PRP Records

Probable Primes Top 10000

(173006 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 ?
32512^321187-115996687Yves Minet11/2012
32522^321182-185008196686Enzo Doria08/2015
32532^321116-11282996666Enzo Doria06/2014
32542^321108-10949996664Enzo Doria04/2014
32552^321098+279385996661Enzo Doria03/2016
32562^321057+409796648Lelio R Paula06/2016
3257(4435*29^66081-4)/796640Curtis Bright05/2015
3258p(19849)#/2-6496581Robert Price04/2017
32592^320817+18996576Lelio R Paula12/2012
32602^320788-11032796567Enzo Doria05/2014
32612^320764+79396560Lelio R Paula02/2013
3262(9179*2^320652-1)/22196528Lelio R Paula05/2015
32632^320616-7879596516Lelio R Paula03/2016
32642^320612-46193996514Enzo Doria07/2015
32655*2^320431+796461Lelio R Paula08/2014
326619^75431-9096458Lelio R Paula06/2016
3267(2^320370+3)/6796440Lelio R Paula10/2013
32682^320309+187147796423Enzo Doria05/2016
3269tau(809^6028)96410Nik Lygeros / Olivier Rozier / LR team10/2013
3270(21*2^320252-1)/189596404Lelio R Paula02/2014
32712^320232-17396400Lelio R Paula12/2012
327210^96377+19991196378Patrick De Geest12/2016
327310^96377-2000196377Robert Price11/2016
32742^320124-279044996367Enzo Doria03/2016
32752^320043-10877596343Enzo Doria04/2014
327610^96338+42493996339Patrick De Geest03/2016
327710^96338-928196338Robert Price09/2015
3278(3*2^320008+1)/796332Lelio R Paula09/2013
32792^319838+425796281Lelio R Paula03/2016
32802^319830-1699596279Lelio R Paula03/2016
32816^123713+14396268Lelio R Paula05/2016
3282(28*10^96265-97)/396266Robert Price07/2016
3283103^47825-10296264Norbert Schneider10/2016
32842^319713-8196244Lelio R Paula11/2012
3285(55459*2^319706+1)/2016796242Lelio R Paula07/2014
328612^89153-4396213Lelio R Paula06/2016
3287(2*10^96195-59)/396195Robert Price05/2017
32882^319545+14796193Lelio R Paula11/2012
3289(50^56597+1)/5196155Robert Price03/2014
32902^319353-11034396135Enzo Doria05/2014
329111^92309-4296130Lelio R Paula05/2016
329214^83869-13^8386996125Jean-Louis Charton01/2009
3293(7*10^96112+143)/396113Robert Price04/2016
32942^319237+6583596100Lelio R Paula03/2016
32952^319194-184196087Yves Minet03/2013
329620^73847-3196078Lelio R Paula05/2016
32972^319107-10955596061Enzo Doria04/2014
3298(3*2^319114-1)/262796060Lelio R Paula02/2014
32992^319098-11215796059Enzo Doria06/2014
330015^81673+9496055Lelio R Paula07/2016
33012^319074+187174996051Enzo Doria05/2016
33022^319007-11211196031Enzo Doria06/2014
33032^318946-142196013Yves Minet01/2013
33042^318834-11041195979Enzo Doria05/2014
33052^318831-196595978Lelio R Paula03/2016
3306(5*10^95976+7)/395977Erik Branger03/2014
33075*3^201089-895945Lelio R Paula08/2014
33082^318711-13995942Lelio R Paula11/2012
33092^318635-116795919Lelio R Paula03/2016
331015^81555+1695917Lelio R Paula07/2016
3311(22699*2^318527+1)/2195890Lelio R Paula07/2014
33122^318496-9730595877Lelio R Paula03/2016
33132^318466+1501595868Lelio R Paula03/2016
33146^123187-17312995859Mike Oakes04/2011
33152^318423-48795855Yves Minet03/2012
3316(10223*2^318350+1)/156395834Lelio R Paula07/2014
331745369!2+102495787Robert Price02/2015
33183^200758-8695786Lelio R Paula05/2016
3319(509203*2^317881-1)/5280595693Lelio R Paula04/2015
3320(11*10^95641-113)/395642Robert Price01/2017
3321(13*10^95588+11)/395589Robert Price05/2015
3322Phi(191188,10)/19118995587Maksym Voznyy11/2015
33233^200325+7095580Lelio R Paula05/2016
3324(25*10^95574-7)/995575Robert Price12/2014
3325(2^317485-3)/2131395569Lelio R Paula06/2013
33262^317464+3195567Lelio R Paula11/2012
33277^113073+8295558Lelio R Paula04/2016
33282^317251+46595503Lelio R Paula03/2016
332919^74684+5895503Lelio R Paula06/2016
3330(2^317250-7)/33995500Lelio R Paula07/2013
33316^122718-7995494Lelio R Paula05/2016
33322^317141-11049195469Enzo Doria05/2014
33332^317094+7630995455Enzo Doria05/2016
