PRP Records

Probable Primes Top 10000

(193013 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 (> 30000) Who ? When ?
325113^88754-9098867Lelio R Paula08/2016
32522^328406+70998861Lelio R Paula02/2013
3253(17*2^328413-1)/1617398860Lelio R Paula03/2014
32547^116976+7698857Lelio R Paula08/2016
32552^328335+115598839Lelio R Paula08/2016
3257(3*2^328311+1)/598832Lelio R Paula11/2013
3256287^40210+40210^28798832Norbert Schneider11/2014
3258(2^328284+9)/132598821Lelio R Paula10/2013
3259(21*2^328258+1)/212598814Lelio R Paula11/2013
326065^54491+4898788Lelio R Paula04/2016
32613^207042+9898785Lelio R Paula08/2016
32623^206977-11275698754Enzo Doria07/2014
32637^116846-5098747Lelio R Paula08/2016
32642^327967-2863598728Lelio R Paula08/2016
32656^126850-4798709Lelio R Paula08/2016
32668*6^126830-798694Lelio R Paula11/2014
326711^94770-27098693Enzo Doria08/2012
32682^327832+4398688Lelio R Paula12/2012
32692^327795+76198677Lelio R Paula02/2013
327010^98669+14741198670Patrick De Geest11/2016
327210^98669-9^(98669-1)98669Robert Price05/2016
327110^98669-10524998669Patrick De Geest11/2016
32732^327671-10980198639Enzo Doria04/2014
32745^141090-1498618Lelio R Paula08/2016
327520^75799+4798617Lelio R Paula08/2016
32762^327515-101798592Lelio R Paula08/2016
32776^126692+9768198586Mike Oakes04/2011
32782^327467-74198578Lelio R Paula08/2016
3279(2^327329+9)/1998535Lelio R Paula10/2013
32807^116577-6698519Lelio R Paula08/2016
3281(3*2^327250+1)/798512Lelio R Paula11/2013
3282(19*2^327192+1)/27598494Lelio R Paula11/2013
32832^327162-6694598486Lelio R Paula08/2016
32844*10^98472-398473Erik Branger11/2013
3285(6883*2^327047-1)/7798453Lelio R Paula05/2015
3286(71*10^98446+1)/998447Serge Batalov11/2010
328713^88363+9498432Lelio R Paula08/2016
328848^58543-47^5854398425Jean-Louis Charton11/2005
32896^126481+4198422Lelio R Paula08/2016
329078*10^98413-798415Robert Price05/2017
32917^116416+4698383Lelio R Paula08/2016
32927^116407-2498376Lelio R Paula07/2016
32942^326782-186067198372Enzo Doria03/2016
329317^79948+5898372Lelio R Paula08/2016
32953^206143-9898356Lelio R Paula08/2016
32968*5^140705+798350Lelio R Paula11/2014
32972^326585+1198312Lelio R Paula12/2012
32982^326582-45916198311Enzo Doria05/2015
3299(2^326548+9)/598301Lelio R Paula10/2013
33002^326538+7165998298Enzo Doria04/2016
330115^83575-5898292Lelio R Paula08/2016
330210^98288+398289Robert Price03/2011
330310^98288-11701798288Patrick De Geest11/2011
3304(44*10^98284-719)/998285Robert Price12/2017
33052^326421-279757398263Enzo Doria04/2016
33062^326401+1609598257Lelio R Paula07/2016
33077^116240-116240^798235Norbert Schneider05/2017
330817^79826-7898222Lelio R Paula08/2016
33092^326268-80998217Yves Minet04/2011
3310(418*10^98199+23)/998201Robert Price08/2017
331112*10^98198-798200Robert Price11/2017
331215^83496-7698199Lelio R Paula08/2016
3313(10223*2^326179+1)/612598190Lelio R Paula07/2014
33149*5^140471-498186Lelio R Paula11/2014
33152^326069-238398157Yves Minet10/2013
33162^325973+118598128Lelio R Paula07/2016
3317(25*2^325949-1)/1798121Lelio R Paula02/2014
33182^325945-184726998120Enzo Doria07/2015
33198*10^98111-6798112Robert Price10/2017
33202^325866+1598096Lelio R Paula12/2012
33212^325765+197430598066Enzo Doria06/2016
33222^325733-5869598056Lelio R Paula07/2016
33232^325717-364598051Lelio R Paula07/2016
3324(23*2^325583-1)/2198011Lelio R Paula02/2014
3325(7*10^98007-13)/398008Robert Price06/2016
33262^325512-45995997989Enzo Doria05/2015
3327(3^205354-8)/1797978Lelio R Paula09/2013
33282^325433+7681797966Enzo Doria05/2016
33295*10^97963+8197964Robert Price08/2017
33302^325390-10906197953Enzo Doria04/2014
333113^87921+2497940Lelio R Paula08/2016
3332961^32831-960^3283197926Jean-Louis Charton02/2011
33332^325215+1290997900Lelio R Paula07/2016
