PRP Records

Probable Primes Top 10000

(252932 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 ?
4001961^32831-960^3283197926Jean-Louis Charton02/2011
40022^325215+1290997900Lelio R Paula07/2016
40037*10^97874-6997875Robert Price01/2017
4005(17^79537+5^79537)/2297865Robert Price06/2013
400415^83212+2297865Lelio R Paula08/2016
40062^325087-10905797861Enzo Doria04/2014
40072^325074+187065797858Enzo Doria05/2016
40092^325066-211197855Yves Minet08/2013
4008CopelandErdos(97855)97855Eric W. Weisstein10/2015
401018^77944-8997841Lelio R Paula07/2016
4011119^47136+11897833Norbert Schneider09/2018
40126^125720-1766397830Enzo Doria02/2013
40132^324972-206997827Yves Minet05/2013
40142^324958-469197823Yves Minet05/2019
40152^324944-278831997818Enzo Doria03/2016
40174*10^97799-997800Erik Branger11/2013
40162^324882+57729457597800Lelio R Paula09/2016
40182^324863-186792197794Enzo Doria04/2016
40196^125662-1847397785Enzo Doria03/2013
402012^90604+1197779Lelio R Paula07/2016
40215^139830+2497737Lelio R Paula04/2016
40222^324612+115597718Lelio R Paula07/2016
402319^76404-4497702Lelio R Paula07/2016
40242^324505-298397686Yves Minet04/2011
4025(31*2^324496-1)/4597683Lelio R Paula02/2014
40266^125488-1784397649Enzo Doria02/2013
40277^115515-297622Lelio R Paula09/2013
4028(89^50069-1)/8897603Paul Bourdelais08/2017
40296^125418-597595Lelio R Paula11/2014
40302^324076+115597557Lelio R Paula07/2016
4031(2^324074+9)/1397555Lelio R Paula10/2013
4032(55459*2^323993+1)/2197536Lelio R Paula07/2014
403313^87557-12^8755797534Jean-Louis Charton12/2008
40342^323946+7393997518Enzo Doria04/2016
40352^323937+186694797515Enzo Doria03/2016
40366^125290-1853397495Enzo Doria03/2013
40372^323845+10197488Lelio R Paula12/2012
403818^77662+6597487Lelio R Paula07/2016
40392^323772+7677197466Enzo Doria05/2016
40402^323765-11221397463Enzo Doria06/2014
40412^323720-655597450Lelio R Paula07/2016
40422^323694-186040197442Enzo Doria03/2016
404320^74886+397429Lelio R Paula06/2016
40453*10^97399+7397400Robert Price04/2016
40447^115252-5097400Lelio R Paula07/2016
4046224737#+39358197389Nicolas PALAU12/2016
4047(26*10^97353+31)/397354Robert Price07/2016
404861^54517-60^5451797331Jean-Louis Charton09/2005
4049(38*10^97329+187)/997330Robert Price11/2017
4050p(19982)#/2-102497293Robert Price09/2017
40516^125021-8597286Lelio R Paula08/2016
40522^323164-4735597283Lelio R Paula07/2016
4053(3^203902+4)/3605101515797276Lelio R Paula09/2013
40542^323054-655597249Lelio R Paula07/2016
40559*10^97247-2997248Robert Price05/2017
4056(31*10^97242+41)/997243Robert Price04/2015
4057GoldenRatioPrime[97241]97241Eric W. Weisstein06/2009
405812^90098-4197233Lelio R Paula07/2016
40592^322928-21692997212Enzo Doria05/2014
4060(7*2^322896-1)/5797201Lelio R Paula02/2014
4061(2^322897+5)/314610748997193Lelio R Paula10/2013
40622^322725+7576197150Enzo Doria04/2016
4063(13*2^322686+1)/11997138Lelio R Paula11/2013
4064(41*10^97085+373)/997086Robert Price04/2017
40652^322413+7797056Lelio R Paula12/2012
40662^322406+17797054Lelio R Paula12/2012
4067(14*10^97044+31)/997045Robert Price02/2015
40682^322302+25525597023Lelio R Paula07/2016
40692^322196-11309396991Enzo Doria07/2014
40702^322000-186146996932Enzo Doria03/2016
40712^321971-11274796923Enzo Doria06/2014
407211^93062-9296915Lelio R Paula06/2016
4073(11*2^321841-7)/1596884Renaud Lifchitz03/2011
40743^203051+3496880Lelio R Paula05/2016
40752*10^96867-5196868Robert Price11/2017
4076(64*10^96863-1)/2796864Serge Batalov05/2010
40772^321716-278693996847Enzo Doria03/2016
40782^321701-11305396842Enzo Doria07/2014
40792^321700-2863596842Lelio R Paula06/2016
4080(5*2^321691-1)/2796838Lelio R Paula02/2014
40816^124433-12443396828Robert Price01/2014
40822^321631+6996821Lelio R Paula12/2012
4083(13*2^321606+1)/11996813Lelio R Paula11/2013
