PRP Records

Probable Primes Top 10000

(183432 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 ?
32519*5^140471-498186Lelio R Paula11/2014
32522^326069-238398157Yves Minet10/2013
32532^325973+118598128Lelio R Paula07/2016
3254(25*2^325949-1)/1798121Lelio R Paula02/2014
32552^325945-184726998120Enzo Doria07/2015
32562^325866+1598096Lelio R Paula12/2012
32572^325765+197430598066Enzo Doria06/2016
32582^325733-5869598056Lelio R Paula07/2016
32592^325717-364598051Lelio R Paula07/2016
3260(23*2^325583-1)/2198011Lelio R Paula02/2014
3261(7*10^98007-13)/398008Robert Price06/2016
32622^325512-45995997989Enzo Doria05/2015
3263(3^205354-8)/1797978Lelio R Paula09/2013
32642^325433+7681797966Enzo Doria05/2016
32655*10^97963+8197964Robert Price08/2017
32662^325390-10906197953Enzo Doria04/2014
326713^87921+2497940Lelio R Paula08/2016
3268961^32831-960^3283197926Jean-Louis Charton02/2011
32692^325215+1290997900Lelio R Paula07/2016
32707*10^97874-6997875Robert Price01/2017
3272(17^79537+5^79537)/2297865Robert Price06/2013
327115^83212+2297865Lelio R Paula08/2016
32732^325087-10905797861Enzo Doria04/2014
32742^325074+187065797858Enzo Doria05/2016
32762^325066-211197855Yves Minet08/2013
3275CopelandErdos(97855)97855Eric W. Weisstein10/2015
327718^77944-8997841Lelio R Paula07/2016
32786^125720-1766397830Enzo Doria02/2013
32792^324972-206997827Yves Minet05/2013
32802^324944-278831997818Enzo Doria03/2016
32824*10^97799-997800Erik Branger11/2013
32812^324882+57729457597800Lelio R Paula09/2016
32832^324863-186792197794Enzo Doria04/2016
32846^125662-1847397785Enzo Doria03/2013
328512^90604+1197779Lelio R Paula07/2016
32865^139830+2497737Lelio R Paula04/2016
32872^324612+115597718Lelio R Paula07/2016
328819^76404-4497702Lelio R Paula07/2016
32892^324505-298397686Yves Minet04/2011
3290(31*2^324496-1)/4597683Lelio R Paula02/2014
32916^125488-1784397649Enzo Doria02/2013
32927^115515-297622Lelio R Paula09/2013
3293(89^50069-1)/8897603Paul Bourdelais08/2017
32946^125418-597595Lelio R Paula11/2014
32952^324076+115597557Lelio R Paula07/2016
3296(2^324074+9)/1397555Lelio R Paula10/2013
3297(55459*2^323993+1)/2197536Lelio R Paula07/2014
329813^87557-12^8755797534Jean-Louis Charton12/2008
32992^323946+7393997518Enzo Doria04/2016
33002^323937+186694797515Enzo Doria03/2016
33016^125290-1853397495Enzo Doria03/2013
33022^323845+10197488Lelio R Paula12/2012
330318^77662+6597487Lelio R Paula07/2016
33042^323772+7677197466Enzo Doria05/2016
33052^323765-11221397463Enzo Doria06/2014
33062^323720-655597450Lelio R Paula07/2016
33072^323694-186040197442Enzo Doria03/2016
330820^74886+397429Lelio R Paula06/2016
33103*10^97399+7397400Robert Price04/2016
33097^115252-5097400Lelio R Paula07/2016
3311224737#+39358197389Nicolas PALAU12/2016
3312(26*10^97353+31)/397354Robert Price07/2016
331361^54517-60^5451797331Jean-Louis Charton09/2005
3314p(19982)#/2-102497293Robert Price09/2017
33156^125021-8597286Lelio R Paula08/2016
33162^323164-4735597283Lelio R Paula07/2016
3317(3^203902+4)/3605101515797276Lelio R Paula09/2013
33182^323054-655597249Lelio R Paula07/2016
33199*10^97247-2997248Robert Price05/2017
3320(31*10^97242+41)/997243Robert Price04/2015
3321GoldenRatioPrime[97241]97241Eric W. Weisstein06/2009
332212^90098-4197233Lelio R Paula07/2016
33232^322928-21692997212Enzo Doria05/2014
3324(7*2^322896-1)/5797201Lelio R Paula02/2014
3325(2^322897+5)/314610748997193Lelio R Paula10/2013
33262^322725+7576197150Enzo Doria04/2016
3327(13*2^322686+1)/11997138Lelio R Paula11/2013
3328(41*10^97085+373)/997086Robert Price04/2017
33292^322413+7797056Lelio R Paula12/2012
33302^322406+17797054Lelio R Paula12/2012
3331(14*10^97044+31)/997045Robert Price02/2015
33322^322302+25525597023Lelio R Paula07/2016
33332^322196-11309396991Enzo Doria07/2014
