PRP Records

Probable Primes Top 10000

(252675 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 ?
40016^124433-12443396828Robert Price01/2014
40022^321631+6996821Lelio R Paula12/2012
4003(13*2^321606+1)/11996813Lelio R Paula11/2013
4004(46*10^96798-1)/996799Serge Batalov10/2014
4005(59*10^96798+31)/996799Robert Price09/2015
4006223319#+23122396790Makoto Morimoto02/2016
40072^321519-2863596787Lelio R Paula06/2016
40082^321487-186723796778Enzo Doria03/2016
40092^321461-6396770Lelio R Paula12/2012
40102^321439+12396763Lelio R Paula12/2012
40112^321434+70996762Lelio R Paula02/2013
401214^84413+8996749Lelio R Paula07/2016
4013(28*10^96743+71)/996744Serge Batalov12/2008
401413^86847+9696743Lelio R Paula06/2016
40159*2^321336-796733Lelio R Paula08/2014
4016(209*10^96722-17)/396724Robert Price05/2017
40172^321187-115996687Yves Minet11/2012
40182^321182-185008196686Enzo Doria08/2015
40192^321116-11282996666Enzo Doria06/2014
40202^321108-10949996664Enzo Doria04/2014
40212^321098+279385996661Enzo Doria03/2016
40222^321057+409796648Lelio R Paula06/2016
4023(4435*29^66081-4)/796640Curtis Bright05/2015
4024p(19849)#/2-6496581Robert Price04/2017
40252^320817+18996576Lelio R Paula12/2012
4026(361*10^96567-163)/996569Robert Price10/2017
40272^320788-11032796567Enzo Doria05/2014
40282^320764+79396560Lelio R Paula02/2013
4029(9179*2^320652-1)/22196528Lelio R Paula05/2015
40302^320616-7879596516Lelio R Paula03/2016
40312^320612-46193996514Enzo Doria07/2015
40325*2^320431+796461Lelio R Paula08/2014
403319^75431-9096458Lelio R Paula06/2016
4034(2^320370+3)/6796440Lelio R Paula10/2013
40352^320309+187147796423Enzo Doria05/2016
4036tau(809^6028)96410Nik Lygeros / Olivier Rozier / LR team10/2013
4037(21*2^320252-1)/189596404Lelio R Paula02/2014
40382^320232-17396400Lelio R Paula12/2012
4039175^42975-296395Lelio R Paula10/2017
404010^96377+19991196378Patrick De Geest12/2016
404110^96377-2000196377Robert Price11/2016
40422^320124-279044996367Enzo Doria03/2016
40432^320043-10877596343Enzo Doria04/2014
404410^96338+42493996339Patrick De Geest03/2016
404510^96338-928196338Robert Price09/2015
4046(3*2^320008+1)/796332Lelio R Paula09/2013
40472^319838+425796281Lelio R Paula03/2016
40482^319830-1699596279Lelio R Paula03/2016
40496^123713+14396268Lelio R Paula05/2016
4050(28*10^96265-97)/396266Robert Price07/2016
4051103^47825-10296264Norbert Schneider10/2016
40522^319713-8196244Lelio R Paula11/2012
4053(55459*2^319706+1)/2016796242Lelio R Paula07/2014
405412^89153-4396213Lelio R Paula06/2016
4055(2*10^96195-59)/396195Robert Price05/2017
40562^319545+14796193Lelio R Paula11/2012
4057(50^56597+1)/5196155Robert Price03/2014
4058(41*10^96137-59)/996138Robert Price10/2017
40592^319353-11034396135Enzo Doria05/2014
406011^92309-4296130Lelio R Paula05/2016
406114^83869-13^8386996125Jean-Louis Charton01/2009
4062(7*10^96112+143)/396113Robert Price04/2016
40632^319237+6583596100Lelio R Paula03/2016
40642^319194-184196087Yves Minet03/2013
406520^73847-3196078Lelio R Paula05/2016
406650^56543-4996065Norbert Schneider09/2018
40672^319107-10955596061Enzo Doria04/2014
4068(3*2^319114-1)/262796060Lelio R Paula02/2014
40692^319098-11215796059Enzo Doria06/2014
407015^81673+9496055Lelio R Paula07/2016
40712^319074+187174996051Enzo Doria05/2016
40722^319007-11211196031Enzo Doria06/2014
40732^318946-142196013Yves Minet01/2013
40742^318834-11041195979Enzo Doria05/2014
40752^318831-196595978Lelio R Paula03/2016
4076(5*10^95976+7)/395977Erik Branger03/2014
40775*3^201089-895945Lelio R Paula08/2014
40782^318711-13995942Lelio R Paula11/2012
40792^318635-116795919Lelio R Paula03/2016
408015^81555+1695917Lelio R Paula07/2016
4081(37*10^95895+377)/995896Robert Price10/2017
4082(22699*2^318527+1)/2195890Lelio R Paula07/2014
40832^318496-9730595877Lelio R Paula03/2016
40842^318466+1501595868Lelio R Paula03/2016
40856^123187-17312995859Mike Oakes04/2011
