PRP Records

Probable Primes Top 10000

(290751 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
325129863^24790+24790^29863131227Hans Havermann03/2021
3252(5*10^131223-29)/3131224Robert Price03/2018
325329524^27825+27825^29524131218Hans Havermann03/2021
3254(23*2^435891-1)/699131215Lelio R Paula07/2015
3255(11*2^435879+1)/3337131211Lelio R Paula06/2015
325630639^19136+19136^30639131192Hans Havermann04/2021
3257(2^435808+1)/641/6700417131182Lelio R Paula02/2012
3258(2^435808+1)/4294967297131182Serge Batalov12/2016
32592^435773+1875557131181Enzo Doria06/2016
3261(16*10^131180+167)/3131181Robert Price06/2019
3260(26*10^131180-77)/3131181Robert Price11/2019
3262(25*10^131144-7)/9131145Robert Price05/2018
326329299^29358-29358^29299131138Norbert Schneider03/2022
32642^435612-2789939131133Enzo Doria12/2015
326533976^7231+7231^33976131121Hans Havermann03/2021
326633715^7746+7746^33715131121Hans Havermann03/2021
326766^72047-65^72047131093Robert Price09/2013
3268(5*10^131090+37)/3131091Robert Price03/2018
32692^435468+75631131089Enzo Doria04/2016
327037^83588-2131083Lelio R Paula08/2015
3271(4^217720+11)/3131081Robert Price02/2017
327230407^20448+20448^30407131074Hans Havermann04/2021
3273(22*10^131070+179)/3131071Robert Price02/2022
327429487^27836+27836^29487131059Hans Havermann04/2021
327529962^23615+23615^29962131030Hans Havermann03/2021
32762^435202-113193131009Enzo Doria07/2014
327741705^1384+1384^41705131002Hans Havermann04/2021
32789*10^130998-19130999Robert Price07/2019
327936243^4108+4108^36243130969Hans Havermann04/2021
3280floor((sqrt(5)-1)/2*10^130911)130911Serge Batalov06/2017
32812^434835-111937130899Enzo Doria05/2014
3282(62*10^130895-629)/9130896Robert Price07/2021
32832^434685+72257130854Enzo Doria04/2016
3284(7*10^130825+113)/3130826Robert Price02/2018
32852^434539-29317130810Enzo Doria07/2015
3286(74*10^130791+637)/9130792Robert Price01/2022
32872^434469-114259130789Enzo Doria01/2015
3288(5*10^130763+103)/9130763Robert Price04/2022
32892^434246+33130722Robert Price11/2015
329030156^21599+21599^30156130710Hans Havermann04/2021
3291(17*10^130695-161)/9130695Robert Price02/2021
329230513^19148+19148^30513130661Hans Havermann03/2021
329329736^24761+24761^29736130654Hans Havermann04/2021
32949*10^130638+41130639Robert Price08/2020
32952^433911-91130621Lelio R Paula06/2017
329630786^17449+17449^30786130588Hans Havermann03/2021
32972^433744-114419130570Enzo Doria02/2015
32992^433708+1869451130560Enzo Doria05/2016
32982^433710+93130560Lelio R Paula06/2017
3300(9629^32768+1)/120501441265666130520Kellen Shenton05/2021
3301(29*2^433547-1)/27130511Lelio R Paula06/2015
33023^273521+10130503Tyler NeSmith01/2021
330341659^1356+1356^41659130487Hans Havermann03/2021
33044*10^130480+9130481Robert Price05/2015
3305(23*2^433449-1)/75130481Lelio R Paula06/2015
3306(23*2^433334-1)/3731130445Lelio R Paula06/2015
3307(31*10^130414-49)/9130415Robert Price11/2021
330833481^7848+7848^33481130401Hans Havermann03/2021
3309(22*10^130392+203)/9130393Robert Price10/2021
331029773^23950+23950^29773130386Hans Havermann04/2021
33112^433023-113497130353Enzo Doria08/2014
331231175^15178+15178^31175130350Hans Havermann04/2021