4084(46*10^96798-1)/996799Serge Batalov10/2014
4085(59*10^96798+31)/996799Robert Price09/2015
4086223319#+23122396790Makoto Morimoto02/2016
40872^321519-2863596787Lelio R Paula06/2016
40882^321487-186723796778Enzo Doria03/2016
40892^321461-6396770Lelio R Paula12/2012
40902^321439+12396763Lelio R Paula12/2012
40912^321434+70996762Lelio R Paula02/2013
409214^84413+8996749Lelio R Paula07/2016
4093(28*10^96743+71)/996744Serge Batalov12/2008
409413^86847+9696743Lelio R Paula06/2016
40959*2^321336-796733Lelio R Paula08/2014
4096(209*10^96722-17)/396724Robert Price05/2017
40972^321237-461596702Yves Minet05/2019
40982^321187-115996687Yves Minet11/2012
40992^321182-185008196686Enzo Doria08/2015
41002^321116-11282996666Enzo Doria06/2014
41012^321108-10949996664Enzo Doria04/2014
41022^321098+279385996661Enzo Doria03/2016
41032^321057+409796648Lelio R Paula06/2016
4104(4435*29^66081-4)/796640Curtis Bright05/2015
4105p(19849)#/2-6496581Robert Price04/2017
41062^320817+18996576Lelio R Paula12/2012
41072^320816-468596576Yves Minet05/2019
4108(361*10^96567-163)/996569Robert Price10/2017
41092^320788-11032796567Enzo Doria05/2014
41102^320764+79396560Lelio R Paula02/2013
4111(9179*2^320652-1)/22196528Lelio R Paula05/2015
41122^320616-7879596516Lelio R Paula03/2016
41132^320612-46193996514Enzo Doria07/2015
41145*2^320431+796461Lelio R Paula08/2014
411519^75431-9096458Lelio R Paula06/2016
4116(2^320370+3)/6796440Lelio R Paula10/2013
41172^320309+187147796423Enzo Doria05/2016
4118tau(809^6028)96410Nik Lygeros / Olivier Rozier / LR team10/2013
4119(21*2^320252-1)/189596404Lelio R Paula02/2014
41202^320232-17396400Lelio R Paula12/2012
4121175^42975-296395Lelio R Paula10/2017
412210^96377+19991196378Patrick De Geest12/2016
412310^96377-2000196377Robert Price11/2016
41242^320124-279044996367Enzo Doria03/2016
41252^320043-10877596343Enzo Doria04/2014
412610^96338+42493996339Patrick De Geest03/2016
412710^96338-928196338Robert Price09/2015
4128(3*2^320008+1)/796332Lelio R Paula09/2013
41292^319838+425796281Lelio R Paula03/2016
41302^319830-1699596279Lelio R Paula03/2016
41316^123713+14396268Lelio R Paula05/2016
4132(28*10^96265-97)/396266Robert Price07/2016
4133103^47825-10296264Norbert Schneider10/2016
41342^319713-8196244Lelio R Paula11/2012
4135(55459*2^319706+1)/2016796242Lelio R Paula07/2014
413612^89153-4396213Lelio R Paula06/2016
4137(2*10^96195-59)/396195Robert Price05/2017
41382^319545+14796193Lelio R Paula11/2012
4139(50^56597+1)/5196155Robert Price03/2014
4140(41*10^96137-59)/996138Robert Price10/2017
41412^319353-11034396135Enzo Doria05/2014
414211^92309-4296130Lelio R Paula05/2016
414314^83869-13^8386996125Jean-Louis Charton01/2009
4144(7*10^96112+143)/396113Robert Price04/2016
41452^319237+6583596100Lelio R Paula03/2016
41462^319194-184196087Yves Minet03/2013
414720^73847-3196078Lelio R Paula05/2016
414850^56543-4996065Norbert Schneider09/2018
41492^319107-10955596061Enzo Doria04/2014
4150(3*2^319114-1)/262796060Lelio R Paula02/2014
41512^319098-11215796059Enzo Doria06/2014
415215^81673+9496055Lelio R Paula07/2016
41532^319074+187174996051Enzo Doria05/2016
41542^319007-11211196031Enzo Doria06/2014
41552^318946-142196013Yves Minet01/2013
41562^318834-11041195979Enzo Doria05/2014
41572^318831-196595978Lelio R Paula03/2016
4158(5*10^95976+7)/395977Erik Branger03/2014
41595*3^201089-895945Lelio R Paula08/2014
41602^318711-13995942Lelio R Paula11/2012
41612^318635-116795919Lelio R Paula03/2016
416215^81555+1695917Lelio R Paula07/2016
4163(37*10^95895+377)/995896Robert Price10/2017
4164(22699*2^318527+1)/2195890Lelio R Paula07/2014
41652^318496-9730595877Lelio R Paula03/2016
41662^318466+1501595868Lelio R Paula03/2016
41676^123187-17312995859Mike Oakes04/2011
41682^318423-48795855Yves Minet03/2012
4169(10223*2^318350+1)/156395834Lelio R Paula07/2014
