PRP Records

Probable Primes Top 10000

(180278 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 ?
32512^323720-655597450Lelio R Paula07/2016
32522^323694-186040197442Enzo Doria03/2016
325320^74886+397429Lelio R Paula06/2016
32553*10^97399+7397400Robert Price04/2016
32547^115252-5097400Lelio R Paula07/2016
3256224737#+39358197389Nicolas PALAU12/2016
3257(26*10^97353+31)/397354Robert Price07/2016
325861^54517-60^5451797331Jean-Louis Charton09/2005
32596^125021-8597286Lelio R Paula08/2016
32602^323164-4735597283Lelio R Paula07/2016
3261(3^203902+4)/3605101515797276Lelio R Paula09/2013
32622^323054-655597249Lelio R Paula07/2016
32639*10^97247-2997248Robert Price05/2017
3264(31*10^97242+41)/997243Robert Price04/2015
3265GoldenRatioPrime[97241]97241Eric W. Weisstein06/2009
326612^90098-4197233Lelio R Paula07/2016
32672^322928-21692997212Enzo Doria05/2014
3268(7*2^322896-1)/5797201Lelio R Paula02/2014
3269(2^322897+5)/314610748997193Lelio R Paula10/2013
32702^322725+7576197150Enzo Doria04/2016
3271(13*2^322686+1)/11997138Lelio R Paula11/2013
3272(41*10^97085+373)/997086Robert Price04/2017
32732^322413+7797056Lelio R Paula12/2012
32742^322406+17797054Lelio R Paula12/2012
3275(14*10^97044+31)/997045Robert Price02/2015
32762^322302+25525597023Lelio R Paula07/2016
32772^322196-11309396991Enzo Doria07/2014
32782^322000-186146996932Enzo Doria03/2016
32792^321971-11274796923Enzo Doria06/2014
328011^93062-9296915Lelio R Paula06/2016
3281(11*2^321841-7)/1596884Renaud Lifchitz03/2011
32823^203051+3496880Lelio R Paula05/2016
3283(64*10^96863-1)/2796864Serge Batalov05/2010
32842^321716-278693996847Enzo Doria03/2016
32852^321701-11305396842Enzo Doria07/2014
32862^321700-2863596842Lelio R Paula06/2016
3287(5*2^321691-1)/2796838Lelio R Paula02/2014
32886^124433-12443396828Robert Price01/2014
32892^321631+6996821Lelio R Paula12/2012
3290(13*2^321606+1)/11996813Lelio R Paula11/2013
3291(46*10^96798-1)/996799Serge Batalov10/2014
3292(59*10^96798+31)/996799Robert Price09/2015
3293223319#+23122396790Makoto Morimoto02/2016
32942^321519-2863596787Lelio R Paula06/2016
32952^321487-186723796778Enzo Doria03/2016
32962^321461-6396770Lelio R Paula12/2012
32972^321439+12396763Lelio R Paula12/2012
32982^321434+70996762Lelio R Paula02/2013
329914^84413+8996749Lelio R Paula07/2016
3300(28*10^96743+71)/996744Serge Batalov12/2008
330113^86847+9696743Lelio R Paula06/2016
33029*2^321336-796733Lelio R Paula08/2014
3303(209*10^96722-17)/396724Robert Price05/2017
33042^321187-115996687Yves Minet11/2012
33052^321182-185008196686Enzo Doria08/2015
33062^321116-11282996666Enzo Doria06/2014
33072^321108-10949996664Enzo Doria04/2014
33082^321098+279385996661Enzo Doria03/2016
33092^321057+409796648Lelio R Paula06/2016
3310(4435*29^66081-4)/796640Curtis Bright05/2015
3311p(19849)#/2-6496581Robert Price04/2017
33122^320817+18996576Lelio R Paula12/2012
33132^320788-11032796567Enzo Doria05/2014
33142^320764+79396560Lelio R Paula02/2013
3315(9179*2^320652-1)/22196528Lelio R Paula05/2015
33162^320616-7879596516Lelio R Paula03/2016
33172^320612-46193996514Enzo Doria07/2015
33185*2^320431+796461Lelio R Paula08/2014
331919^75431-9096458Lelio R Paula06/2016
3320(2^320370+3)/6796440Lelio R Paula10/2013
33212^320309+187147796423Enzo Doria05/2016
3322tau(809^6028)96410Nik Lygeros / Olivier Rozier / LR team10/2013
3323(21*2^320252-1)/189596404Lelio R Paula02/2014
33242^320232-17396400Lelio R Paula12/2012
332510^96377+19991196378Patrick De Geest12/2016
332610^96377-2000196377Robert Price11/2016
33272^320124-279044996367Enzo Doria03/2016
33282^320043-10877596343Enzo Doria04/2014
332910^96338+42493996339Patrick De Geest03/2016
333010^96338-928196338Robert Price09/2015
3331(3*2^320008+1)/796332Lelio R Paula09/2013
33322^319838+425796281Lelio R Paula03/2016