33132^433002+1179379130347Enzo Doria06/2016
33142^432974+19130339Robert Price08/2015
331531903^12168+12168^31903130331Hans Havermann04/2021
331629387^27112+27112^29387130278Hans Havermann04/2021
331729577^25370+25370^29577130267Hans Havermann04/2021
331831738^12685+12685^31738130231Hans Havermann03/2021
331944235^878+878^44235130206Hans Havermann04/2021
332032160^11171+11171^32160130187Hans Havermann04/2021
332129489^25956+25956^29489130172Hans Havermann04/2021
3322(2^432457-1)/1672739247834685086279697130159Tony Prest / Never Odd Or Even09/2013
332333005^8766+8766^33005130133Hans Havermann04/2021
3324(35*10^130132-611)/9130133Robert Price02/2022
33252^432217+41130111Lelio R Paula06/2017
3326(2^216089*(2^216091-1)-339)/25130098Makoto Morimoto03/2017
3327((2^216091+1066)^2+(2^216091+1066)+41)/47/2069130095Makoto Morimoto05/2016
332897^65480-2130094Lelio R Paula05/2017
332936007^4102+4102^36007130094Hans Havermann04/2021
33304*10^130088-89130089Robert Price11/2018
33312^432117-113215130081Enzo Doria07/2014
33322^431804+72511129986Enzo Doria04/2016
3333(13*10^129896+137)/3129897Robert Price06/2021
3334(13*10^129890+71)/3129891Robert Price06/2021
333529048^29101-29101^29048129882Norbert Schneider03/2022
333637832^2709+2709^37832129871Hans Havermann04/2021
333731055^15184+15184^31055129853Hans Havermann04/2021
3338(3^272141-3^136071+1)/7129844Serge Batalov03/2014
333931385^13702+13702^31385129833Hans Havermann04/2021
334028901^29102-29102^28901129822Norbert Schneider03/2022
3341(47*10^129789-119)/9129790Robert Price05/2019
3342(9*2^431141+1)/17129787Lelio R Paula06/2015
3343(29*2^430881-1)/21129709Lelio R Paula06/2015
33442^430807+1869563129686Enzo Doria05/2016
33452^430721-21429129660Enzo Doria07/2013
3346(4*10^129618+89)/3129619Robert Price08/2021
33472^430415-276271129568Enzo Doria07/2015
334832282^10311+10311^32282129558Hans Havermann04/2021
334929486^24741+24741^29486129545Hans Havermann04/2021
3350(29*10^129543+313)/9129544Robert Price04/2021
335137095^3104+3104^37095129533Hans Havermann04/2021
335231132^14459+14459^31132129514Hans Havermann04/2021
335332582^9435+9435^32582129506Hans Havermann03/2021
335430442^17953+17953^30442129505Hans Havermann03/2021
3355(199*10^129487-7)/3129489Robert Price05/2020
33562^430142-2791721129486Enzo Doria03/2016
3357(7*10^129472-13)/3129473Robert Price07/2018
3358(8*10^129469+79)/3129470Robert Price10/2020
335931678^12213+12213^31678129463Hans Havermann04/2021
3360(772*10^129406-7)/9129408Robert Price06/2022
336131100^14439+14439^31100129362Hans Havermann04/2021
336233009^8288+8288^33009129345Hans Havermann04/2021
336329675^22804+22804^29675129324Hans Havermann04/2021
336429068^28099+28099^29068129315Hans Havermann04/2021
33652^429568-21017129313Enzo Doria07/2013
3366(10^129295+83)/3129295Robert Price08/2021
3367(853*10^129274-7)/9129276Robert Price07/2021
336830958^14961+14961^30958129249Hans Havermann04/2021
3369(11*10^129239-179)/3129240Robert Price09/2018
337028659^28988+28988^28659129208Norbert Schneider02/2021
337129423^24616+24616^29423129203Hans Havermann03/2021
33722^429194-112685129201Enzo Doria06/2014
33732^429145-2780449129186Enzo Doria04/2016