33342^322000-186146996932Enzo Doria03/2016
33352^321971-11274796923Enzo Doria06/2014
333611^93062-9296915Lelio R Paula06/2016
3337(11*2^321841-7)/1596884Renaud Lifchitz03/2011
33383^203051+3496880Lelio R Paula05/2016
3339(64*10^96863-1)/2796864Serge Batalov05/2010
33402^321716-278693996847Enzo Doria03/2016
33412^321701-11305396842Enzo Doria07/2014
33422^321700-2863596842Lelio R Paula06/2016
3343(5*2^321691-1)/2796838Lelio R Paula02/2014
33446^124433-12443396828Robert Price01/2014
33452^321631+6996821Lelio R Paula12/2012
3346(13*2^321606+1)/11996813Lelio R Paula11/2013
3347(46*10^96798-1)/996799Serge Batalov10/2014
3348(59*10^96798+31)/996799Robert Price09/2015
3349223319#+23122396790Makoto Morimoto02/2016
33502^321519-2863596787Lelio R Paula06/2016
33512^321487-186723796778Enzo Doria03/2016
33522^321461-6396770Lelio R Paula12/2012
33532^321439+12396763Lelio R Paula12/2012
33542^321434+70996762Lelio R Paula02/2013
335514^84413+8996749Lelio R Paula07/2016
3356(28*10^96743+71)/996744Serge Batalov12/2008
335713^86847+9696743Lelio R Paula06/2016
33589*2^321336-796733Lelio R Paula08/2014
3359(209*10^96722-17)/396724Robert Price05/2017
33602^321187-115996687Yves Minet11/2012
33612^321182-185008196686Enzo Doria08/2015
33622^321116-11282996666Enzo Doria06/2014
33632^321108-10949996664Enzo Doria04/2014
33642^321098+279385996661Enzo Doria03/2016
33652^321057+409796648Lelio R Paula06/2016
3366(4435*29^66081-4)/796640Curtis Bright05/2015
3367p(19849)#/2-6496581Robert Price04/2017
33682^320817+18996576Lelio R Paula12/2012
33692^320788-11032796567Enzo Doria05/2014
33702^320764+79396560Lelio R Paula02/2013
3371(9179*2^320652-1)/22196528Lelio R Paula05/2015
33722^320616-7879596516Lelio R Paula03/2016
33732^320612-46193996514Enzo Doria07/2015
33745*2^320431+796461Lelio R Paula08/2014
337519^75431-9096458Lelio R Paula06/2016
3376(2^320370+3)/6796440Lelio R Paula10/2013
33772^320309+187147796423Enzo Doria05/2016
3378tau(809^6028)96410Nik Lygeros / Olivier Rozier / LR team10/2013
3379(21*2^320252-1)/189596404Lelio R Paula02/2014
33802^320232-17396400Lelio R Paula12/2012
3381175^42975-296395Lelio R Paula10/2017
338210^96377+19991196378Patrick De Geest12/2016
338310^96377-2000196377Robert Price11/2016
33842^320124-279044996367Enzo Doria03/2016
33852^320043-10877596343Enzo Doria04/2014
338610^96338+42493996339Patrick De Geest03/2016
338710^96338-928196338Robert Price09/2015
3388(3*2^320008+1)/796332Lelio R Paula09/2013
33892^319838+425796281Lelio R Paula03/2016
33902^319830-1699596279Lelio R Paula03/2016
33916^123713+14396268Lelio R Paula05/2016
3392(28*10^96265-97)/396266Robert Price07/2016
3393103^47825-10296264Norbert Schneider10/2016
33942^319713-8196244Lelio R Paula11/2012
3395(55459*2^319706+1)/2016796242Lelio R Paula07/2014
339612^89153-4396213Lelio R Paula06/2016
3397(2*10^96195-59)/396195Robert Price05/2017
33982^319545+14796193Lelio R Paula11/2012
3399(50^56597+1)/5196155Robert Price03/2014
3400(41*10^96137-59)/996138Robert Price10/2017
34012^319353-11034396135Enzo Doria05/2014
340211^92309-4296130Lelio R Paula05/2016
340314^83869-13^8386996125Jean-Louis Charton01/2009
3404(7*10^96112+143)/396113Robert Price04/2016
34052^319237+6583596100Lelio R Paula03/2016
34062^319194-184196087Yves Minet03/2013
340720^73847-3196078Lelio R Paula05/2016
34082^319107-10955596061Enzo Doria04/2014
3409(3*2^319114-1)/262796060Lelio R Paula02/2014
34102^319098-11215796059Enzo Doria06/2014
341115^81673+9496055Lelio R Paula07/2016
34122^319074+187174996051Enzo Doria05/2016
34132^319007-11211196031Enzo Doria06/2014
34142^318946-142196013Yves Minet01/2013
34152^318834-11041195979Enzo Doria05/2014
34162^318831-196595978Lelio R Paula03/2016
3417(5*10^95976+7)/395977Erik Branger03/2014
34185*3^201089-895945Lelio R Paula08/2014