33342^317085+9595453Lelio R Paula11/2012
33352^317057-10955195444Enzo Doria04/2014
33363^200026+2895437Lelio R Paula05/2016
33372^317024+9395434Donovan Johnson06/2008
33382^316999+160595427Lelio R Paula03/2016
33392^316995-11042795426Enzo Doria05/2014
33402^316937+17795408Lelio R Paula11/2012
33412^316908+191595399Lelio R Paula03/2016
33422^316894+9995395Lelio R Paula11/2012
33436^122547+1195361Lelio R Paula05/2016
33442^316771+8287595358Lelio R Paula03/2016
3346(23*10^95326+1)/395327Serge Batalov05/2009
33451*10^95326+5795327Robert Price03/2011
334710^95326-39368795326Patrick De Geest09/2013
3348(3^199803+4)/47953995325Lelio R Paula04/2013
33492^316654-10948195323Enzo Doria04/2014
33508*10^95316+5195317Robert Price05/2017
3351(50^56099+43^56099)/9395309Serge Batalov12/2016
3352(23*2^316559+1)/392595292Lelio R Paula09/2013
335319^74503-5695271Lelio R Paula06/2016
335411^91475-438095262Enzo Doria01/2013
3355(2^316321-509203)/6937795218Lelio R Paula06/2013
3356(79*10^95214-43)/995215Erik Branger11/2013
3357(9*2^316233-1)/175195194Lelio R Paula02/2014
33585*2^316213+995191Lelio R Paula08/2014
33592^316205-184816395188Enzo Doria07/2015
33602^316185-278791395182Enzo Doria04/2016
3361(9787*2^316142-1)/395172Lelio R Paula04/2015
33622^316140-595168Henri Lifchitz02/2006
3363(15185*2^316117-1)/395165Lelio R Paula04/2015
3364(34*10^95153-7)/9/19/1915795149Makoto Morimoto05/2016
33652^316069+7681795147Enzo Doria05/2016
3366(199*10^95134-7)/395136Robert Price02/2017
33672^316027-9730595134Lelio R Paula03/2016
33682^316006-279805195128Enzo Doria04/2016
33692^315921-279760395102Enzo Doria04/2016
33702^315857+129995083Lelio R Paula03/2016
337114^82955-4395078Lelio R Paula06/2016
3372(2*10^95072-17)/395072Robert Price08/2014
33732^315727+6595044Lelio R Paula11/2012
33742^315725+188575795043Enzo Doria03/2017
33751*10^94983+2194984Robert Price03/2011
337610^94983-71794983Patrick De Geest08/2013
337717^77187-8294975Lelio R Paula07/2016
3378(2^315481-1017)/2062728594962Lelio R Paula06/2013
33792^315423-11032994952Enzo Doria05/2014
338011^91169-723094943Enzo Doria02/2013
33817*10^94938+6194939Robert Price02/2017
33822^315351+102594931Lelio R Paula03/2016
33832^315350-11225394930Enzo Doria06/2014
3385((1001327^(15817)+1)/1001328)94906Faysal YAtim10/2010
33842^315268+794906Lelio R Paula10/2012
338611^91133+6294906Lelio R Paula05/2016
338730^64244+4194897Lelio R Paula08/2012
33884^157583+2214794875Mike Oakes01/2011
33892^315098+12394854Lelio R Paula11/2012
33903^198791-3494848Robert Price11/2013
33913*2^315067+794846Lelio R Paula08/2014
3392(9*2^315057+1)/7394841Lelio R Paula09/2013
3393(16*10^94822+53)/394823Robert Price12/2016
33948*6^121849-794818Lelio R Paula10/2014
3395(85*10^94802+473)/994803Robert Price03/2017
33962^314870-10876194786Enzo Doria03/2014
33975*2^314841-394778Lelio R Paula08/2014
33986^121772+11394758Lelio R Paula05/2016
33996^121756-1625394745Enzo Doria02/2013
34002^314718-11279394740Enzo Doria06/2014
34012^314697-184729394734Enzo Doria07/2015
34032^314548-24994689Yves Minet02/2012
34025^135469+4294689Lelio R Paula04/2016
3404gcd(V(1137755),5*F(227551)*(F(227551)-1)+1)94676Serge Batalov04/2015
34053*2^314152+594570Lelio R Paula08/2014
34062*6^121530-594570Lelio R Paula10/2014
34077*10^94563+8794564Robert Price11/2016
34082^314114-10967794558Enzo Doria04/2014
34092^314059+7658394542Enzo Doria05/2016
34102^314041-403594536Lelio R Paula03/2016
3411(7*2^314003-11)/1594524Renaud Lifchitz03/2011
341211^90760-471094517Enzo Doria01/2013
3413(7*2^313926-1)/14882194497Lelio R Paula02/2014
341494*10^94493-394495Robert Price11/2016
3415(1000547^15749+1)/100054894492Faysal YAtim12/2008
34167^111792-3294476Lelio R Paula04/2016
341711^90680-585094434Enzo Doria01/2013
