PRP Records

Probable Primes Top 10000

(174961 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 ?
3251(11*2^321841-7)/1596884Renaud Lifchitz03/2011
32523^203051+3496880Lelio R Paula05/2016
3253(64*10^96863-1)/2796864Serge Batalov05/2010
32542^321716-278693996847Enzo Doria03/2016
32552^321701-11305396842Enzo Doria07/2014
32562^321700-2863596842Lelio R Paula06/2016
3257(5*2^321691-1)/2796838Lelio R Paula02/2014
32586^124433-12443396828Robert Price01/2014
32592^321631+6996821Lelio R Paula12/2012
3260(13*2^321606+1)/11996813Lelio R Paula11/2013
3261(46*10^96798-1)/996799Serge Batalov10/2014
3262(59*10^96798+31)/996799Robert Price09/2015
3263223319#+23122396790Makoto Morimoto02/2016
32642^321519-2863596787Lelio R Paula06/2016
32652^321487-186723796778Enzo Doria03/2016
32662^321461-6396770Lelio R Paula12/2012
32672^321439+12396763Lelio R Paula12/2012
32682^321434+70996762Lelio R Paula02/2013
326914^84413+8996749Lelio R Paula07/2016
3270(28*10^96743+71)/996744Serge Batalov12/2008
327113^86847+9696743Lelio R Paula06/2016
32729*2^321336-796733Lelio R Paula08/2014
3273(209*10^96722-17)/396724Robert Price05/2017
32742^321187-115996687Yves Minet11/2012
32752^321182-185008196686Enzo Doria08/2015
32762^321116-11282996666Enzo Doria06/2014
32772^321108-10949996664Enzo Doria04/2014
32782^321098+279385996661Enzo Doria03/2016
32792^321057+409796648Lelio R Paula06/2016
3280(4435*29^66081-4)/796640Curtis Bright05/2015
3281p(19849)#/2-6496581Robert Price04/2017
32822^320817+18996576Lelio R Paula12/2012
32832^320788-11032796567Enzo Doria05/2014
32842^320764+79396560Lelio R Paula02/2013
3285(9179*2^320652-1)/22196528Lelio R Paula05/2015
32862^320616-7879596516Lelio R Paula03/2016
32872^320612-46193996514Enzo Doria07/2015
32885*2^320431+796461Lelio R Paula08/2014
328919^75431-9096458Lelio R Paula06/2016
3290(2^320370+3)/6796440Lelio R Paula10/2013
32912^320309+187147796423Enzo Doria05/2016
3292tau(809^6028)96410Nik Lygeros / Olivier Rozier / LR team10/2013
3293(21*2^320252-1)/189596404Lelio R Paula02/2014
32942^320232-17396400Lelio R Paula12/2012
329510^96377+19991196378Patrick De Geest12/2016
329610^96377-2000196377Robert Price11/2016
32972^320124-279044996367Enzo Doria03/2016
32982^320043-10877596343Enzo Doria04/2014
329910^96338+42493996339Patrick De Geest03/2016
330010^96338-928196338Robert Price09/2015
3301(3*2^320008+1)/796332Lelio R Paula09/2013
33022^319838+425796281Lelio R Paula03/2016
33032^319830-1699596279Lelio R Paula03/2016
33046^123713+14396268Lelio R Paula05/2016
3305(28*10^96265-97)/396266Robert Price07/2016
3306103^47825-10296264Norbert Schneider10/2016
33072^319713-8196244Lelio R Paula11/2012
3308(55459*2^319706+1)/2016796242Lelio R Paula07/2014
330912^89153-4396213Lelio R Paula06/2016
3310(2*10^96195-59)/396195Robert Price05/2017
33112^319545+14796193Lelio R Paula11/2012
3312(50^56597+1)/5196155Robert Price03/2014
33132^319353-11034396135Enzo Doria05/2014
331411^92309-4296130Lelio R Paula05/2016
331514^83869-13^8386996125Jean-Louis Charton01/2009
3316(7*10^96112+143)/396113Robert Price04/2016
33172^319237+6583596100Lelio R Paula03/2016
33182^319194-184196087Yves Minet03/2013
331920^73847-3196078Lelio R Paula05/2016
33202^319107-10955596061Enzo Doria04/2014
3321(3*2^319114-1)/262796060Lelio R Paula02/2014
33222^319098-11215796059Enzo Doria06/2014
332315^81673+9496055Lelio R Paula07/2016
33242^319074+187174996051Enzo Doria05/2016
33252^319007-11211196031Enzo Doria06/2014
33262^318946-142196013Yves Minet01/2013
33272^318834-11041195979Enzo Doria05/2014
33282^318831-196595978Lelio R Paula03/2016
3329(5*10^95976+7)/395977Erik Branger03/2014
33305*3^201089-895945Lelio R Paula08/2014
33312^318711-13995942Lelio R Paula11/2012
33322^318635-116795919Lelio R Paula03/2016
333315^81555+1695917Lelio R Paula07/2016