34192^318711-13995942Lelio R Paula11/2012
34202^318635-116795919Lelio R Paula03/2016
342115^81555+1695917Lelio R Paula07/2016
3422(22699*2^318527+1)/2195890Lelio R Paula07/2014
34232^318496-9730595877Lelio R Paula03/2016
34242^318466+1501595868Lelio R Paula03/2016
34256^123187-17312995859Mike Oakes04/2011
34262^318423-48795855Yves Minet03/2012
3427(10223*2^318350+1)/156395834Lelio R Paula07/2014
342845369!2+102495787Robert Price02/2015
34293^200758-8695786Lelio R Paula05/2016
34303*10^95776-5995777Robert Price10/2017
3431193^41901-295768Lelio R Paula10/2017
3432(509203*2^317881-1)/5280595693Lelio R Paula04/2015
3433(11*10^95641-113)/395642Robert Price01/2017
3434(13*10^95588+11)/395589Robert Price05/2015
3435Phi(191188,10)/19118995587Maksym Voznyy11/2015
34363^200325+7095580Lelio R Paula05/2016
3437(25*10^95574-7)/995575Robert Price12/2014
3438(2^317485-3)/2131395569Lelio R Paula06/2013
34392^317464+3195567Lelio R Paula11/2012
34407^113073+8295558Lelio R Paula04/2016
34412^317251+46595503Lelio R Paula03/2016
344219^74684+5895503Lelio R Paula06/2016
3443(2^317250-7)/33995500Lelio R Paula07/2013
34446^122718-7995494Lelio R Paula05/2016
34452^317141-11049195469Enzo Doria05/2014
34462^317094+7630995455Enzo Doria05/2016
34472^317085+9595453Lelio R Paula11/2012
34482^317057-10955195444Enzo Doria04/2014
34493^200026+2895437Lelio R Paula05/2016
34502^317024+9395434Donovan Johnson06/2008
34512^316999+160595427Lelio R Paula03/2016
34522^316995-11042795426Enzo Doria05/2014
34532^316937+17795408Lelio R Paula11/2012
34542^316908+191595399Lelio R Paula03/2016
34552^316894+9995395Lelio R Paula11/2012
34566^122547+1195361Lelio R Paula05/2016
34572^316771+8287595358Lelio R Paula03/2016
3458(23*10^95326+1)/395327Serge Batalov05/2009
34591*10^95326+5795327Robert Price03/2011
346010^95326-39368795326Patrick De Geest09/2013
3461(3^199803+4)/47953995325Lelio R Paula04/2013
34622^316654-10948195323Enzo Doria04/2014
34638*10^95316+5195317Robert Price05/2017
3464(50^56099+43^56099)/9395309Serge Batalov12/2016
3465(23*2^316559+1)/392595292Lelio R Paula09/2013
346619^74503-5695271Lelio R Paula06/2016
346711^91475-438095262Enzo Doria01/2013
3468(62*10^95251-611)/995252Robert Price05/2017
3469(2^316321-509203)/6937795218Lelio R Paula06/2013
3470(79*10^95214-43)/995215Erik Branger11/2013
3471(9*2^316233-1)/175195194Lelio R Paula02/2014
34725*2^316213+995191Lelio R Paula08/2014
34732^316205-184816395188Enzo Doria07/2015
34742^316185-278791395182Enzo Doria04/2016
3475(9787*2^316142-1)/395172Lelio R Paula04/2015
34762^316140-595168Henri Lifchitz02/2006
3477(15185*2^316117-1)/395165Lelio R Paula04/2015
3478(34*10^95153-7)/9/19/1915795149Makoto Morimoto05/2016
34792^316069+7681795147Enzo Doria05/2016
3480(199*10^95134-7)/395136Robert Price02/2017
34812^316027-9730595134Lelio R Paula03/2016
34822^316006-279805195128Enzo Doria04/2016
34832^315921-279760395102Enzo Doria04/2016
34842*10^95095+6395096Robert Price10/2017
34852^315857+129995083Lelio R Paula03/2016
348614^82955-4395078Lelio R Paula06/2016
3487(2*10^95072-17)/395072Robert Price08/2014
34882^315727+6595044Lelio R Paula11/2012
34892^315725+188575795043Enzo Doria03/2017
34901*10^94983+2194984Robert Price03/2011
349110^94983-71794983Patrick De Geest08/2013
349217^77187-8294975Lelio R Paula07/2016
3493(2^315481-1017)/2062728594962Lelio R Paula06/2013
34942^315423-11032994952Enzo Doria05/2014
349511^91169-723094943Enzo Doria02/2013
34967*10^94938+6194939Robert Price02/2017
34972^315351+102594931Lelio R Paula03/2016
34982^315350-11225394930Enzo Doria06/2014
35002^315268+794906Lelio R Paula10/2012
349911^91133+6294906Lelio R Paula05/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 17 2017 09:44 (Time in France)

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