33332^319830-1699596279Lelio R Paula03/2016
33346^123713+14396268Lelio R Paula05/2016
3335(28*10^96265-97)/396266Robert Price07/2016
3336103^47825-10296264Norbert Schneider10/2016
33372^319713-8196244Lelio R Paula11/2012
3338(55459*2^319706+1)/2016796242Lelio R Paula07/2014
333912^89153-4396213Lelio R Paula06/2016
3340(2*10^96195-59)/396195Robert Price05/2017
33412^319545+14796193Lelio R Paula11/2012
3342(50^56597+1)/5196155Robert Price03/2014
33432^319353-11034396135Enzo Doria05/2014
334411^92309-4296130Lelio R Paula05/2016
334514^83869-13^8386996125Jean-Louis Charton01/2009
3346(7*10^96112+143)/396113Robert Price04/2016
33472^319237+6583596100Lelio R Paula03/2016
33482^319194-184196087Yves Minet03/2013
334920^73847-3196078Lelio R Paula05/2016
33502^319107-10955596061Enzo Doria04/2014
3351(3*2^319114-1)/262796060Lelio R Paula02/2014
33522^319098-11215796059Enzo Doria06/2014
335315^81673+9496055Lelio R Paula07/2016
33542^319074+187174996051Enzo Doria05/2016
33552^319007-11211196031Enzo Doria06/2014
33562^318946-142196013Yves Minet01/2013
33572^318834-11041195979Enzo Doria05/2014
33582^318831-196595978Lelio R Paula03/2016
3359(5*10^95976+7)/395977Erik Branger03/2014
33605*3^201089-895945Lelio R Paula08/2014
33612^318711-13995942Lelio R Paula11/2012
33622^318635-116795919Lelio R Paula03/2016
336315^81555+1695917Lelio R Paula07/2016
3364(22699*2^318527+1)/2195890Lelio R Paula07/2014
33652^318496-9730595877Lelio R Paula03/2016
33662^318466+1501595868Lelio R Paula03/2016
33676^123187-17312995859Mike Oakes04/2011
33682^318423-48795855Yves Minet03/2012
3369(10223*2^318350+1)/156395834Lelio R Paula07/2014
337045369!2+102495787Robert Price02/2015
33713^200758-8695786Lelio R Paula05/2016
3372(509203*2^317881-1)/5280595693Lelio R Paula04/2015
3373(11*10^95641-113)/395642Robert Price01/2017
3374(13*10^95588+11)/395589Robert Price05/2015
3375Phi(191188,10)/19118995587Maksym Voznyy11/2015
33763^200325+7095580Lelio R Paula05/2016
3377(25*10^95574-7)/995575Robert Price12/2014
3378(2^317485-3)/2131395569Lelio R Paula06/2013
33792^317464+3195567Lelio R Paula11/2012
33807^113073+8295558Lelio R Paula04/2016
33812^317251+46595503Lelio R Paula03/2016
338219^74684+5895503Lelio R Paula06/2016
3383(2^317250-7)/33995500Lelio R Paula07/2013
33846^122718-7995494Lelio R Paula05/2016
33852^317141-11049195469Enzo Doria05/2014
33862^317094+7630995455Enzo Doria05/2016
33872^317085+9595453Lelio R Paula11/2012
33882^317057-10955195444Enzo Doria04/2014
33893^200026+2895437Lelio R Paula05/2016
33902^317024+9395434Donovan Johnson06/2008
33912^316999+160595427Lelio R Paula03/2016
33922^316995-11042795426Enzo Doria05/2014
33932^316937+17795408Lelio R Paula11/2012
33942^316908+191595399Lelio R Paula03/2016
33952^316894+9995395Lelio R Paula11/2012
33966^122547+1195361Lelio R Paula05/2016
33972^316771+8287595358Lelio R Paula03/2016
3399(23*10^95326+1)/395327Serge Batalov05/2009
33981*10^95326+5795327Robert Price03/2011
340010^95326-39368795326Patrick De Geest09/2013
3401(3^199803+4)/47953995325Lelio R Paula04/2013
34022^316654-10948195323Enzo Doria04/2014
34038*10^95316+5195317Robert Price05/2017
3404(50^56099+43^56099)/9395309Serge Batalov12/2016
3405(23*2^316559+1)/392595292Lelio R Paula09/2013
340619^74503-5695271Lelio R Paula06/2016
340711^91475-438095262Enzo Doria01/2013
3408(62*10^95251-611)/995252Robert Price05/2017
3409(2^316321-509203)/6937795218Lelio R Paula06/2013
3410(79*10^95214-43)/995215Erik Branger11/2013
3411(9*2^316233-1)/175195194Lelio R Paula02/2014
34125*2^316213+995191Lelio R Paula08/2014
34132^316205-184816395188Enzo Doria07/2015
34142^316185-278791395182Enzo Doria04/2016
3415(9787*2^316142-1)/395172Lelio R Paula04/2015
34162^316140-595168Henri Lifchitz02/2006
3417(15185*2^316117-1)/395165Lelio R Paula04/2015