417045369!2+102495787Robert Price02/2015
41713^200758-8695786Lelio R Paula05/2016
4172(2^318271+1)/(3*46031404238891*654090604244843)95781Gord Palameta12/2018
41733*10^95776-5995777Robert Price10/2017
4174193^41901-295768Lelio R Paula10/2017
41754*10^95752-7195753Robert Price11/2017
4176((10^47850-1)*10000/9+6421)*10^47850+(10^47850-1)/995704Hans Havermann05/2019
4177(509203*2^317881-1)/5280595693Lelio R Paula04/2015
41784*10^95672+9195673Robert Price11/2017
4179(11*10^95641-113)/395642Robert Price01/2017
4180(13*10^95588+11)/395589Robert Price05/2015
4181Phi(191188,10)/19118995587Maksym Voznyy11/2015
41823^200325+7095580Lelio R Paula05/2016
4183(25*10^95574-7)/995575Robert Price12/2014
4184(2^317485-3)/2131395569Lelio R Paula06/2013
41852^317464+3195567Lelio R Paula11/2012
41867^113073+8295558Lelio R Paula04/2016
41872^317251+46595503Lelio R Paula03/2016
418819^74684+5895503Lelio R Paula06/2016
4189(2^317250-7)/33995500Lelio R Paula07/2013
41906^122718-7995494Lelio R Paula05/2016
41912^317141-11049195469Enzo Doria05/2014
41922^317094+7630995455Enzo Doria05/2016
41932^317085+9595453Lelio R Paula11/2012
4194(17*10^95451-377)/995452Robert Price11/2017
41952^317057-10955195444Enzo Doria04/2014
41963^200026+2895437Lelio R Paula05/2016
41972^317024+9395434Donovan Johnson06/2008
41982^316999+160595427Lelio R Paula03/2016
41992^316995-11042795426Enzo Doria05/2014
42012^316937+17795408Lelio R Paula11/2012
42004*10^95407+9195408Robert Price11/2017
42022^316908+191595399Lelio R Paula03/2016
42032^316894+9995395Lelio R Paula11/2012
42046^122547+1195361Lelio R Paula05/2016
42052^316771+8287595358Lelio R Paula03/2016
4207(23*10^95326+1)/395327Serge Batalov05/2009
42061*10^95326+5795327Robert Price03/2011
420810^95326-39368795326Patrick De Geest09/2013
4209(3^199803+4)/47953995325Lelio R Paula04/2013
42102^316654-10948195323Enzo Doria04/2014
42118*10^95316+5195317Robert Price05/2017
4212(50^56099+43^56099)/9395309Serge Batalov12/2016
4213(23*2^316559+1)/392595292Lelio R Paula09/2013
4214(71*10^95277-539)/995278Robert Price11/2017
421519^74503-5695271Lelio R Paula06/2016
421611^91475-438095262Enzo Doria01/2013
4217(62*10^95251-611)/995252Robert Price05/2017
4218(2^316321-509203)/6937795218Lelio R Paula06/2013
4219(79*10^95214-43)/995215Erik Branger11/2013
4220(9*2^316233-1)/175195194Lelio R Paula02/2014
42215*2^316213+995191Lelio R Paula08/2014
42222^316205-184816395188Enzo Doria07/2015
42232^316185-278791395182Enzo Doria04/2016
4224(9787*2^316142-1)/395172Lelio R Paula04/2015
42252^316140-595168Henri Lifchitz02/2006
4226(15185*2^316117-1)/395165Lelio R Paula04/2015
4227(34*10^95153-7)/9/19/1915795149Makoto Morimoto05/2016
42282^316069+7681795147Enzo Doria05/2016
4229(199*10^95134-7)/395136Robert Price02/2017
42302^316027-9730595134Lelio R Paula03/2016
42312^316006-279805195128Enzo Doria04/2016
42322^315921-279760395102Enzo Doria04/2016
42332*10^95095+6395096Robert Price10/2017
42342^315857+129995083Lelio R Paula03/2016
423514^82955-4395078Lelio R Paula06/2016
4236(2*10^95072-17)/395072Robert Price08/2014
42372^315727+6595044Lelio R Paula11/2012
42382^315725+188575795043Enzo Doria03/2017
42391*10^94983+2194984Robert Price03/2011
424010^94983-71794983Patrick De Geest08/2013
424117^77187-8294975Lelio R Paula07/2016
42423*10^94964+3794965Robert Price10/2017
4243(2^315481-1017)/2062728594962Lelio R Paula06/2013
42442^315423-11032994952Enzo Doria05/2014
424511^91169-723094943Enzo Doria02/2013
42467*10^94938+6194939Robert Price02/2017
42472^315351+102594931Lelio R Paula03/2016
42482^315350-11225394930Enzo Doria06/2014
4250((1001327^(15817)+1)/1001328)94906Faysal YAtim10/2010
42492^315268+794906Lelio R Paula10/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2019 07:14 (Time in France)

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