3334(22699*2^318527+1)/2195890Lelio R Paula07/2014
33352^318496-9730595877Lelio R Paula03/2016
33362^318466+1501595868Lelio R Paula03/2016
33376^123187-17312995859Mike Oakes04/2011
33382^318423-48795855Yves Minet03/2012
3339(10223*2^318350+1)/156395834Lelio R Paula07/2014
334045369!2+102495787Robert Price02/2015
33413^200758-8695786Lelio R Paula05/2016
3342(509203*2^317881-1)/5280595693Lelio R Paula04/2015
3343(11*10^95641-113)/395642Robert Price01/2017
3344(13*10^95588+11)/395589Robert Price05/2015
3345Phi(191188,10)/19118995587Maksym Voznyy11/2015
33463^200325+7095580Lelio R Paula05/2016
3347(25*10^95574-7)/995575Robert Price12/2014
3348(2^317485-3)/2131395569Lelio R Paula06/2013
33492^317464+3195567Lelio R Paula11/2012
33507^113073+8295558Lelio R Paula04/2016
33512^317251+46595503Lelio R Paula03/2016
335219^74684+5895503Lelio R Paula06/2016
3353(2^317250-7)/33995500Lelio R Paula07/2013
33546^122718-7995494Lelio R Paula05/2016
33552^317141-11049195469Enzo Doria05/2014
33562^317094+7630995455Enzo Doria05/2016
33572^317085+9595453Lelio R Paula11/2012
33582^317057-10955195444Enzo Doria04/2014
33593^200026+2895437Lelio R Paula05/2016
33602^317024+9395434Donovan Johnson06/2008
33612^316999+160595427Lelio R Paula03/2016
33622^316995-11042795426Enzo Doria05/2014
33632^316937+17795408Lelio R Paula11/2012
33642^316908+191595399Lelio R Paula03/2016
33652^316894+9995395Lelio R Paula11/2012
33666^122547+1195361Lelio R Paula05/2016
33672^316771+8287595358Lelio R Paula03/2016
3369(23*10^95326+1)/395327Serge Batalov05/2009
33681*10^95326+5795327Robert Price03/2011
337010^95326-39368795326Patrick De Geest09/2013
3371(3^199803+4)/47953995325Lelio R Paula04/2013
33722^316654-10948195323Enzo Doria04/2014
33738*10^95316+5195317Robert Price05/2017
3374(50^56099+43^56099)/9395309Serge Batalov12/2016
3375(23*2^316559+1)/392595292Lelio R Paula09/2013
337619^74503-5695271Lelio R Paula06/2016
337711^91475-438095262Enzo Doria01/2013
3378(62*10^95251-611)/995252Robert Price05/2017
3379(2^316321-509203)/6937795218Lelio R Paula06/2013
3380(79*10^95214-43)/995215Erik Branger11/2013
3381(9*2^316233-1)/175195194Lelio R Paula02/2014
33825*2^316213+995191Lelio R Paula08/2014
33832^316205-184816395188Enzo Doria07/2015
33842^316185-278791395182Enzo Doria04/2016
3385(9787*2^316142-1)/395172Lelio R Paula04/2015
33862^316140-595168Henri Lifchitz02/2006
3387(15185*2^316117-1)/395165Lelio R Paula04/2015
3388(34*10^95153-7)/9/19/1915795149Makoto Morimoto05/2016
33892^316069+7681795147Enzo Doria05/2016
3390(199*10^95134-7)/395136Robert Price02/2017
33912^316027-9730595134Lelio R Paula03/2016
33922^316006-279805195128Enzo Doria04/2016
33932^315921-279760395102Enzo Doria04/2016
33942^315857+129995083Lelio R Paula03/2016
339514^82955-4395078Lelio R Paula06/2016
3396(2*10^95072-17)/395072Robert Price08/2014
33972^315727+6595044Lelio R Paula11/2012
33982^315725+188575795043Enzo Doria03/2017
33991*10^94983+2194984Robert Price03/2011
340010^94983-71794983Patrick De Geest08/2013
340117^77187-8294975Lelio R Paula07/2016
3402(2^315481-1017)/2062728594962Lelio R Paula06/2013
34032^315423-11032994952Enzo Doria05/2014
340411^91169-723094943Enzo Doria02/2013
34057*10^94938+6194939Robert Price02/2017
34062^315351+102594931Lelio R Paula03/2016
34072^315350-11225394930Enzo Doria06/2014
3408((1001327^(15817)+1)/1001328)94906Faysal YAtim10/2010
34102^315268+794906Lelio R Paula10/2012
340911^91133+6294906Lelio R Paula05/2016
341130^64244+4194897Lelio R Paula08/2012
34124^157583+2214794875Mike Oakes01/2011
34132^315098+12394854Lelio R Paula11/2012
34143^198791-3494848Robert Price11/2013
34153*2^315067+794846Lelio R Paula08/2014
3416(9*2^315057+1)/7394841Lelio R Paula09/2013
3417(16*10^94822+53)/394823Robert Price12/2016
34188*6^121849-794818Lelio R Paula10/2014
