PRP Records

Probable Primes Top 10000

(255244 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 ?
42512^321971-11274796923Enzo Doria06/2014
425211^93062-9296915Lelio R Paula06/2016
4253(11*2^321841-7)/1596884Renaud Lifchitz03/2011
42543^203051+3496880Lelio R Paula05/2016
42552*10^96867-5196868Robert Price11/2017
4256(64*10^96863-1)/2796864Serge Batalov05/2010
42572^321716-278693996847Enzo Doria03/2016
42592^321701-11305396842Enzo Doria07/2014
42582^321700-2863596842Lelio R Paula06/2016
4260(5*2^321691-1)/2796838Lelio R Paula02/2014
42616^124433-12443396828Robert Price01/2014
42622^321631+6996821Lelio R Paula12/2012
4263(13*2^321606+1)/11996813Lelio R Paula11/2013
4264(46*10^96798-1)/996799Serge Batalov10/2014
4265(59*10^96798+31)/996799Robert Price09/2015
4266223319#+23122396790Makoto Morimoto02/2016
42672^321519-2863596787Lelio R Paula06/2016
42682^321487-186723796778Enzo Doria03/2016
42692^321461-6396770Lelio R Paula12/2012
42702^321439+12396763Lelio R Paula12/2012
42712^321434+70996762Lelio R Paula02/2013
427214^84413+8996749Lelio R Paula07/2016
4273(28*10^96743+71)/996744Serge Batalov12/2008
427413^86847+9696743Lelio R Paula06/2016
42759*2^321336-796733Lelio R Paula08/2014
4276(209*10^96722-17)/396724Robert Price05/2017
42772^321237-461596702Yves Minet05/2019
42782^321187-115996687Yves Minet11/2012
42792^321182-185008196686Enzo Doria08/2015
42802^321116-11282996666Enzo Doria06/2014
42812^321108-10949996664Enzo Doria04/2014
42822^321098+279385996661Enzo Doria03/2016
42832^321057+409796648Lelio R Paula06/2016
4284(4435*29^66081-4)/796640Curtis Bright05/2015
4285p(19849)#/2-6496581Robert Price04/2017
42872^320817+18996576Lelio R Paula12/2012
42862^320816-468596576Yves Minet05/2019
4288(361*10^96567-163)/996569Robert Price10/2017
42892^320788-11032796567Enzo Doria05/2014
42902^320764+79396560Lelio R Paula02/2013
4291(9179*2^320652-1)/22196528Lelio R Paula05/2015
42922^320616-7879596516Lelio R Paula03/2016
42932^320612-46193996514Enzo Doria07/2015
42945*2^320431+796461Lelio R Paula08/2014
429519^75431-9096458Lelio R Paula06/2016
4296(2^320370+3)/6796440Lelio R Paula10/2013
42972^320309+187147796423Enzo Doria05/2016
4298tau(809^6028)96410Nik Lygeros / Olivier Rozier / LR team10/2013
4299(21*2^320252-1)/189596404Lelio R Paula02/2014
43002^320232-17396400Lelio R Paula12/2012
4301175^42975-296395Lelio R Paula10/2017
430210^96377+19991196378Patrick De Geest12/2016
430310^96377-2000196377Robert Price11/2016
43042^320124-279044996367Enzo Doria03/2016
43062^320043-10877596343Enzo Doria04/2014
430524989^7168+7168^2498996343Hans Havermann11/2019
430710^96338+42493996339Patrick De Geest03/2016
430810^96338-928196338Robert Price09/2015
4309(3*2^320008+1)/796332Lelio R Paula09/2013
43102^319838+425796281Lelio R Paula03/2016
43112^319830-1699596279Lelio R Paula03/2016
43126^123713+14396268Lelio R Paula05/2016
4313(28*10^96265-97)/396266Robert Price07/2016
4314103^47825-10296264Norbert Schneider10/2016
43152^319713-8196244Lelio R Paula11/2012
4316(55459*2^319706+1)/2016796242Lelio R Paula07/2014
431712^89153-4396213Lelio R Paula06/2016
4318(2*10^96195-59)/396195Robert Price05/2017
43192^319545+14796193Lelio R Paula11/2012
4320(50^56597+1)/5196155Robert Price03/2014
4321(41*10^96137-59)/996138Robert Price10/2017
43222^319353-11034396135Enzo Doria05/2014
432311^92309-4296130Lelio R Paula05/2016
432414^83869-13^8386996125Jean-Louis Charton01/2009
4325(7*10^96112+143)/396113Robert Price04/2016
43262^319237+6583596100Lelio R Paula03/2016
43272^319194-184196087Yves Minet03/2013
432820^73847-3196078Lelio R Paula05/2016
432950^56543-4996065Norbert Schneider09/2018
43302^319107-10955596061Enzo Doria04/2014
4331(3*2^319114-1)/262796060Lelio R Paula02/2014
43322^319098-11215796059Enzo Doria06/2014
433315^81673+9496055Lelio R Paula07/2016