337432500^9427+9427^32500129168Hans Havermann04/2021
337533577^7014+7014^33577129136Hans Havermann03/2021
33762^428892-113453129110Enzo Doria07/2014
3377(11*2^428881-7)/15129106Renaud Lifchitz03/2011
33782^428727-113959129060Enzo Doria10/2014
3379(7*2^428725-1)/13129059Lelio R Paula05/2014
3380(10^129051-31)/3129051Serge Batalov12/2014
3381(134*10^129038+7)/3129040Robert Price02/2020
33822^428564+71161129011Enzo Doria04/2016
338328781^28930+28930^28781129002Norbert Schneider02/2021
338429065^27424+27424^29065128995Hans Havermann04/2021
33852^428502-113285128992Enzo Doria07/2014
33862^428421-21373128968Enzo Doria06/2013
3387L(616787)128901Henri Lifchitz09/2008
338820^99055-3128874Paul Bourdelais12/2020
338991^65772-2128851Lelio R Paula05/2017
33902^428022+43128848Lelio R Paula05/2017
33912^427999-459397128841Enzo Doria05/2015
33922^427993+76847128839Enzo Doria05/2016
339331059^14060+14060^31059128833Hans Havermann03/2021
339410^128805+152871128806Patrick De Geest05/2021
339510^128805-10001128805Robert Price02/2021
33962^427824-1851507128788Enzo Doria08/2015
33972^427807-21469128783Enzo Doria07/2013
339829082^26783+26783^29082128772Hans Havermann04/2021
339940055^1638+1638^40055128750Hans Havermann04/2021
340011^123594-240128710Enzo Doria09/2012
34012^427504-21503128692Enzo Doria07/2013
340237727^2574+2574^37727128673Hans Havermann04/2021
340329686^21591+21591^29686128668Hans Havermann04/2021
340410^128668-70000000001128668Robert Price08/2021
34052^427420+91128667Lelio R Paula05/2017
34068*10^128651-37128652Robert Price03/2022
3407(68*10^128645-257)/9128646Robert Price07/2019
34082^427269-113635128621Enzo Doria08/2014
34092^427130+1877569128579Enzo Doria08/2016
34102^427016-115349128545Enzo Doria07/2015
3411(4*10^128510+137)/3128511Robert Price03/2018
34122^426889-112879128507Enzo Doria06/2014
34132^426804+1869931128481Enzo Doria05/2016
34142^426750+77635128465Enzo Doria05/2016
341536988^2969+2969^36988128445Hans Havermann03/2021
341636664^3185+3185^36664128439Hans Havermann03/2021
341732618^8649+8649^32618128416Hans Havermann04/2021
341828883^27874+27874^28883128391Hans Havermann04/2021
34192^426425-91128367Lelio R Paula05/2017
3420(15*2^426398-1)/11128359Lelio R Paula05/2014
34212^426352+74971128345Enzo Doria04/2016
3422(199*10^128343-7)/3128345Robert Price05/2020
34234*10^128343-21128344Robert Price09/2018
3424(65*10^128338+493)/9128339Robert Price08/2021
342535632^3997+3997^35632128337Hans Havermann04/2021
34262^426300-1863689128330Enzo Doria03/2016
34272^426293+1881017128327Enzo Doria11/2016
3428(88*10^128324-637)/9128325Robert Price11/2020
3429(491*10^128285+31)/9128287Robert Price04/2022
343039103^1908+1908^39103128281Hans Havermann04/2021
34312^426043+35128252Robert Price11/2015
3432(4*10^128244-19)/3128245Robert Price03/2018
343335489^4102+4102^35489128222Hans Havermann04/2021
343434721^4926+4926^34721128208Hans Havermann04/2021
3435(305*10^128198+1)/9128200Robert Price02/2020
34362^425808-459959128181Enzo Doria06/2015
343730632^15291+15291^30632128178Hans Havermann04/2021
343835981^3648+3648^35981128167Hans Havermann04/2021
34392^425627-113605128127Enzo Doria08/2014