33347*10^97874-6997875Robert Price01/2017
3336(17^79537+5^79537)/2297865Robert Price06/2013
333515^83212+2297865Lelio R Paula08/2016
33372^325087-10905797861Enzo Doria04/2014
33382^325074+187065797858Enzo Doria05/2016
33402^325066-211197855Yves Minet08/2013
3339CopelandErdos(97855)97855Eric W. Weisstein10/2015
334118^77944-8997841Lelio R Paula07/2016
33426^125720-1766397830Enzo Doria02/2013
33432^324972-206997827Yves Minet05/2013
33442^324944-278831997818Enzo Doria03/2016
33464*10^97799-997800Erik Branger11/2013
33452^324882+57729457597800Lelio R Paula09/2016
33472^324863-186792197794Enzo Doria04/2016
33486^125662-1847397785Enzo Doria03/2013
334912^90604+1197779Lelio R Paula07/2016
33505^139830+2497737Lelio R Paula04/2016
33512^324612+115597718Lelio R Paula07/2016
335219^76404-4497702Lelio R Paula07/2016
33532^324505-298397686Yves Minet04/2011
3354(31*2^324496-1)/4597683Lelio R Paula02/2014
33556^125488-1784397649Enzo Doria02/2013
33567^115515-297622Lelio R Paula09/2013
3357(89^50069-1)/8897603Paul Bourdelais08/2017
33586^125418-597595Lelio R Paula11/2014
33592^324076+115597557Lelio R Paula07/2016
3360(2^324074+9)/1397555Lelio R Paula10/2013
3361(55459*2^323993+1)/2197536Lelio R Paula07/2014
336213^87557-12^8755797534Jean-Louis Charton12/2008
33632^323946+7393997518Enzo Doria04/2016
33642^323937+186694797515Enzo Doria03/2016
33656^125290-1853397495Enzo Doria03/2013
33662^323845+10197488Lelio R Paula12/2012
336718^77662+6597487Lelio R Paula07/2016
33682^323772+7677197466Enzo Doria05/2016
33692^323765-11221397463Enzo Doria06/2014
33702^323720-655597450Lelio R Paula07/2016
33712^323694-186040197442Enzo Doria03/2016
337220^74886+397429Lelio R Paula06/2016
33743*10^97399+7397400Robert Price04/2016
33737^115252-5097400Lelio R Paula07/2016
3375224737#+39358197389Nicolas PALAU12/2016
3376(26*10^97353+31)/397354Robert Price07/2016
337761^54517-60^5451797331Jean-Louis Charton09/2005
3378(38*10^97329+187)/997330Robert Price11/2017
3379p(19982)#/2-102497293Robert Price09/2017
33806^125021-8597286Lelio R Paula08/2016
33812^323164-4735597283Lelio R Paula07/2016
3382(3^203902+4)/3605101515797276Lelio R Paula09/2013
33832^323054-655597249Lelio R Paula07/2016
33849*10^97247-2997248Robert Price05/2017
3385(31*10^97242+41)/997243Robert Price04/2015
3386GoldenRatioPrime[97241]97241Eric W. Weisstein06/2009
338712^90098-4197233Lelio R Paula07/2016
33882^322928-21692997212Enzo Doria05/2014
3389(7*2^322896-1)/5797201Lelio R Paula02/2014
3390(2^322897+5)/314610748997193Lelio R Paula10/2013
33912^322725+7576197150Enzo Doria04/2016
3392(13*2^322686+1)/11997138Lelio R Paula11/2013
3393(41*10^97085+373)/997086Robert Price04/2017
33942^322413+7797056Lelio R Paula12/2012
33952^322406+17797054Lelio R Paula12/2012
3396(14*10^97044+31)/997045Robert Price02/2015
33972^322302+25525597023Lelio R Paula07/2016
33982^322196-11309396991Enzo Doria07/2014
33992^322000-186146996932Enzo Doria03/2016
34002^321971-11274796923Enzo Doria06/2014
340111^93062-9296915Lelio R Paula06/2016
3402(11*2^321841-7)/1596884Renaud Lifchitz03/2011
34033^203051+3496880Lelio R Paula05/2016
34042*10^96867-5196868Robert Price11/2017
3405(64*10^96863-1)/2796864Serge Batalov05/2010
34062^321716-278693996847Enzo Doria03/2016
34072^321701-11305396842Enzo Doria07/2014
34082^321700-2863596842Lelio R Paula06/2016
3409(5*2^321691-1)/2796838Lelio R Paula02/2014
34106^124433-12443396828Robert Price01/2014
34112^321631+6996821Lelio R Paula12/2012
3412(13*2^321606+1)/11996813Lelio R Paula11/2013
3413(46*10^96798-1)/996799Serge Batalov10/2014
3414(59*10^96798+31)/996799Robert Price09/2015
3415223319#+23122396790Makoto Morimoto02/2016
34162^321519-2863596787Lelio R Paula06/2016
34172^321487-186723796778Enzo Doria03/2016
34182^321461-6396770Lelio R Paula12/2012
