PRP Records

Probable Primes Top 10000

(225451 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 ?
37512^322928-21692997212Enzo Doria05/2014
3752(7*2^322896-1)/5797201Lelio R Paula02/2014
3753(2^322897+5)/314610748997193Lelio R Paula10/2013
37542^322725+7576197150Enzo Doria04/2016
3755(13*2^322686+1)/11997138Lelio R Paula11/2013
3756(41*10^97085+373)/997086Robert Price04/2017
37572^322413+7797056Lelio R Paula12/2012
37582^322406+17797054Lelio R Paula12/2012
3759(14*10^97044+31)/997045Robert Price02/2015
37602^322302+25525597023Lelio R Paula07/2016
37612^322196-11309396991Enzo Doria07/2014
37622^322000-186146996932Enzo Doria03/2016
37632^321971-11274796923Enzo Doria06/2014
376411^93062-9296915Lelio R Paula06/2016
3765(11*2^321841-7)/1596884Renaud Lifchitz03/2011
37663^203051+3496880Lelio R Paula05/2016
37672*10^96867-5196868Robert Price11/2017
3768(64*10^96863-1)/2796864Serge Batalov05/2010
37692^321716-278693996847Enzo Doria03/2016
37702^321701-11305396842Enzo Doria07/2014
37712^321700-2863596842Lelio R Paula06/2016
3772(5*2^321691-1)/2796838Lelio R Paula02/2014
37736^124433-12443396828Robert Price01/2014
37742^321631+6996821Lelio R Paula12/2012
3775(13*2^321606+1)/11996813Lelio R Paula11/2013
3776(46*10^96798-1)/996799Serge Batalov10/2014
3777(59*10^96798+31)/996799Robert Price09/2015
3778223319#+23122396790Makoto Morimoto02/2016
37792^321519-2863596787Lelio R Paula06/2016
37802^321487-186723796778Enzo Doria03/2016
37812^321461-6396770Lelio R Paula12/2012
37822^321439+12396763Lelio R Paula12/2012
37832^321434+70996762Lelio R Paula02/2013
378414^84413+8996749Lelio R Paula07/2016
3785(28*10^96743+71)/996744Serge Batalov12/2008
378613^86847+9696743Lelio R Paula06/2016
37879*2^321336-796733Lelio R Paula08/2014
3788(209*10^96722-17)/396724Robert Price05/2017
37892^321187-115996687Yves Minet11/2012
37902^321182-185008196686Enzo Doria08/2015
37912^321116-11282996666Enzo Doria06/2014
37922^321108-10949996664Enzo Doria04/2014
37932^321098+279385996661Enzo Doria03/2016
37942^321057+409796648Lelio R Paula06/2016
3795(4435*29^66081-4)/796640Curtis Bright05/2015
3796p(19849)#/2-6496581Robert Price04/2017
37972^320817+18996576Lelio R Paula12/2012
3798(361*10^96567-163)/996569Robert Price10/2017
37992^320788-11032796567Enzo Doria05/2014
38002^320764+79396560Lelio R Paula02/2013
3801(9179*2^320652-1)/22196528Lelio R Paula05/2015
38022^320616-7879596516Lelio R Paula03/2016
38032^320612-46193996514Enzo Doria07/2015
38045*2^320431+796461Lelio R Paula08/2014
380519^75431-9096458Lelio R Paula06/2016
3806(2^320370+3)/6796440Lelio R Paula10/2013
38072^320309+187147796423Enzo Doria05/2016
3808tau(809^6028)96410Nik Lygeros / Olivier Rozier / LR team10/2013
3809(21*2^320252-1)/189596404Lelio R Paula02/2014
38102^320232-17396400Lelio R Paula12/2012
3811175^42975-296395Lelio R Paula10/2017
381210^96377+19991196378Patrick De Geest12/2016
381310^96377-2000196377Robert Price11/2016
38142^320124-279044996367Enzo Doria03/2016
38152^320043-10877596343Enzo Doria04/2014
381610^96338+42493996339Patrick De Geest03/2016
381710^96338-928196338Robert Price09/2015
3818(3*2^320008+1)/796332Lelio R Paula09/2013
38192^319838+425796281Lelio R Paula03/2016
38202^319830-1699596279Lelio R Paula03/2016
38216^123713+14396268Lelio R Paula05/2016
3822(28*10^96265-97)/396266Robert Price07/2016
3823103^47825-10296264Norbert Schneider10/2016
38242^319713-8196244Lelio R Paula11/2012
3825(55459*2^319706+1)/2016796242Lelio R Paula07/2014
382612^89153-4396213Lelio R Paula06/2016
3827(2*10^96195-59)/396195Robert Price05/2017
38282^319545+14796193Lelio R Paula11/2012
3829(50^56597+1)/5196155Robert Price03/2014
3830(41*10^96137-59)/996138Robert Price10/2017
38312^319353-11034396135Enzo Doria05/2014
383211^92309-4296130Lelio R Paula05/2016
