PRP Records

Probable Primes Top 10000

(271023 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 ?
5001(41*10^97085+373)/997086Robert Price04/2017
50022^322413+7797056Lelio R Paula12/2012
50032^322406+17797054Lelio R Paula12/2012
5004(14*10^97044+31)/997045Robert Price02/2015
50052^322302+25525597023Lelio R Paula07/2016
50062^322196-11309396991Enzo Doria07/2014
5007(2^322169+2690)/296983Stefano Morozzi09/2020
500823109^15668+15668^2310996943Hans Havermann07/2020
50092^322000-186146996932Enzo Doria03/2016
50102^321971-11274796923Enzo Doria06/2014
501123754^12023+12023^2375496917Hans Havermann07/2020
501211^93062-9296915Lelio R Paula06/2016
5013(2^321922+2214)/296908Stefano Morozzi09/2020
5014(2^321900+2086)/296902Stefano Morozzi09/2020
5015(11*2^321841-7)/1596884Renaud Lifchitz03/2011
50163^203051+3496880Lelio R Paula05/2016
50172*10^96867-5196868Robert Price11/2017
5018(2^321779+2618)/296865Stefano Morozzi09/2020
5019(64*10^96863-1)/2796864Serge Batalov05/2010
50202^321716-278693996847Enzo Doria03/2016
502122496^20181+20181^2249696844Hans Havermann03/2020
50222^321701-11305396842Enzo Doria07/2014
50232^321700-2863596842Lelio R Paula06/2016
5024(5*2^321691-1)/2796838Lelio R Paula02/2014
50256^124433-12443396828Robert Price01/2014
50262^321631+6996821Lelio R Paula12/2012
5027(13*2^321606+1)/11996813Lelio R Paula11/2013
5028(46*10^96798-1)/996799Serge Batalov10/2014
5029(59*10^96798+31)/996799Robert Price09/2015
5030(2^321536+2062)/296792Stefano Morozzi09/2020
5031223319#+23122396790Makoto Morimoto02/2016
50322^321519-2863596787Lelio R Paula06/2016
50332^321487-186723796778Enzo Doria03/2016
50342^321461-6396770Lelio R Paula12/2012
50352^321439+12396763Lelio R Paula12/2012
50362^321434+70996762Lelio R Paula02/2013
5037(2^321415+554)/296756Stefano Morozzi09/2020
503814^84413+8996749Lelio R Paula07/2016
5039(28*10^96743+71)/996744Serge Batalov12/2008
504013^86847+9696743Lelio R Paula06/2016
50419*2^321336-796733Lelio R Paula08/2014
5042(209*10^96722-17)/396724Robert Price05/2017
50432^321237-461596702Yves Minet05/2019
50442^321187-115996687Yves Minet11/2012
50452^321182-185008196686Enzo Doria08/2015
504623359^13768+13768^2335996680Hans Havermann06/2020
50472^321116-11282996666Enzo Doria06/2014
50482^321108-10949996664Enzo Doria04/2014
50502^321098+279385996661Enzo Doria03/2016
5049(2^321100+1170)/296661Stefano Morozzi09/2020
50512^321057+409796648Lelio R Paula06/2016
5053(4435*29^66081-4)/796640Curtis Bright05/2015
505222743^17750+17750^2274396640Hans Havermann04/2020
505422882^16679+16679^2288296612Hans Havermann02/2020
505523452^13163+13163^2345296608Hans Havermann02/2020
5056(2^320863+666)/296590Stefano Morozzi09/2020
5057p(19849)#/2-6496581Robert Price04/2017
50592^320817+18996576Lelio R Paula12/2012
50582^320816-468596576Yves Minet05/2019
5060(361*10^96567-163)/996569Robert Price10/2017
50612^320788-11032796567Enzo Doria05/2014
50622^320764+79396560Lelio R Paula02/2013
5063(9179*2^320652-1)/22196528Lelio R Paula05/2015