43342^319074+187174996051Enzo Doria05/2016
43352^319007-11211196031Enzo Doria06/2014
43362^318946-142196013Yves Minet01/2013
43372^318834-11041195979Enzo Doria05/2014
43382^318831-196595978Lelio R Paula03/2016
4339(5*10^95976+7)/395977Erik Branger03/2014
43405*3^201089-895945Lelio R Paula08/2014
43412^318711-13995942Lelio R Paula11/2012
43422^318635-116795919Lelio R Paula03/2016
434315^81555+1695917Lelio R Paula07/2016
4344(37*10^95895+377)/995896Robert Price10/2017
4345(22699*2^318527+1)/2195890Lelio R Paula07/2014
43462^318496-9730595877Lelio R Paula03/2016
43472^318466+1501595868Lelio R Paula03/2016
43486^123187-17312995859Mike Oakes04/2011
43492^318423-48795855Yves Minet03/2012
4350(10223*2^318350+1)/156395834Lelio R Paula07/2014
435145369!2+102495787Robert Price02/2015
43523^200758-8695786Lelio R Paula05/2016
4353(2^318271+1)/(3*46031404238891*654090604244843)95781Gord Palameta12/2018
43543*10^95776-5995777Robert Price10/2017
4355193^41901-295768Lelio R Paula10/2017
43564*10^95752-7195753Robert Price11/2017
4357((10^47850-1)*10000/9+6421)*10^47850+(10^47850-1)/995704Hans Havermann05/2019
4358(509203*2^317881-1)/5280595693Lelio R Paula04/2015
43594*10^95672+9195673Robert Price11/2017
4360(11*10^95641-113)/395642Robert Price01/2017
4361(13*10^95588+11)/395589Robert Price05/2015
4362Phi(191188,10)/19118995587Maksym Voznyy11/2015
43633^200325+7095580Lelio R Paula05/2016
4364(25*10^95574-7)/995575Robert Price12/2014
4365(2^317485-3)/2131395569Lelio R Paula06/2013
43662^317464+3195567Lelio R Paula11/2012
43677^113073+8295558Lelio R Paula04/2016
43682^317251+46595503Lelio R Paula03/2016
436919^74684+5895503Lelio R Paula06/2016
4370(2^317250-7)/33995500Lelio R Paula07/2013
43716^122718-7995494Lelio R Paula05/2016
437222168^20291+20291^2216895485Hans Havermann10/2019
43732^317141-11049195469Enzo Doria05/2014
43742^317094+7630995455Enzo Doria05/2016
43752^317085+9595453Lelio R Paula11/2012
4376(17*10^95451-377)/995452Robert Price11/2017
43772^317057-10955195444Enzo Doria04/2014
43783^200026+2895437Lelio R Paula05/2016
43792^317024+9395434Donovan Johnson06/2008
43802^316999+160595427Lelio R Paula03/2016
43812^316995-11042795426Enzo Doria05/2014
43832^316937+17795408Lelio R Paula11/2012
43824*10^95407+9195408Robert Price11/2017
43842^316908+191595399Lelio R Paula03/2016
43852^316894+9995395Lelio R Paula11/2012
43866^122547+1195361Lelio R Paula05/2016
43872^316771+8287595358Lelio R Paula03/2016
4388(23*10^95326+1)/395327Serge Batalov05/2009
43891*10^95326+5795327Robert Price03/2011
439010^95326-39368795326Patrick De Geest09/2013
4391(3^199803+4)/47953995325Lelio R Paula04/2013
43922^316654-10948195323Enzo Doria04/2014
43938*10^95316+5195317Robert Price05/2017
4394(50^56099+43^56099)/9395309Serge Batalov12/2016
4395(23*2^316559+1)/392595292Lelio R Paula09/2013
4396(71*10^95277-539)/995278Robert Price11/2017
439723422^11691+11691^2342295278Hans Havermann10/2019
439819^74503-5695271Lelio R Paula06/2016
439911^91475-438095262Enzo Doria01/2013
4400(62*10^95251-611)/995252Robert Price05/2017
4401(2^316321-509203)/6937795218Lelio R Paula06/2013
4402(79*10^95214-43)/995215Erik Branger11/2013
4403(9*2^316233-1)/175195194Lelio R Paula02/2014
44045*2^316213+995191Lelio R Paula08/2014
44052^316205-184816395188Enzo Doria07/2015
44062^316185-278791395182Enzo Doria04/2016
4407(9787*2^316142-1)/395172Lelio R Paula04/2015
44082^316140-595168Henri Lifchitz02/2006
4409(15185*2^316117-1)/395165Lelio R Paula04/2015
4410(34*10^95153-7)/9/19/1915795149Makoto Morimoto05/2016
44112^316069+7681795147Enzo Doria05/2016
4412(199*10^95134-7)/395136Robert Price02/2017
44132^316027-9730595134Lelio R Paula03/2016
44142^316006-279805195128Enzo Doria04/2016
44152^315921-279760395102Enzo Doria04/2016
44162*10^95095+6395096Robert Price10/2017
44172^315857+129995083Lelio R Paula03/2016
