Paula07/2015
30368*10^132994-27132995Robert Price10/2021
30382^441781-2787883132990Enzo Doria03/2016
3039(3*2^441685+1)/749132959Lelio R Paula07/2015
30402^441618+37132941Lelio R Paula08/2017
304134857^6514+6514^34857132940Hans Havermann04/2021
304234065^7988+7988^34065132937Hans Havermann04/2021
304335571^5452+5452^35571132914Hans Havermann04/2021
30442^441521-113575132912Enzo Doria08/2014
30457*10^132884-99132885Robert Price06/2019
3046(103*10^132879+17)/3132881Robert Price08/2020
30472^441396-65132874Lelio R Paula08/2017
304833350^9633+9633^33350132859Hans Havermann04/2021
30492^441330+1871959132854Enzo Doria05/2016
30502^441063+383132774Lelio R Paula06/2012
3051(10^132753+7)/17/19132751Alfred Reich06/2021
3052(22*10^132746+53)/3132747Robert Price07/2019
3053(22*10^132732+119)/3132733Robert Price04/2021
30542^440846+1870909132708Enzo Doria05/2016
30552^440656-113489132651Enzo Doria08/2014
3056numbpart(14180123587)132646Serge Batalov04/2017
305732950^10591+10591^32950132622Hans Havermann04/2021
305833302^9597+9597^33302132614Hans Havermann04/2021
3059(19*10^132550+191)/3132551Robert Price05/2019
3060(2^440399-1)/(16210820281161978209*31518475633*880799)132538Dario Alpern01/2015
3061(38^83891+1)/39132529Robert Price09/2013
30622*10^132493-43132494Robert Price04/2018
306331352^16809+16809^31352132480Hans Havermann04/2021
3064(418*10^132441+23)/9132443Robert Price02/2020
30652^439931-21132433Lelio R Paula08/2017
306647^79201-46^79201132432Robert Price10/2012
30672^439897-113653132423Enzo Doria08/2014
306835505^5362+5362^35505132410Hans Havermann03/2021
306930079^25222+25222^30079132402Hans Havermann04/2021
3070(5*2^439822+1)/9132400Lelio R Paula06/2015
3071(695*10^132356+7)/9132358Robert Price12/2021
3072(112*10^132337-1)/3132339Serge Batalov12/2014
30732^439576-113247132326Enzo Doria07/2014
307430059^25230+25230^30059132318Hans Havermann04/2021
30752^439497-29143132302Enzo Doria07/2015
30762^439409-114193132276Enzo Doria12/2014
3077(44*10^132233-233)/9132234Robert Price01/2019
30789*10^132148-7132149Robert Price09/2015
3079(47*10^132125-119)/9132126Robert Price05/2019
30802^438845+1870217132106Enzo Doria05/2016
30812^438789+87855132089Lelio R Paula01/2016
30822^438774-2786411132085Enzo Doria03/2016
30832^438755-1848205132079Enzo Doria07/2015
308430502^21381+21381^30502132075Hans Havermann04/2021
30852^438739-112087132074Enzo Doria06/2014
308635872^4777+4777^35872131979Hans Havermann04/2021
308731198^16945+16945^31198131938Hans Havermann03/2021
308813907#+(318259#)/(13907#)131923Makoto Morimoto10/2017
3089L(631181)131910Henri Lifchitz09/2008
3090(47*10^131886-119)/9131887Robert Price05/2019
3091(3*2^438121+1)/4308193883131879Lelio R Paula06/2015
30922^438079-1863877131875Enzo Doria03/2016
3093(16*10^131872-37)/3131873Robert Price05/2021
3094(2^438067+5)/329131869Lelio R Paula06/2015
30952^437908-113855131824Enzo Doria09/2014
30962^437884-286349131817Enzo Doria07/2015
30975^188558+4131797Tyler NeSmith05/2021
3098(11*10^131784-17)/3131785Robert Price06/2018
31004*10^131719-93131720Robert Price07/2020
309931629^14606+14606^31629131720Hans Havermann04/2021
31013^276062-112292131716Enzo Doria07/2014
3102(7*10^131682+89)/3131683Robert Price08/2020
310329512^28969+28969^29512131681Hans Havermann03/2021
31042^437343+75953131654Enzo Doria04/2016
310535^85243-34^85243131621Robert Price05/2012
3106(28*10^131586+59)/3131587Robert Price05/2021
3107(59*10^131575+391)/9131576Robert Price03/2021
310839984^1945+1945^39984131505Hans Havermann03/2021
3109(203*10^131457+1)/3131459Robert Price03/2020