34182^313675-11012594426Enzo Doria04/2014
3419(2999*29^64556-2427)/494410Curtis Bright05/2015
34202^313609-11222594406Enzo Doria06/2014
34212^313584+7290194399Enzo Doria04/2016
34222^313510-11286594376Enzo Doria06/2014
34237*10^94373+8794374Robert Price11/2016
3424(9^98897+8^98897)/1794371Robert Price12/2012
34252^313453-11470394359Enzo Doria04/2015
34262^313344-313344+194326Robert Price10/2014
342720^72481-4994300Lelio R Paula05/2016
342844725!2+12894289Robert Price03/2015
34294*10^94286+994287Robert Price05/2015
343017^76621+2494279Lelio R Paula07/2016
34312^313156-11285994270Enzo Doria06/2014
34326^121130-5994258Lelio R Paula05/2016
34333^197542+2894252Robert Price11/2013
3434(3^197521+2)/5165594237Lelio R Paula04/2013
34352^313045-595594236Lelio R Paula03/2016
3436(67*10^94212+23)/994213Ray Chandler02/2011
34372^312909-186520394195Enzo Doria03/2016
34382^312848-14994177Lelio R Paula11/2012
34394^156403-7759794164Mike Oakes04/2011
344018^75004-8594151Lelio R Paula06/2016
344119^73622-4894145Lelio R Paula06/2016
3442(11^90397-3^90397)/894138Robert Price04/2011
3443(3^197287+5)/1694129Lelio R Paula04/2013
344412^87212-3794118Lelio R Paula06/2016
344511^90376+7694117Lelio R Paula05/2016
3446(6^120946-11)/594114Paul Bourdelais11/2011
34472^312562-11268594091Enzo Doria06/2014
34482^312404-86968810594043Lelio R Paula09/2016
34492^312387+279353394038Enzo Doria03/2016
345010^94016+9194017Robert Price04/2011
3451(15*2^312325-1)/720194017Lelio R Paula02/2014
345310^94016-18896394016Patrick De Geest08/2013
3452(17*2^312315-1)/4594016Lelio R Paula02/2014
34546^120802+766194003Mike Oakes04/2011
3455(67607*2^312254+1)/17794001Lelio R Paula06/2014
3456(11*2^312207+1)/1993984Lelio R Paula09/2013
34572^312201+5193982Lelio R Paula11/2012
3458(4*6^120749+1)/593961Serge Batalov10/2014
34593^196892+5893942Lelio R Paula05/2016
34602^312060+1891593940Lelio R Paula03/2016
34612^311992-1620993919Enzo Doria04/2013
34622^311965-3993911Lelio R Paula11/2012
34632^311920-11168993898Enzo Doria05/2014
34647*10^93887-4793888Robert Price02/2017
346512^86965-1393851Lelio R Paula06/2016
34662^311705+1609593833Lelio R Paula03/2016
34672^311665-8193821Lelio R Paula11/2012
346811^90073+9293802Lelio R Paula05/2016
34696*10^93792+4193793Robert Price01/2017
3470(2^311580+7)/59132993790Lelio R Paula06/2013
347112^86900-7793781Lelio R Paula06/2016
34722^311508-10976993774Enzo Doria04/2014
34732^311486-185962193767Enzo Doria03/2016
3474Phi(93811,10)/968129521/2109997013/3280113810431/63963778254583193765Kurt Beschorner04/2015
34752^311471+31146993763Renaud Lifchitz01/2003
34762^311426+7945993749Enzo Doria06/2016
34772^311294+577593709Lelio R Paula03/2016
34782^311252-101793697Lelio R Paula03/2016
34792^311247-11204193695Enzo Doria06/2014
34802^311205-10964593683Enzo Doria04/2014
34815^134027-8493681Lelio R Paula04/2016
3482(2^311148-1017)/55793663Lelio R Paula06/2013
3483(2^311027-2^155514+1)/59362811/2006
34843^196192-2893608Robert Price12/2013
3485216091#+26143393606Makoto Morimoto12/2015
34865^133917+6893604Lelio R Paula04/2016
34872^310924-170993598Yves Minet03/2013
3488(266*10^93577-11)/393579Robert Price09/2016
3489(16*10^93577+161)/393578Robert Price05/2016
34903^196113-5693570Lelio R Paula04/2016
34912^310806-11034593562Enzo Doria05/2014
34923^196093+8693561Lelio R Paula04/2016
34932^310780-232793555Yves Minet10/2013
349430^63332+4193550Lelio R Paula08/2012
3495(21181*2^310707+1)/2193536Lelio R Paula06/2014
34968*5^133807+793528Lelio R Paula10/2014
34972^310686+819393526Lelio R Paula03/2016
34982^310646+6393514Lelio R Paula11/2012
3499(77*10^93508+31)/993509Robert Price10/2015
3500(1000907^15583+1)/100090893499Faysal YAtim04/2009


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

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