441814^82955-4395078Lelio R Paula06/2016
4419(2*10^95072-17)/395072Robert Price08/2014
44202^315727+6595044Lelio R Paula11/2012
44212^315725+188575795043Enzo Doria03/2017
44221*10^94983+2194984Robert Price03/2011
442310^94983-71794983Patrick De Geest08/2013
442417^77187-8294975Lelio R Paula07/2016
44253*10^94964+3794965Robert Price10/2017
4426(2^315481-1017)/2062728594962Lelio R Paula06/2013
44272^315423-11032994952Enzo Doria05/2014
442811^91169-723094943Enzo Doria02/2013
44297*10^94938+6194939Robert Price02/2017
44302^315351+102594931Lelio R Paula03/2016
44312^315350-11225394930Enzo Doria06/2014
4434((1001327^(15817)+1)/1001328)94906Faysal YAtim10/2010
44332^315268+794906Lelio R Paula10/2012
443211^91133+6294906Lelio R Paula05/2016
443530^64244+4194897Lelio R Paula08/2012
4436(151*10^94885-7)/994887Robert Price07/2017
44374^157583+2214794875Mike Oakes01/2011
44382^315098+12394854Lelio R Paula11/2012
44393^198791-3494848Robert Price11/2013
44403*2^315067+794846Lelio R Paula08/2014
4441(9*2^315057+1)/7394841Lelio R Paula09/2013
4442(16*10^94822+53)/394823Robert Price12/2016
44438*6^121849-794818Lelio R Paula10/2014
4444(85*10^94802+473)/994803Robert Price03/2017
44452^314870-10876194786Enzo Doria03/2014
44465*2^314841-394778Lelio R Paula08/2014
44476^121772+11394758Lelio R Paula05/2016
44486^121756-1625394745Enzo Doria02/2013
44492^314718-11279394740Enzo Doria06/2014
44502^314697-184729394734Enzo Doria07/2015
44522^314548-24994689Yves Minet02/2012
44515^135469+4294689Lelio R Paula04/2016
4453gcd(V(1137755),5*F(227551)*(F(227551)-1)+1)94676Serge Batalov04/2015
4454(2*10^94604+547)/994604Robert Price10/2017
44553*2^314152+594570Lelio R Paula08/2014
44562*6^121530-594570Lelio R Paula10/2014
44577*10^94563+8794564Robert Price11/2016
44582^314114-10967794558Enzo Doria04/2014
4459(218389#+240867)/(3*11*811)94557Makoto Morimoto10/2017
44602^314059+7658394542Enzo Doria05/2016
44612^314041-403594536Lelio R Paula03/2016
4462(7*2^314003-11)/1594524Renaud Lifchitz03/2011
446311^90760-471094517Enzo Doria01/2013
4464(7*2^313926-1)/14882194497Lelio R Paula02/2014
446594*10^94493-394495Robert Price11/2016
4466(1000547^15749+1)/100054894492Faysal YAtim12/2008
4467(F(3*75345)^2+L(3*75345)^2)/494477Henri Lifchitz10/2017
44687^111792-3294476Lelio R Paula04/2016
446911^90680-585094434Enzo Doria01/2013
44702^313675-11012594426Enzo Doria04/2014
4471(2999*29^64556-2427)/494410Curtis Bright05/2015
44722^313609-11222594406Enzo Doria06/2014
44732^313584+7290194399Enzo Doria04/2016
44742^313510-11286594376Enzo Doria06/2014
44757*10^94373+8794374Robert Price11/2016
4476(9^98897+8^98897)/1794371Robert Price12/2012
44772^313453-11470394359Enzo Doria04/2015
44788*10^94357-5194358Robert Price10/2017
4479(379*10^94337-1)/994339Robert Price08/2017
44802^313344-313344+194326Robert Price10/2014
448120^72481-4994300Lelio R Paula05/2016
448244725!2+12894289Robert Price03/2015
44834*10^94286+994287Robert Price05/2015
448417^76621+2494279Lelio R Paula07/2016
44852^313156-11285994270Enzo Doria06/2014
44866^121130-5994258Lelio R Paula05/2016
44873^197542+2894252Robert Price11/2013
4488(3^197521+2)/5165594237Lelio R Paula04/2013
44892^313045-595594236Lelio R Paula03/2016
4490(67*10^94212+23)/994213Ray Chandler02/2011
44912^312909-186520394195Enzo Doria03/2016
44922^312848-14994177Lelio R Paula11/2012
44934^156403-7759794164Mike Oakes04/2011
449418^75004-8594151Lelio R Paula06/2016
449519^73622-4894145Lelio R Paula06/2016
4496(11^90397-3^90397)/894138Robert Price04/2011
4497(3^197287+5)/1694129Lelio R Paula04/2013
449812^87212-3794118Lelio R Paula06/2016
449911^90376+7694117Lelio R Paula05/2016
4500(6^120946-11)/594114Paul Bourdelais11/2011


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 10 2019 12:07 (Time in France)

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