31107*10^131421-41131422Robert Price08/2021
311187309^32+32^87309131414Hans Havermann03/2021
3112(68^71713+1)/69131413Paul Bourdelais09/2017
31132^436451+1884713131385Enzo Doria03/2017
31142^436365+35131359Robert Price11/2015
31152^436300+1866871131340Enzo Doria03/2016
3116(7*10^131339+179)/3131340Robert Price09/2018
311714^114592-3131338Paul Bourdelais12/2020
311836197^4236+4236^36197131285Hans Havermann04/2021
3119(37*10^131270+341)/9131271Robert Price08/2018
312029863^24790+24790^29863131227Hans Havermann03/2021
3121(5*10^131223-29)/3131224Robert Price03/2018
312229524^27825+27825^29524131218Hans Havermann03/2021
3123(23*2^435891-1)/699131215Lelio R Paula07/2015
3124(11*2^435879+1)/3337131211Lelio R Paula06/2015
312530639^19136+19136^30639131192Hans Havermann04/2021
3126(2^435808+1)/641/6700417131182Lelio R Paula02/2012
3127(2^435808+1)/4294967297131182Serge Batalov12/2016
31282^435773+1875557131181Enzo Doria06/2016
3130(16*10^131180+167)/3131181Robert Price06/2019
3129(26*10^131180-77)/3131181Robert Price11/2019
3131(25*10^131144-7)/9131145Robert Price05/2018
31322^435612-2789939131133Enzo Doria12/2015
313333976^7231+7231^33976131121Hans Havermann03/2021
313433715^7746+7746^33715131121Hans Havermann03/2021
313566^72047-65^72047131093Robert Price09/2013
3136(5*10^131090+37)/3131091Robert Price03/2018
31372^435468+75631131089Enzo Doria04/2016
313837^83588-2131083Lelio R Paula08/2015
3139(4^217720+11)/3131081Robert Price02/2017
314030407^20448+20448^30407131074Hans Havermann04/2021
314129487^27836+27836^29487131059Hans Havermann04/2021
314229962^23615+23615^29962131030Hans Havermann03/2021
31432^435202-113193131009Enzo Doria07/2014
314441705^1384+1384^41705131002Hans Havermann04/2021
31459*10^130998-19130999Robert Price07/2019
314636243^4108+4108^36243130969Hans Havermann04/2021
3147floor((sqrt(5)-1)/2*10^130911)130911Serge Batalov06/2017
31482^434835-111937130899Enzo Doria05/2014
3149(62*10^130895-629)/9130896Robert Price07/2021
31502^434685+72257130854Enzo Doria04/2016
3151(7*10^130825+113)/3130826Robert Price02/2018
31522^434539-29317130810Enzo Doria07/2015
3153(74*10^130791+637)/9130792Robert Price01/2022
31542^434469-114259130789Enzo Doria01/2015
31552^434246+33130722Robert Price11/2015
315630156^21599+21599^30156130710Hans Havermann04/2021
3157(17*10^130695-161)/9130695Robert Price02/2021
315830513^19148+19148^30513130661Hans Havermann03/2021
315929736^24761+24761^29736130654Hans Havermann04/2021
31609*10^130638+41130639Robert Price08/2020
31612^433911-91130621Lelio R Paula06/2017
316230786^17449+17449^30786130588Hans Havermann03/2021
31632^433744-114419130570Enzo Doria02/2015
31652^433708+1869451130560Enzo Doria05/2016
31642^433710+93130560Lelio R Paula06/2017
3166(9629^32768+1)/120501441265666130520Kellen Shenton05/2021
3167(29*2^433547-1)/27130511Lelio R Paula06/2015
31683^273521+10130503Tyler NeSmith01/2021
316941659^1356+1356^41659130487Hans Havermann03/2021
31704*10^130480+9130481Robert Price05/2015
3171(23*2^433449-1)/75130481Lelio R Paula06/2015
3172(23*2^433334-1)/3731130445Lelio R Paula06/2015
3173(31*10^130414-49)/9130415Robert Price11/2021
317433481^7848+7848^33481130401Hans Havermann03/2021
3175(22*10^130392+203)/9130393Robert Price10/2021
317629773^23950+23950^29773130386Hans Havermann04/2021
31772^433023-113497130353Enzo Doria08/2014
317831175^15178+15178^31175130350Hans Havermann04/2021
31792^433002+1179379130347Enzo Doria06/2016
31802^432974+19130339Robert Price08/2015
318131903^12168+12168^31903130331Hans Havermann04/2021
318229387^27112+27112^29387130278Hans Havermann04/2021