506423288^13947+13947^2328896517Hans Havermann07/2020
50652^320616-7879596516Lelio R Paula03/2016
50662^320612-46193996514Enzo Doria07/2015
506710^96504+98765432196505Robert Price12/2019
506810^96504+7188796505Patrick De Geest02/2020
506922654^18195+18195^2265496505Hans Havermann07/2020
507010^96504-13927796504Patrick De Geest02/2020
50715*2^320431+796461Lelio R Paula08/2014
507219^75431-9096458Lelio R Paula06/2016
5073(2^320370+3)/6796440Lelio R Paula10/2013
50742^320309+187147796423Enzo Doria05/2016
5075tau(809^6028)96410Nik Lygeros / Olivier Rozier / LR team10/2013
5076(21*2^320252-1)/189596404Lelio R Paula02/2014
50772^320232-17396400Lelio R Paula12/2012
5078175^42975-296395Lelio R Paula10/2017
5079(2^320170+2718)/296381Stefano Morozzi09/2020
508010^96377+19991196378Patrick De Geest12/2016
508110^96377-2000196377Robert Price11/2016
50822^320124-279044996367Enzo Doria03/2016
508322488^19255+19255^2248896351Hans Havermann11/2019
508423248^13939+13939^2324896346Hans Havermann11/2019
50862^320043-10877596343Enzo Doria04/2014
508524989^7168+7168^2498996343Hans Havermann11/2019
508710^96338+42493996339Patrick De Geest03/2016
508810^96338-928196338Robert Price09/2015
5089(3*2^320008+1)/796332Lelio R Paula09/2013
509025699^5596+5596^2569996317Hans Havermann07/2020
509126502^4297+4297^2650296287Hans Havermann07/2020
50922^319838+425796281Lelio R Paula03/2016
50932^319830-1699596279Lelio R Paula03/2016
50946^123713+14396268Lelio R Paula05/2016
5095(28*10^96265-97)/396266Robert Price07/2016
5096103^47825-10296264Norbert Schneider10/2016
5097(2^319777+2082)/296263Stefano Morozzi09/2020
5098(2^319771+3686)/296261Stefano Morozzi09/2020
50992^319713-8196244Lelio R Paula11/2012
5100(55459*2^319706+1)/2016796242Lelio R Paula07/2014
510122834^16393+16393^2283496238Hans Havermann05/2020
510212^89153-4396213Lelio R Paula06/2016
5104(2*10^96195-59)/396195Robert Price05/2017
51039*10^96194-7796195Robert Price08/2020
51052^319545+14796193Lelio R Paula11/2012
510623357^13128+13128^2335796189Hans Havermann02/2020
510725952^5073+5073^2595296160Hans Havermann12/2019
5108(50^56597+1)/5196155Robert Price03/2014
510922313^20374+20374^2231396149Hans Havermann12/2019
511022279^20668+20668^2227996141Hans Havermann11/2019
5111(41*10^96137-59)/996138Robert Price10/2017
51122^319353-11034396135Enzo Doria05/2014
511311^92309-4296130Lelio R Paula05/2016
511414^83869-13^8386996125Jean-Louis Charton01/2009
5115(7*10^96112+143)/396113Robert Price04/2016
511626731^3940+3940^2673196112Hans Havermann07/2020
511722640^17583+17583^2264096109Hans Havermann07/2020
51182^319237+6583596100Lelio R Paula03/2016
51192^319194-184196087Yves Minet03/2013
512023949^10280+10280^2394996084Hans Havermann07/2020
512120^73847-3196078Lelio R Paula05/2016
512250^56543-4996065Norbert Schneider09/2018
51232^319107-10955596061Enzo Doria04/2014
5124(3*2^319114-1)/262796060Lelio R Paula02/2014
51252^319098-11215796059Enzo Doria06/2014