383314^83869-13^8386996125Jean-Louis Charton01/2009
3834(7*10^96112+143)/396113Robert Price04/2016
38352^319237+6583596100Lelio R Paula03/2016
38362^319194-184196087Yves Minet03/2013
383720^73847-3196078Lelio R Paula05/2016
383850^56543-4996065Norbert Schneider09/2018
38392^319107-10955596061Enzo Doria04/2014
3840(3*2^319114-1)/262796060Lelio R Paula02/2014
38412^319098-11215796059Enzo Doria06/2014
384215^81673+9496055Lelio R Paula07/2016
38432^319074+187174996051Enzo Doria05/2016
38442^319007-11211196031Enzo Doria06/2014
38452^318946-142196013Yves Minet01/2013
38462^318834-11041195979Enzo Doria05/2014
38472^318831-196595978Lelio R Paula03/2016
3848(5*10^95976+7)/395977Erik Branger03/2014
38495*3^201089-895945Lelio R Paula08/2014
38502^318711-13995942Lelio R Paula11/2012
38512^318635-116795919Lelio R Paula03/2016
385215^81555+1695917Lelio R Paula07/2016
3853(37*10^95895+377)/995896Robert Price10/2017
3854(22699*2^318527+1)/2195890Lelio R Paula07/2014
38552^318496-9730595877Lelio R Paula03/2016
38562^318466+1501595868Lelio R Paula03/2016
38576^123187-17312995859Mike Oakes04/2011
38582^318423-48795855Yves Minet03/2012
3859(10223*2^318350+1)/156395834Lelio R Paula07/2014
386045369!2+102495787Robert Price02/2015
38613^200758-8695786Lelio R Paula05/2016
38623*10^95776-5995777Robert Price10/2017
3863193^41901-295768Lelio R Paula10/2017
38644*10^95752-7195753Robert Price11/2017
3865(509203*2^317881-1)/5280595693Lelio R Paula04/2015
38664*10^95672+9195673Robert Price11/2017
3867(11*10^95641-113)/395642Robert Price01/2017
3868(13*10^95588+11)/395589Robert Price05/2015
3869Phi(191188,10)/19118995587Maksym Voznyy11/2015
38703^200325+7095580Lelio R Paula05/2016
3871(25*10^95574-7)/995575Robert Price12/2014
3872(2^317485-3)/2131395569Lelio R Paula06/2013
38732^317464+3195567Lelio R Paula11/2012
38747^113073+8295558Lelio R Paula04/2016
38752^317251+46595503Lelio R Paula03/2016
387619^74684+5895503Lelio R Paula06/2016
3877(2^317250-7)/33995500Lelio R Paula07/2013
38786^122718-7995494Lelio R Paula05/2016
38792^317141-11049195469Enzo Doria05/2014
38802^317094+7630995455Enzo Doria05/2016
38812^317085+9595453Lelio R Paula11/2012
3882(17*10^95451-377)/995452Robert Price11/2017
38832^317057-10955195444Enzo Doria04/2014
38843^200026+2895437Lelio R Paula05/2016
38852^317024+9395434Donovan Johnson06/2008
38862^316999+160595427Lelio R Paula03/2016
38872^316995-11042795426Enzo Doria05/2014
38892^316937+17795408Lelio R Paula11/2012
38884*10^95407+9195408Robert Price11/2017
38902^316908+191595399Lelio R Paula03/2016
38912^316894+9995395Lelio R Paula11/2012
38926^122547+1195361Lelio R Paula05/2016
38932^316771+8287595358Lelio R Paula03/2016
3895(23*10^95326+1)/395327Serge Batalov05/2009
38941*10^95326+5795327Robert Price03/2011
389610^95326-39368795326Patrick De Geest09/2013
3897(3^199803+4)/47953995325Lelio R Paula04/2013
38982^316654-10948195323Enzo Doria04/2014
38998*10^95316+5195317Robert Price05/2017
3900(50^56099+43^56099)/9395309Serge Batalov12/2016
3901(23*2^316559+1)/392595292Lelio R Paula09/2013
3902(71*10^95277-539)/995278Robert Price11/2017
390319^74503-5695271Lelio R Paula06/2016
390411^91475-438095262Enzo Doria01/2013
3905(62*10^95251-611)/995252Robert Price05/2017
3906(2^316321-509203)/6937795218Lelio R Paula06/2013
3907(79*10^95214-43)/995215Erik Branger11/2013
3908(9*2^316233-1)/175195194Lelio R Paula02/2014
39095*2^316213+995191Lelio R Paula08/2014
39102^316205-184816395188Enzo Doria07/2015
39112^316185-278791395182Enzo Doria04/2016
3912(9787*2^316142-1)/395172Lelio R Paula04/2015
39132^316140-595168Henri Lifchitz02/2006
3914(15185*2^316117-1)/395165Lelio R Paula04/2015
3915(34*10^95153-7)/9/19/1915795149Makoto Morimoto05/2016
39162^316069+7681795147Enzo Doria05/2016
3917(199*10^95134-7)/395136Robert Price02/2017