3440(4*10^128109+119)/3128110Robert Price12/2021
3441(22*10^128094+53)/3128095Robert Price07/2019
3442(86*10^128086-221)/9128087Robert Price09/2019
344318565^30002-30002^18565128070Norbert Schneider01/2015
3444(2^425287-9)/2737128021Lelio R Paula05/2015
3445(3*2^425233-1)/25128007Lelio R Paula05/2014
34462^425205+4911128000Marek Hubal02/2017
344729241^23836+23836^29241127995Hans Havermann04/2021
34482^425118-113663127974Enzo Doria08/2014
3449(86*10^127967-329)/9127968Robert Price01/2020
34502^425061+1869761127957Enzo Doria05/2016
3451746^44541+44541^746127955Norbert Schneider07/2019
345230236^17043+17043^30236127946Hans Havermann03/2021
34532^424918-21141127914Enzo Doria07/2013
3454(62*10^127903+91)/9127904Robert Price07/2021
34552^424864-29489127897Enzo Doria08/2015
345630438^15893+15893^30438127877Hans Havermann02/2021
3457(97*10^127858-1)/3127860Serge Batalov12/2014
345828929^26258+26258^28929127845Hans Havermann03/2021
345930563^15220+15220^30563127828Hans Havermann03/2021
34602^424632-2786639127827Enzo Doria03/2016
346110^127821-700001127821Robert Price08/2021
34622^424577-113755127811Enzo Doria09/2014
3463(7*2^424512-1)/3127792Lelio R Paula05/2014
3464(56*10^127752+691)/9127753Robert Price05/2019
346511^122629-720127705Enzo Doria11/2012
346622*10^127645+3127647Robert Price01/2020
346728715^27844+27844^28715127631Hans Havermann03/2021
3468(56*10^127612+187)/9127613Robert Price10/2021
3469(5*36^81995+821)/7127609Eric Chen01/2021
34704*10^127562-39127563Robert Price09/2020
347132595^8186+8186^32595127547Hans Havermann03/2021
34722^423696-21429127546Enzo Doria07/2013
34732^423664-1864559127536Enzo Doria03/2016
347437889^2322+2322^37889127530Hans Havermann03/2021
347537668^2429+2429^37668127523Hans Havermann03/2021
34763^267267-4127519Henri Lifchitz10/2014
3477(103*10^127491+17)/3127493Robert Price08/2020
347829376^21869+21869^29376127487Hans Havermann03/2021
347931186^12241+12241^31186127483Hans Havermann02/2021
3480(19^99689+5^99689)/24127477Robert Price09/2013
3481(21*2^423372+1)/101127447Lelio R Paula05/2014
348230594^14645+14645^30594127446Hans Havermann03/2021
34832^423328-21537127435Enzo Doria07/2013
3484(67*10^127413-7)/3127415Robert Price01/2020
3485(2*10^127407+73)/3127407Robert Price09/2020
3486(2^423165-7)/25127384Lelio R Paula05/2015
3487(7726^32768+1)/13917994151414876602369127379Kellen Shenton04/2021
348829512^20647+20647^29512127341Hans Havermann03/2021
3489(112*10^127324+17)/3127326Robert Price03/2020
349029565^20252+20252^29565127321Hans Havermann03/2021
3492(F(5)^182099-F(4)^182099)/F(3)127282Wayne Halsdorf08/2013
3491(5^182099-3^182099)/2127282Kellen Shenton05/2022
3493(16*10^127259+197)/3127260Robert Price04/2019
3494(26*10^127240+61)/3127241Robert Price10/2019
3495(234483*27^88884-145)/26127230Curtis Bright05/2015
34962^422515-114997127190Enzo Doria06/2015
34975*10^127179-3127180Robert Price07/2015
349831678^10343+10343^31678127176Hans Havermann03/2021
3499(44*10^127169-233)/9127170Robert Price01/2019
350034947^4352+4352^34947127162Hans Havermann03/2021


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 23 2022 21:24 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!