512615^81673+9496055Lelio R Paula07/2016
51272^319074+187174996051Enzo Doria05/2016
512825670^5517+5517^2567096050Hans Havermann06/2020
51292^319007-11211196031Enzo Doria06/2014
51302^318946-142196013Yves Minet01/2013
513122830^16003+16003^2283095982Hans Havermann02/2020
51322^318834-11041195979Enzo Doria05/2014
51332^318831-196595978Lelio R Paula03/2016
5134(5*10^95976+7)/395977Erik Branger03/2014
513522871^15696+15696^2287195962Hans Havermann01/2020
513623167^13860+13860^2316795953Hans Havermann01/2020
51375*3^201089-895945Lelio R Paula08/2014
51382^318711-13995942Lelio R Paula11/2012
51392^318635-116795919Lelio R Paula03/2016
514015^81555+1695917Lelio R Paula07/2016
5141(37*10^95895+377)/995896Robert Price10/2017
5142(22699*2^318527+1)/2195890Lelio R Paula07/2014
51432^318496-9730595877Lelio R Paula03/2016
514422129^21496+21496^2212995871Hans Havermann07/2020
51462^318466+1501595868Lelio R Paula03/2016
514524847^7216+7216^2484795868Hans Havermann07/2020
514723706^11065+11065^2370695866Hans Havermann07/2020
51486^123187-17312995859Mike Oakes04/2011
51492^318423-48795855Yves Minet03/2012
5150(2^318359+678)/295836Stefano Morozzi09/2020
5151(10223*2^318350+1)/156395834Lelio R Paula07/2014
5152(2^318267+2550)/295808Stefano Morozzi09/2020
515345369!2+102495787Robert Price02/2015
51543^200758-8695786Lelio R Paula05/2016
5155(2^318271+1)/(3*46031404238891*654090604244843)95781Gord Palameta12/2018
5156(2^318171+2030)/295779Stefano Morozzi09/2020
51573*10^95776-5995777Robert Price10/2017
5158193^41901-295768Lelio R Paula10/2017
5159(2^318124+2502)/295765Stefano Morozzi09/2020
51604*10^95752-7195753Robert Price11/2017
516123640^11197+11197^2364095721Hans Havermann12/2019
5162((10^47850-1)*10000/9+6421)*10^47850+(10^47850-1)/995704Hans Havermann05/2019
5163(509203*2^317881-1)/5280595693Lelio R Paula04/2015
5164(2^317853+1086)/295683Stefano Morozzi09/2020
51654*10^95672+9195673Robert Price11/2017
51666*10^95665+4395666Robert Price07/2020
5167(11*10^95641-113)/395642Robert Price01/2017
5168(13*10^95588+11)/395589Robert Price05/2015
5169Phi(191188,10)/19118995587Maksym Voznyy11/2015
51703^200325+7095580Lelio R Paula05/2016
5171(25*10^95574-7)/995575Robert Price12/2014
5172(2^317485-3)/2131395569Lelio R Paula06/2013
51732^317464+3195567Lelio R Paula11/2012
5174(2^317451+2114)/295562Stefano Morozzi09/2020
51757^113073+8295558Lelio R Paula04/2016
51762^317251+46595503Lelio R Paula03/2016
517719^74684+5895503Lelio R Paula06/2016
5178(2^317250-7)/33995500Lelio R Paula07/2013
51796^122718-7995494Lelio R Paula05/2016
518022168^20291+20291^2216895485Hans Havermann10/2019
51812^317141-11049195469Enzo Doria05/2014
5182(2^317097+3014)/295456Stefano Morozzi09/2020
51832^317094+7630995455Enzo Doria05/2016
51842^317085+9595453Lelio R Paula11/2012
5185(17*10^95451-377)/995452Robert Price11/2017
51862^317057-10955195444Enzo Doria04/2014
51873^200026+2895437Lelio R Paula05/2016
51882^317024+9395434Donovan Johnson06/2008