39182^316027-9730595134Lelio R Paula03/2016
39192^316006-279805195128Enzo Doria04/2016
39202^315921-279760395102Enzo Doria04/2016
39212*10^95095+6395096Robert Price10/2017
39222^315857+129995083Lelio R Paula03/2016
392314^82955-4395078Lelio R Paula06/2016
3924(2*10^95072-17)/395072Robert Price08/2014
39252^315727+6595044Lelio R Paula11/2012
39262^315725+188575795043Enzo Doria03/2017
39271*10^94983+2194984Robert Price03/2011
392810^94983-71794983Patrick De Geest08/2013
392917^77187-8294975Lelio R Paula07/2016
39303*10^94964+3794965Robert Price10/2017
3931(2^315481-1017)/2062728594962Lelio R Paula06/2013
39322^315423-11032994952Enzo Doria05/2014
393311^91169-723094943Enzo Doria02/2013
39347*10^94938+6194939Robert Price02/2017
39352^315351+102594931Lelio R Paula03/2016
39362^315350-11225394930Enzo Doria06/2014
3937((1001327^(15817)+1)/1001328)94906Faysal YAtim10/2010
39392^315268+794906Lelio R Paula10/2012
393811^91133+6294906Lelio R Paula05/2016
394030^64244+4194897Lelio R Paula08/2012
3941(151*10^94885-7)/994887Robert Price07/2017
39424^157583+2214794875Mike Oakes01/2011
39432^315098+12394854Lelio R Paula11/2012
39443^198791-3494848Robert Price11/2013
39453*2^315067+794846Lelio R Paula08/2014
3946(9*2^315057+1)/7394841Lelio R Paula09/2013
3947(16*10^94822+53)/394823Robert Price12/2016
39488*6^121849-794818Lelio R Paula10/2014
3949(85*10^94802+473)/994803Robert Price03/2017
39502^314870-10876194786Enzo Doria03/2014
39515*2^314841-394778Lelio R Paula08/2014
39526^121772+11394758Lelio R Paula05/2016
39536^121756-1625394745Enzo Doria02/2013
39542^314718-11279394740Enzo Doria06/2014
39552^314697-184729394734Enzo Doria07/2015
39572^314548-24994689Yves Minet02/2012
39565^135469+4294689Lelio R Paula04/2016
3958gcd(V(1137755),5*F(227551)*(F(227551)-1)+1)94676Serge Batalov04/2015
3959(2*10^94604+547)/994604Robert Price10/2017
39603*2^314152+594570Lelio R Paula08/2014
39612*6^121530-594570Lelio R Paula10/2014
39627*10^94563+8794564Robert Price11/2016
39632^314114-10967794558Enzo Doria04/2014
3964(218389#+240867)/(3*11*811)94557Makoto Morimoto10/2017
39652^314059+7658394542Enzo Doria05/2016
39662^314041-403594536Lelio R Paula03/2016
3967(7*2^314003-11)/1594524Renaud Lifchitz03/2011
396811^90760-471094517Enzo Doria01/2013
3969(7*2^313926-1)/14882194497Lelio R Paula02/2014
397094*10^94493-394495Robert Price11/2016
3971(1000547^15749+1)/100054894492Faysal YAtim12/2008
3972(F(3*75345)^2+L(3*75345)^2)/494477Henri Lifchitz10/2017
39737^111792-3294476Lelio R Paula04/2016
397411^90680-585094434Enzo Doria01/2013
39752^313675-11012594426Enzo Doria04/2014
3976(2999*29^64556-2427)/494410Curtis Bright05/2015
39772^313609-11222594406Enzo Doria06/2014
39782^313584+7290194399Enzo Doria04/2016
39792^313510-11286594376Enzo Doria06/2014
39807*10^94373+8794374Robert Price11/2016
3981(9^98897+8^98897)/1794371Robert Price12/2012
39822^313453-11470394359Enzo Doria04/2015
39838*10^94357-5194358Robert Price10/2017
3984(379*10^94337-1)/994339Robert Price08/2017
39852^313344-313344+194326Robert Price10/2014
398620^72481-4994300Lelio R Paula05/2016
398744725!2+12894289Robert Price03/2015
39884*10^94286+994287Robert Price05/2015
398917^76621+2494279Lelio R Paula07/2016
39902^313156-11285994270Enzo Doria06/2014
39916^121130-5994258Lelio R Paula05/2016
39923^197542+2894252Robert Price11/2013
3993(3^197521+2)/5165594237Lelio R Paula04/2013
39942^313045-595594236Lelio R Paula03/2016
3995(67*10^94212+23)/994213Ray Chandler02/2011
39962^312909-186520394195Enzo Doria03/2016
39972^312848-14994177Lelio R Paula11/2012
39984^156403-7759794164Mike Oakes04/2011
399918^75004-8594151Lelio R Paula06/2016
400019^73622-4894145Lelio R Paula06/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 20 2018 23:15 (Time in France)

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