PRP Records

Probable Primes Top 10000

(252402 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 (> 50000) Who ? When ?
37512^325733-5869598056Lelio R Paula07/2016
37522^325717-364598051Lelio R Paula07/2016
3753(23*2^325583-1)/2198011Lelio R Paula02/2014
3754(7*10^98007-13)/398008Robert Price06/2016
37552^325512-45995997989Enzo Doria05/2015
3756(3^205354-8)/1797978Lelio R Paula09/2013
37572^325433+7681797966Enzo Doria05/2016
37585*10^97963+8197964Robert Price08/2017
37592^325390-10906197953Enzo Doria04/2014
376013^87921+2497940Lelio R Paula08/2016
3761961^32831-960^3283197926Jean-Louis Charton02/2011
37622^325215+1290997900Lelio R Paula07/2016
37637*10^97874-6997875Robert Price01/2017
3765(17^79537+5^79537)/2297865Robert Price06/2013
376415^83212+2297865Lelio R Paula08/2016
37662^325087-10905797861Enzo Doria04/2014
37672^325074+187065797858Enzo Doria05/2016
37682^325066-211197855Yves Minet08/2013
3769CopelandErdos(97855)97855Eric W. Weisstein10/2015
377018^77944-8997841Lelio R Paula07/2016
3771119^47136+11897833Norbert Schneider09/2018
37726^125720-1766397830Enzo Doria02/2013
37732^324972-206997827Yves Minet05/2013
37742^324944-278831997818Enzo Doria03/2016
37764*10^97799-997800Erik Branger11/2013
37752^324882+57729457597800Lelio R Paula09/2016
37772^324863-186792197794Enzo Doria04/2016
37786^125662-1847397785Enzo Doria03/2013
377912^90604+1197779Lelio R Paula07/2016
37805^139830+2497737Lelio R Paula04/2016
37812^324612+115597718Lelio R Paula07/2016
378219^76404-4497702Lelio R Paula07/2016
37832^324505-298397686Yves Minet04/2011
3784(31*2^324496-1)/4597683Lelio R Paula02/2014
37856^125488-1784397649Enzo Doria02/2013
37867^115515-297622Lelio R Paula09/2013
3787(89^50069-1)/8897603Paul Bourdelais08/2017
37886^125418-597595Lelio R Paula11/2014
37892^324076+115597557Lelio R Paula07/2016
3790(2^324074+9)/1397555Lelio R Paula10/2013
3791(55459*2^323993+1)/2197536Lelio R Paula07/2014
379213^87557-12^8755797534Jean-Louis Charton12/2008
37932^323946+7393997518Enzo Doria04/2016
37942^323937+186694797515Enzo Doria03/2016
37956^125290-1853397495Enzo Doria03/2013
37962^323845+10197488Lelio R Paula12/2012
379718^77662+6597487Lelio R Paula07/2016
37982^323772+7677197466Enzo Doria05/2016
37992^323765-11221397463Enzo Doria06/2014
38002^323720-655597450Lelio R Paula07/2016
38012^323694-186040197442Enzo Doria03/2016
380220^74886+397429Lelio R Paula06/2016
38043*10^97399+7397400Robert Price04/2016
38037^115252-5097400Lelio R Paula07/2016
3805224737#+39358197389Nicolas PALAU12/2016
3806(26*10^97353+31)/397354Robert Price07/2016
380761^54517-60^5451797331Jean-Louis Charton09/2005
3808(38*10^97329+187)/997330Robert Price11/2017
3809p(19982)#/2-102497293Robert Price09/2017
38106^125021-8597286Lelio R Paula08/2016
38112^323164-4735597283Lelio R Paula07/2016
3812(3^203902+4)/3605101515797276Lelio R Paula09/2013
38132^323054-655597249Lelio R Paula07/2016
38149*10^97247-2997248Robert Price05/2017
3815(31*10^97242+41)/997243Robert Price04/2015
3816GoldenRatioPrime[97241]97241Eric W. Weisstein06/2009
381712^90098-4197233Lelio R Paula07/2016
38182^322928-21692997212Enzo Doria05/2014
3819(7*2^322896-1)/5797201Lelio R Paula02/2014
3820(2^322897+5)/314610748997193Lelio R Paula10/2013
38212^322725+7576197150Enzo Doria04/2016
3822(13*2^322686+1)/11997138Lelio R Paula11/2013
3823(41*10^97085+373)/997086Robert Price04/2017
38242^322413+7797056Lelio R Paula12/2012
38252^322406+17797054Lelio R Paula12/2012
3826(14*10^97044+31)/997045Robert Price02/2015
38272^322302+25525597023Lelio R Paula07/2016
38282^322196-11309396991Enzo Doria07/2014
38292^322000-186146996932Enzo Doria03/2016
38302^321971-11274796923Enzo Doria06/2014
383111^93062-9296915Lelio R Paula06/2016
3832(11*2^321841-7)/1596884Renaud Lifchitz03/2011
38333^203051+3496880Lelio R Paula05/2016