51892^316999+160595427Lelio R Paula03/2016
5190(2^317000+3210)/295427Stefano Morozzi09/2020
51912^316995-11042795426Enzo Doria05/2014
519222300^18987+18987^2230095410Hans Havermann06/2020
51942^316937+17795408Lelio R Paula11/2012
51934*10^95407+9195408Robert Price11/2017
51952^316908+191595399Lelio R Paula03/2016
51962^316894+9995395Lelio R Paula11/2012
5197(2^316887+2546)/295393Stefano Morozzi09/2020
51982*10^95374-2195375Robert Price09/2020
51996^122547+1195361Lelio R Paula05/2016
52002^316771+8287595358Lelio R Paula03/2016
5201(2^316765+3102)/295356Stefano Morozzi09/2020
5202(23*10^95326+1)/395327Serge Batalov05/2009
52031*10^95326+5795327Robert Price03/2011
520410^95326-39368795326Patrick De Geest09/2013
5205(3^199803+4)/47953995325Lelio R Paula04/2013
52062^316654-10948195323Enzo Doria04/2014
52078*10^95316+5195317Robert Price05/2017
5208(50^56099+43^56099)/9395309Serge Batalov12/2016
5209(23*2^316559+1)/392595292Lelio R Paula09/2013
5211(71*10^95277-539)/995278Robert Price11/2017
521023422^11691+11691^2342295278Hans Havermann10/2019
521219^74503-5695271Lelio R Paula06/2016
521311^91475-438095262Enzo Doria01/2013
5214(62*10^95251-611)/995252Robert Price05/2017
5215(2^316321-509203)/6937795218Lelio R Paula06/2013
521626541^3868+3868^2654195216Hans Havermann07/2020
5217(79*10^95214-43)/995215Erik Branger11/2013
5218(9*2^316233-1)/175195194Lelio R Paula02/2014
52195*2^316213+995191Lelio R Paula08/2014
52202*10^95188-9195189Robert Price04/2020
52212^316205-184816395188Enzo Doria07/2015
52222^316185-278791395182Enzo Doria04/2016
5223(2^316174+3538)/295178Stefano Morozzi09/2020
5224(9787*2^316142-1)/395172Lelio R Paula04/2015
52252^316140-595168Henri Lifchitz02/2006
5226(15185*2^316117-1)/395165Lelio R Paula04/2015
5227(34*10^95153-7)/9/19/1915795149Makoto Morimoto05/2016
52282^316069+7681795147Enzo Doria05/2016
5229(199*10^95134-7)/395136Robert Price02/2017
52302^316027-9730595134Lelio R Paula03/2016
52312^316006-279805195128Enzo Doria04/2016
523224994^6397+6397^2499495127Hans Havermann02/2020
52332^315921-279760395102Enzo Doria04/2016
52342*10^95095+6395096Robert Price10/2017
52352^315857+129995083Lelio R Paula03/2016
5236(2^315858+2598)/295083Stefano Morozzi09/2020
523714^82955-4395078Lelio R Paula06/2016
5238(2*10^95072-17)/395072Robert Price08/2014
5239(2^315779+1610)/295059Stefano Morozzi09/2020
524021938^21513+21513^2193895051Hans Havermann09/2020
52412^315727+6595044Lelio R Paula11/2012
52422^315725+188575795043Enzo Doria03/2017
524323277^12058+12058^2327795000Hans Havermann09/2020
52441*10^94983+2194984Robert Price03/2011
524510^94983-71794983Patrick De Geest08/2013
524617^77187-8294975Lelio R Paula07/2016
52473*10^94964+3794965Robert Price10/2017
5248(2^315481-1017)/2062728594962Lelio R Paula06/2013
52492^315423-11032994952Enzo Doria05/2014
525011^91169-723094943Enzo Doria02/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 30 2020 00:02 (Time in France)

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