34192^321439+12396763Lelio R Paula12/2012
34202^321434+70996762Lelio R Paula02/2013
342114^84413+8996749Lelio R Paula07/2016
3422(28*10^96743+71)/996744Serge Batalov12/2008
342313^86847+9696743Lelio R Paula06/2016
34249*2^321336-796733Lelio R Paula08/2014
3425(209*10^96722-17)/396724Robert Price05/2017
34262^321187-115996687Yves Minet11/2012
34272^321182-185008196686Enzo Doria08/2015
34282^321116-11282996666Enzo Doria06/2014
34292^321108-10949996664Enzo Doria04/2014
34302^321098+279385996661Enzo Doria03/2016
34312^321057+409796648Lelio R Paula06/2016
3432(4435*29^66081-4)/796640Curtis Bright05/2015
3433p(19849)#/2-6496581Robert Price04/2017
34342^320817+18996576Lelio R Paula12/2012
3435(361*10^96567-163)/996569Robert Price10/2017
34362^320788-11032796567Enzo Doria05/2014
34372^320764+79396560Lelio R Paula02/2013
3438(9179*2^320652-1)/22196528Lelio R Paula05/2015
34392^320616-7879596516Lelio R Paula03/2016
34402^320612-46193996514Enzo Doria07/2015
34415*2^320431+796461Lelio R Paula08/2014
344219^75431-9096458Lelio R Paula06/2016
3443(2^320370+3)/6796440Lelio R Paula10/2013
34442^320309+187147796423Enzo Doria05/2016
3445tau(809^6028)96410Nik Lygeros / Olivier Rozier / LR team10/2013
3446(21*2^320252-1)/189596404Lelio R Paula02/2014
34472^320232-17396400Lelio R Paula12/2012
3448175^42975-296395Lelio R Paula10/2017
344910^96377+19991196378Patrick De Geest12/2016
345010^96377-2000196377Robert Price11/2016
34512^320124-279044996367Enzo Doria03/2016
34522^320043-10877596343Enzo Doria04/2014
345310^96338+42493996339Patrick De Geest03/2016
345410^96338-928196338Robert Price09/2015
3455(3*2^320008+1)/796332Lelio R Paula09/2013
34562^319838+425796281Lelio R Paula03/2016
34572^319830-1699596279Lelio R Paula03/2016
34586^123713+14396268Lelio R Paula05/2016
3459(28*10^96265-97)/396266Robert Price07/2016
3460103^47825-10296264Norbert Schneider10/2016
34612^319713-8196244Lelio R Paula11/2012
3462(55459*2^319706+1)/2016796242Lelio R Paula07/2014
346312^89153-4396213Lelio R Paula06/2016
3464(2*10^96195-59)/396195Robert Price05/2017
34652^319545+14796193Lelio R Paula11/2012
3466(50^56597+1)/5196155Robert Price03/2014
3467(41*10^96137-59)/996138Robert Price10/2017
34682^319353-11034396135Enzo Doria05/2014
346911^92309-4296130Lelio R Paula05/2016
347014^83869-13^8386996125Jean-Louis Charton01/2009
3471(7*10^96112+143)/396113Robert Price04/2016
34722^319237+6583596100Lelio R Paula03/2016
34732^319194-184196087Yves Minet03/2013
347420^73847-3196078Lelio R Paula05/2016
34752^319107-10955596061Enzo Doria04/2014
3476(3*2^319114-1)/262796060Lelio R Paula02/2014
34772^319098-11215796059Enzo Doria06/2014
347815^81673+9496055Lelio R Paula07/2016
34792^319074+187174996051Enzo Doria05/2016
34802^319007-11211196031Enzo Doria06/2014
34812^318946-142196013Yves Minet01/2013
34822^318834-11041195979Enzo Doria05/2014
34832^318831-196595978Lelio R Paula03/2016
3484(5*10^95976+7)/395977Erik Branger03/2014
34855*3^201089-895945Lelio R Paula08/2014
34862^318711-13995942Lelio R Paula11/2012
34872^318635-116795919Lelio R Paula03/2016
348815^81555+1695917Lelio R Paula07/2016
3489(37*10^95895+377)/995896Robert Price10/2017
3490(22699*2^318527+1)/2195890Lelio R Paula07/2014
34912^318496-9730595877Lelio R Paula03/2016
34922^318466+1501595868Lelio R Paula03/2016
34936^123187-17312995859Mike Oakes04/2011
34942^318423-48795855Yves Minet03/2012
3495(10223*2^318350+1)/156395834Lelio R Paula07/2014
349645369!2+102495787Robert Price02/2015
34973^200758-8695786Lelio R Paula05/2016
34983*10^95776-5995777Robert Price10/2017
3499193^41901-295768Lelio R Paula10/2017
35004*10^95752-7195753Robert Price11/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 09 2017 09:21 (Time in France)

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