38342*10^96867-5196868Robert Price11/2017
3835(64*10^96863-1)/2796864Serge Batalov05/2010
38362^321716-278693996847Enzo Doria03/2016
38372^321701-11305396842Enzo Doria07/2014
38382^321700-2863596842Lelio R Paula06/2016
3839(5*2^321691-1)/2796838Lelio R Paula02/2014
38406^124433-12443396828Robert Price01/2014
38412^321631+6996821Lelio R Paula12/2012
3842(13*2^321606+1)/11996813Lelio R Paula11/2013
3843(46*10^96798-1)/996799Serge Batalov10/2014
3844(59*10^96798+31)/996799Robert Price09/2015
3845223319#+23122396790Makoto Morimoto02/2016
38462^321519-2863596787Lelio R Paula06/2016
38472^321487-186723796778Enzo Doria03/2016
38482^321461-6396770Lelio R Paula12/2012
38492^321439+12396763Lelio R Paula12/2012
38502^321434+70996762Lelio R Paula02/2013
385114^84413+8996749Lelio R Paula07/2016
3852(28*10^96743+71)/996744Serge Batalov12/2008
385313^86847+9696743Lelio R Paula06/2016
38549*2^321336-796733Lelio R Paula08/2014
3855(209*10^96722-17)/396724Robert Price05/2017
38562^321187-115996687Yves Minet11/2012
38572^321182-185008196686Enzo Doria08/2015
38582^321116-11282996666Enzo Doria06/2014
38592^321108-10949996664Enzo Doria04/2014
38602^321098+279385996661Enzo Doria03/2016
38612^321057+409796648Lelio R Paula06/2016
3862(4435*29^66081-4)/796640Curtis Bright05/2015
3863p(19849)#/2-6496581Robert Price04/2017
38642^320817+18996576Lelio R Paula12/2012
3865(361*10^96567-163)/996569Robert Price10/2017
38662^320788-11032796567Enzo Doria05/2014
38672^320764+79396560Lelio R Paula02/2013
3868(9179*2^320652-1)/22196528Lelio R Paula05/2015
38692^320616-7879596516Lelio R Paula03/2016
38702^320612-46193996514Enzo Doria07/2015
38715*2^320431+796461Lelio R Paula08/2014
387219^75431-9096458Lelio R Paula06/2016
3873(2^320370+3)/6796440Lelio R Paula10/2013
38742^320309+187147796423Enzo Doria05/2016
3875tau(809^6028)96410Nik Lygeros / Olivier Rozier / LR team10/2013
3876(21*2^320252-1)/189596404Lelio R Paula02/2014
38772^320232-17396400Lelio R Paula12/2012
3878175^42975-296395Lelio R Paula10/2017
387910^96377+19991196378Patrick De Geest12/2016
388010^96377-2000196377Robert Price11/2016
38812^320124-279044996367Enzo Doria03/2016
38822^320043-10877596343Enzo Doria04/2014
388310^96338+42493996339Patrick De Geest03/2016
388410^96338-928196338Robert Price09/2015
3885(3*2^320008+1)/796332Lelio R Paula09/2013
38862^319838+425796281Lelio R Paula03/2016
38872^319830-1699596279Lelio R Paula03/2016
38886^123713+14396268Lelio R Paula05/2016
3889(28*10^96265-97)/396266Robert Price07/2016
3890103^47825-10296264Norbert Schneider10/2016
38912^319713-8196244Lelio R Paula11/2012
3892(55459*2^319706+1)/2016796242Lelio R Paula07/2014
389312^89153-4396213Lelio R Paula06/2016
3894(2*10^96195-59)/396195Robert Price05/2017
38952^319545+14796193Lelio R Paula11/2012
3896(50^56597+1)/5196155Robert Price03/2014
3897(41*10^96137-59)/996138Robert Price10/2017
38982^319353-11034396135Enzo Doria05/2014
389911^92309-4296130Lelio R Paula05/2016
390014^83869-13^8386996125Jean-Louis Charton01/2009
3901(7*10^96112+143)/396113Robert Price04/2016
39022^319237+6583596100Lelio R Paula03/2016
39032^319194-184196087Yves Minet03/2013
390420^73847-3196078Lelio R Paula05/2016
390550^56543-4996065Norbert Schneider09/2018
39062^319107-10955596061Enzo Doria04/2014
3907(3*2^319114-1)/262796060Lelio R Paula02/2014
39082^319098-11215796059Enzo Doria06/2014
390915^81673+9496055Lelio R Paula07/2016
39102^319074+187174996051Enzo Doria05/2016
39112^319007-11211196031Enzo Doria06/2014
39122^318946-142196013Yves Minet01/2013
39132^318834-11041195979Enzo Doria05/2014
39142^318831-196595978Lelio R Paula03/2016
3915(5*10^95976+7)/395977Erik Branger03/2014
39165*3^201089-895945Lelio R Paula08/2014
39172^318711-13995942Lelio R Paula11/2012
39182^318635-116795919Lelio R Paula03/2016
391915^81555+1695917Lelio R Paula07/2016