3418(34*10^95153-7)/9/19/1915795149Makoto Morimoto05/2016
34192^316069+7681795147Enzo Doria05/2016
3420(199*10^95134-7)/395136Robert Price02/2017
34212^316027-9730595134Lelio R Paula03/2016
34222^316006-279805195128Enzo Doria04/2016
34232^315921-279760395102Enzo Doria04/2016
34242^315857+129995083Lelio R Paula03/2016
342514^82955-4395078Lelio R Paula06/2016
3426(2*10^95072-17)/395072Robert Price08/2014
34272^315727+6595044Lelio R Paula11/2012
34282^315725+188575795043Enzo Doria03/2017
34291*10^94983+2194984Robert Price03/2011
343010^94983-71794983Patrick De Geest08/2013
343117^77187-8294975Lelio R Paula07/2016
3432(2^315481-1017)/2062728594962Lelio R Paula06/2013
34332^315423-11032994952Enzo Doria05/2014
343411^91169-723094943Enzo Doria02/2013
34357*10^94938+6194939Robert Price02/2017
34362^315351+102594931Lelio R Paula03/2016
34372^315350-11225394930Enzo Doria06/2014
3440((1001327^(15817)+1)/1001328)94906Faysal YAtim10/2010
34392^315268+794906Lelio R Paula10/2012
343811^91133+6294906Lelio R Paula05/2016
344130^64244+4194897Lelio R Paula08/2012
3442(151*10^94885-7)/994887Robert Price07/2017
34434^157583+2214794875Mike Oakes01/2011
34442^315098+12394854Lelio R Paula11/2012
34453^198791-3494848Robert Price11/2013
34463*2^315067+794846Lelio R Paula08/2014
3447(9*2^315057+1)/7394841Lelio R Paula09/2013
3448(16*10^94822+53)/394823Robert Price12/2016
34498*6^121849-794818Lelio R Paula10/2014
3450(85*10^94802+473)/994803Robert Price03/2017
34512^314870-10876194786Enzo Doria03/2014
34525*2^314841-394778Lelio R Paula08/2014
34536^121772+11394758Lelio R Paula05/2016
34546^121756-1625394745Enzo Doria02/2013
34552^314718-11279394740Enzo Doria06/2014
34562^314697-184729394734Enzo Doria07/2015
34582^314548-24994689Yves Minet02/2012
34575^135469+4294689Lelio R Paula04/2016
3459gcd(V(1137755),5*F(227551)*(F(227551)-1)+1)94676Serge Batalov04/2015
34603*2^314152+594570Lelio R Paula08/2014
34612*6^121530-594570Lelio R Paula10/2014
34627*10^94563+8794564Robert Price11/2016
34632^314114-10967794558Enzo Doria04/2014
34642^314059+7658394542Enzo Doria05/2016
34652^314041-403594536Lelio R Paula03/2016
3466(7*2^314003-11)/1594524Renaud Lifchitz03/2011
346711^90760-471094517Enzo Doria01/2013
3468(7*2^313926-1)/14882194497Lelio R Paula02/2014
346994*10^94493-394495Robert Price11/2016
3470(1000547^15749+1)/100054894492Faysal YAtim12/2008
34717^111792-3294476Lelio R Paula04/2016
347211^90680-585094434Enzo Doria01/2013
34732^313675-11012594426Enzo Doria04/2014
3474(2999*29^64556-2427)/494410Curtis Bright05/2015
34752^313609-11222594406Enzo Doria06/2014
34762^313584+7290194399Enzo Doria04/2016
34772^313510-11286594376Enzo Doria06/2014
34787*10^94373+8794374Robert Price11/2016
3479(9^98897+8^98897)/1794371Robert Price12/2012
34802^313453-11470394359Enzo Doria04/2015
3481(379*10^94337-1)/994339Robert Price08/2017
34822^313344-313344+194326Robert Price10/2014
348320^72481-4994300Lelio R Paula05/2016
348444725!2+12894289Robert Price03/2015
34854*10^94286+994287Robert Price05/2015
348617^76621+2494279Lelio R Paula07/2016
34872^313156-11285994270Enzo Doria06/2014
34886^121130-5994258Lelio R Paula05/2016
34893^197542+2894252Robert Price11/2013
3490(3^197521+2)/5165594237Lelio R Paula04/2013
34912^313045-595594236Lelio R Paula03/2016
3492(67*10^94212+23)/994213Ray Chandler02/2011
34932^312909-186520394195Enzo Doria03/2016
34942^312848-14994177Lelio R Paula11/2012
34954^156403-7759794164Mike Oakes04/2011
349618^75004-8594151Lelio R Paula06/2016
349719^73622-4894145Lelio R Paula06/2016
3498(11^90397-3^90397)/894138Robert Price04/2011
3499(3^197287+5)/1694129Lelio R Paula04/2013
350012^87212-3794118Lelio R Paula06/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 20 2017 08:36 (Time in France)

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