318329577^25370+25370^29577130267Hans Havermann04/2021
318431738^12685+12685^31738130231Hans Havermann03/2021
318544235^878+878^44235130206Hans Havermann04/2021
318632160^11171+11171^32160130187Hans Havermann04/2021
318729489^25956+25956^29489130172Hans Havermann04/2021
3188(2^432457-1)/1672739247834685086279697130159Tony Prest / Never Odd Or Even09/2013
318933005^8766+8766^33005130133Hans Havermann04/2021
31902^432217+41130111Lelio R Paula06/2017
3191(2^216089*(2^216091-1)-339)/25130098Makoto Morimoto03/2017
3192((2^216091+1066)^2+(2^216091+1066)+41)/47/2069130095Makoto Morimoto05/2016
319397^65480-2130094Lelio R Paula05/2017
319436007^4102+4102^36007130094Hans Havermann04/2021
31954*10^130088-89130089Robert Price11/2018
31962^432117-113215130081Enzo Doria07/2014
31972^431804+72511129986Enzo Doria04/2016
3198(13*10^129896+137)/3129897Robert Price06/2021
3199(13*10^129890+71)/3129891Robert Price06/2021
320037832^2709+2709^37832129871Hans Havermann04/2021
320131055^15184+15184^31055129853Hans Havermann04/2021
3202(3^272141-3^136071+1)/7129844Serge Batalov03/2014
320331385^13702+13702^31385129833Hans Havermann04/2021
3204(47*10^129789-119)/9129790Robert Price05/2019
3205(9*2^431141+1)/17129787Lelio R Paula06/2015
3206(29*2^430881-1)/21129709Lelio R Paula06/2015
32072^430807+1869563129686Enzo Doria05/2016
32082^430721-21429129660Enzo Doria07/2013
3209(4*10^129618+89)/3129619Robert Price08/2021
32102^430415-276271129568Enzo Doria07/2015
321132282^10311+10311^32282129558Hans Havermann04/2021
321229486^24741+24741^29486129545Hans Havermann04/2021
3213(29*10^129543+313)/9129544Robert Price04/2021
321437095^3104+3104^37095129533Hans Havermann04/2021
321531132^14459+14459^31132129514Hans Havermann04/2021
321632582^9435+9435^32582129506Hans Havermann03/2021
321730442^17953+17953^30442129505Hans Havermann03/2021
3218(199*10^129487-7)/3129489Robert Price05/2020
32192^430142-2791721129486Enzo Doria03/2016
3220(7*10^129472-13)/3129473Robert Price07/2018
3221(8*10^129469+79)/3129470Robert Price10/2020
322231678^12213+12213^31678129463Hans Havermann04/2021
322331100^14439+14439^31100129362Hans Havermann04/2021
322433009^8288+8288^33009129345Hans Havermann04/2021
322529675^22804+22804^29675129324Hans Havermann04/2021
322629068^28099+28099^29068129315Hans Havermann04/2021
32272^429568-21017129313Enzo Doria07/2013
3228(10^129295+83)/3129295Robert Price08/2021
3229(853*10^129274-7)/9129276Robert Price07/2021
323030958^14961+14961^30958129249Hans Havermann04/2021
3231(11*10^129239-179)/3129240Robert Price09/2018
323228659^28988+28988^28659129208Norbert Schneider02/2021
323329423^24616+24616^29423129203Hans Havermann03/2021
32342^429194-112685129201Enzo Doria06/2014
32352^429145-2780449129186Enzo Doria04/2016
323632500^9427+9427^32500129168Hans Havermann04/2021
323733577^7014+7014^33577129136Hans Havermann03/2021
32382^428892-113453129110Enzo Doria07/2014
3239(11*2^428881-7)/15129106Renaud Lifchitz03/2011
32402^428727-113959129060Enzo Doria10/2014
3241(7*2^428725-1)/13129059Lelio R Paula05/2014
3242(10^129051-31)/3129051Serge Batalov12/2014
3243(134*10^129038+7)/3129040Robert Price02/2020
32442^428564+71161129011Enzo Doria04/2016
324528781^28930+28930^28781129002Norbert Schneider02/2021
324629065^27424+27424^29065128995Hans Havermann04/2021
32472^428502-113285128992Enzo Doria07/2014
32482^428421-21373128968Enzo Doria06/2013
3249L(616787)128901Henri Lifchitz09/2008
325020^99055-3128874Paul Bourdelais12/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 19 2022 17:15 (Time in France)

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