3920(37*10^95895+377)/995896Robert Price10/2017
3921(22699*2^318527+1)/2195890Lelio R Paula07/2014
39222^318496-9730595877Lelio R Paula03/2016
39232^318466+1501595868Lelio R Paula03/2016
39246^123187-17312995859Mike Oakes04/2011
39252^318423-48795855Yves Minet03/2012
3926(10223*2^318350+1)/156395834Lelio R Paula07/2014
392745369!2+102495787Robert Price02/2015
39283^200758-8695786Lelio R Paula05/2016
3929(2^318271+1)/(3*46031404238891*654090604244843)95781Gord Palameta12/2018
39303*10^95776-5995777Robert Price10/2017
3931193^41901-295768Lelio R Paula10/2017
39324*10^95752-7195753Robert Price11/2017
3933(509203*2^317881-1)/5280595693Lelio R Paula04/2015
39344*10^95672+9195673Robert Price11/2017
3935(11*10^95641-113)/395642Robert Price01/2017
3936(13*10^95588+11)/395589Robert Price05/2015
3937Phi(191188,10)/19118995587Maksym Voznyy11/2015
39383^200325+7095580Lelio R Paula05/2016
3939(25*10^95574-7)/995575Robert Price12/2014
3940(2^317485-3)/2131395569Lelio R Paula06/2013
39412^317464+3195567Lelio R Paula11/2012
39427^113073+8295558Lelio R Paula04/2016
39432^317251+46595503Lelio R Paula03/2016
394419^74684+5895503Lelio R Paula06/2016
3945(2^317250-7)/33995500Lelio R Paula07/2013
39466^122718-7995494Lelio R Paula05/2016
39472^317141-11049195469Enzo Doria05/2014
39482^317094+7630995455Enzo Doria05/2016
39492^317085+9595453Lelio R Paula11/2012
3950(17*10^95451-377)/995452Robert Price11/2017
39512^317057-10955195444Enzo Doria04/2014
39523^200026+2895437Lelio R Paula05/2016
39532^317024+9395434Donovan Johnson06/2008
39542^316999+160595427Lelio R Paula03/2016
39552^316995-11042795426Enzo Doria05/2014
39572^316937+17795408Lelio R Paula11/2012
39564*10^95407+9195408Robert Price11/2017
39582^316908+191595399Lelio R Paula03/2016
39592^316894+9995395Lelio R Paula11/2012
39606^122547+1195361Lelio R Paula05/2016
39612^316771+8287595358Lelio R Paula03/2016
3963(23*10^95326+1)/395327Serge Batalov05/2009
39621*10^95326+5795327Robert Price03/2011
396410^95326-39368795326Patrick De Geest09/2013
3965(3^199803+4)/47953995325Lelio R Paula04/2013
39662^316654-10948195323Enzo Doria04/2014
39678*10^95316+5195317Robert Price05/2017
3968(50^56099+43^56099)/9395309Serge Batalov12/2016
3969(23*2^316559+1)/392595292Lelio R Paula09/2013
3970(71*10^95277-539)/995278Robert Price11/2017
397119^74503-5695271Lelio R Paula06/2016
397211^91475-438095262Enzo Doria01/2013
3973(62*10^95251-611)/995252Robert Price05/2017
3974(2^316321-509203)/6937795218Lelio R Paula06/2013
3975(79*10^95214-43)/995215Erik Branger11/2013
3976(9*2^316233-1)/175195194Lelio R Paula02/2014
39775*2^316213+995191Lelio R Paula08/2014
39782^316205-184816395188Enzo Doria07/2015
39792^316185-278791395182Enzo Doria04/2016
3980(9787*2^316142-1)/395172Lelio R Paula04/2015
39812^316140-595168Henri Lifchitz02/2006
3982(15185*2^316117-1)/395165Lelio R Paula04/2015
3983(34*10^95153-7)/9/19/1915795149Makoto Morimoto05/2016
39842^316069+7681795147Enzo Doria05/2016
3985(199*10^95134-7)/395136Robert Price02/2017
39862^316027-9730595134Lelio R Paula03/2016
39872^316006-279805195128Enzo Doria04/2016
39882^315921-279760395102Enzo Doria04/2016
39892*10^95095+6395096Robert Price10/2017
39902^315857+129995083Lelio R Paula03/2016
399114^82955-4395078Lelio R Paula06/2016
3992(2*10^95072-17)/395072Robert Price08/2014
39932^315727+6595044Lelio R Paula11/2012
39942^315725+188575795043Enzo Doria03/2017
39951*10^94983+2194984Robert Price03/2011
399610^94983-71794983Patrick De Geest08/2013
399717^77187-8294975Lelio R Paula07/2016
39983*10^94964+3794965Robert Price10/2017
3999(2^315481-1017)/2062728594962Lelio R Paula06/2013
40002^315423-11032994952Enzo Doria05/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 17 2018 20:37 (Time in France)

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