3419(85*10^94802+473)/994803Robert Price03/2017
34202^314870-10876194786Enzo Doria03/2014
34215*2^314841-394778Lelio R Paula08/2014
34226^121772+11394758Lelio R Paula05/2016
34236^121756-1625394745Enzo Doria02/2013
34242^314718-11279394740Enzo Doria06/2014
34252^314697-184729394734Enzo Doria07/2015
34272^314548-24994689Yves Minet02/2012
34265^135469+4294689Lelio R Paula04/2016
3428gcd(V(1137755),5*F(227551)*(F(227551)-1)+1)94676Serge Batalov04/2015
34293*2^314152+594570Lelio R Paula08/2014
34302*6^121530-594570Lelio R Paula10/2014
34317*10^94563+8794564Robert Price11/2016
34322^314114-10967794558Enzo Doria04/2014
34332^314059+7658394542Enzo Doria05/2016
34342^314041-403594536Lelio R Paula03/2016
3435(7*2^314003-11)/1594524Renaud Lifchitz03/2011
343611^90760-471094517Enzo Doria01/2013
3437(7*2^313926-1)/14882194497Lelio R Paula02/2014
343894*10^94493-394495Robert Price11/2016
3439(1000547^15749+1)/100054894492Faysal YAtim12/2008
34407^111792-3294476Lelio R Paula04/2016
344111^90680-585094434Enzo Doria01/2013
34422^313675-11012594426Enzo Doria04/2014
3443(2999*29^64556-2427)/494410Curtis Bright05/2015
34442^313609-11222594406Enzo Doria06/2014
34452^313584+7290194399Enzo Doria04/2016
34462^313510-11286594376Enzo Doria06/2014
34477*10^94373+8794374Robert Price11/2016
3448(9^98897+8^98897)/1794371Robert Price12/2012
34492^313453-11470394359Enzo Doria04/2015
34502^313344-313344+194326Robert Price10/2014
345120^72481-4994300Lelio R Paula05/2016
345244725!2+12894289Robert Price03/2015
34534*10^94286+994287Robert Price05/2015
345417^76621+2494279Lelio R Paula07/2016
34552^313156-11285994270Enzo Doria06/2014
34566^121130-5994258Lelio R Paula05/2016
34573^197542+2894252Robert Price11/2013
3458(3^197521+2)/5165594237Lelio R Paula04/2013
34592^313045-595594236Lelio R Paula03/2016
3460(67*10^94212+23)/994213Ray Chandler02/2011
34612^312909-186520394195Enzo Doria03/2016
34622^312848-14994177Lelio R Paula11/2012
34634^156403-7759794164Mike Oakes04/2011
346418^75004-8594151Lelio R Paula06/2016
346519^73622-4894145Lelio R Paula06/2016
3466(11^90397-3^90397)/894138Robert Price04/2011
3467(3^197287+5)/1694129Lelio R Paula04/2013
346812^87212-3794118Lelio R Paula06/2016
346911^90376+7694117Lelio R Paula05/2016
3470(6^120946-11)/594114Paul Bourdelais11/2011
34712^312562-11268594091Enzo Doria06/2014
34722^312404-86968810594043Lelio R Paula09/2016
34732^312387+279353394038Enzo Doria03/2016
347510^94016+9194017Robert Price04/2011
3474(15*2^312325-1)/720194017Lelio R Paula02/2014
347710^94016-18896394016Patrick De Geest08/2013
3476(17*2^312315-1)/4594016Lelio R Paula02/2014
34786^120802+766194003Mike Oakes04/2011
3479(67607*2^312254+1)/17794001Lelio R Paula06/2014
3480(11*2^312207+1)/1993984Lelio R Paula09/2013
34812^312201+5193982Lelio R Paula11/2012
3482(4*6^120749+1)/593961Serge Batalov10/2014
34833^196892+5893942Lelio R Paula05/2016
34842^312060+1891593940Lelio R Paula03/2016
34852^311992-1620993919Enzo Doria04/2013
34862^311965-3993911Lelio R Paula11/2012
34872^311920-11168993898Enzo Doria05/2014
34887*10^93887-4793888Robert Price02/2017
348912^86965-1393851Lelio R Paula06/2016
34902^311705+1609593833Lelio R Paula03/2016
34912^311665-8193821Lelio R Paula11/2012
349211^90073+9293802Lelio R Paula05/2016
34936*10^93792+4193793Robert Price01/2017
3494(2^311580+7)/59132993790Lelio R Paula06/2013
349512^86900-7793781Lelio R Paula06/2016
34962^311508-10976993774Enzo Doria04/2014
34972^311486-185962193767Enzo Doria03/2016
3498Phi(93811,10)/968129521/2109997013/3280113810431/63963778254583193765Kurt Beschorner04/2015
34992^311471+31146993763Renaud Lifchitz01/2003
35002^311426+7945993749Enzo Doria06/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 22 2017 08:34 (Time in France)

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