40862^318423-48795855Yves Minet03/2012
4087(10223*2^318350+1)/156395834Lelio R Paula07/2014
408845369!2+102495787Robert Price02/2015
40893^200758-8695786Lelio R Paula05/2016
4090(2^318271+1)/(3*46031404238891*654090604244843)95781Gord Palameta12/2018
40913*10^95776-5995777Robert Price10/2017
4092193^41901-295768Lelio R Paula10/2017
40934*10^95752-7195753Robert Price11/2017
4094(509203*2^317881-1)/5280595693Lelio R Paula04/2015
40954*10^95672+9195673Robert Price11/2017
4096(11*10^95641-113)/395642Robert Price01/2017
4097(13*10^95588+11)/395589Robert Price05/2015
4098Phi(191188,10)/19118995587Maksym Voznyy11/2015
40993^200325+7095580Lelio R Paula05/2016
4100(25*10^95574-7)/995575Robert Price12/2014
4101(2^317485-3)/2131395569Lelio R Paula06/2013
41022^317464+3195567Lelio R Paula11/2012
41037^113073+8295558Lelio R Paula04/2016
41042^317251+46595503Lelio R Paula03/2016
410519^74684+5895503Lelio R Paula06/2016
4106(2^317250-7)/33995500Lelio R Paula07/2013
41076^122718-7995494Lelio R Paula05/2016
41082^317141-11049195469Enzo Doria05/2014
41092^317094+7630995455Enzo Doria05/2016
41102^317085+9595453Lelio R Paula11/2012
4111(17*10^95451-377)/995452Robert Price11/2017
41122^317057-10955195444Enzo Doria04/2014
41133^200026+2895437Lelio R Paula05/2016
41142^317024+9395434Donovan Johnson06/2008
41152^316999+160595427Lelio R Paula03/2016
41162^316995-11042795426Enzo Doria05/2014
41182^316937+17795408Lelio R Paula11/2012
41174*10^95407+9195408Robert Price11/2017
41192^316908+191595399Lelio R Paula03/2016
41202^316894+9995395Lelio R Paula11/2012
41216^122547+1195361Lelio R Paula05/2016
41222^316771+8287595358Lelio R Paula03/2016
4123(23*10^95326+1)/395327Serge Batalov05/2009
41241*10^95326+5795327Robert Price03/2011
412510^95326-39368795326Patrick De Geest09/2013
4126(3^199803+4)/47953995325Lelio R Paula04/2013
41272^316654-10948195323Enzo Doria04/2014
41288*10^95316+5195317Robert Price05/2017
4129(50^56099+43^56099)/9395309Serge Batalov12/2016
4130(23*2^316559+1)/392595292Lelio R Paula09/2013
4131(71*10^95277-539)/995278Robert Price11/2017
413219^74503-5695271Lelio R Paula06/2016
413311^91475-438095262Enzo Doria01/2013
4134(62*10^95251-611)/995252Robert Price05/2017
4135(2^316321-509203)/6937795218Lelio R Paula06/2013
4136(79*10^95214-43)/995215Erik Branger11/2013
4137(9*2^316233-1)/175195194Lelio R Paula02/2014
41385*2^316213+995191Lelio R Paula08/2014
41392^316205-184816395188Enzo Doria07/2015
41402^316185-278791395182Enzo Doria04/2016
4141(9787*2^316142-1)/395172Lelio R Paula04/2015
41422^316140-595168Henri Lifchitz02/2006
4143(15185*2^316117-1)/395165Lelio R Paula04/2015
4144(34*10^95153-7)/9/19/1915795149Makoto Morimoto05/2016
41452^316069+7681795147Enzo Doria05/2016
4146(199*10^95134-7)/395136Robert Price02/2017
41472^316027-9730595134Lelio R Paula03/2016
41482^316006-279805195128Enzo Doria04/2016
41492^315921-279760395102Enzo Doria04/2016
41502*10^95095+6395096Robert Price10/2017
41512^315857+129995083Lelio R Paula03/2016
415214^82955-4395078Lelio R Paula06/2016
4153(2*10^95072-17)/395072Robert Price08/2014
41542^315727+6595044Lelio R Paula11/2012
41552^315725+188575795043Enzo Doria03/2017
41561*10^94983+2194984Robert Price03/2011
415710^94983-71794983Patrick De Geest08/2013
415817^77187-8294975Lelio R Paula07/2016
41593*10^94964+3794965Robert Price10/2017
4160(2^315481-1017)/2062728594962Lelio R Paula06/2013
41612^315423-11032994952Enzo Doria05/2014
416211^91169-723094943Enzo Doria02/2013
41637*10^94938+6194939Robert Price02/2017
41642^315351+102594931Lelio R Paula03/2016
41652^315350-11225394930Enzo Doria06/2014
4166((1001327^(15817)+1)/1001328)94906Faysal YAtim10/2010
41682^315268+794906Lelio R Paula10/2012
416711^91133+6294906Lelio R Paula05/2016
416930^64244+4194897Lelio R Paula08/2012
4170(151*10^94885-7)/994887Robert Price07/2017
41714^157583+2214794875Mike Oakes01/2011
41722^315098+12394854Lelio R Paula11/2012
41733^198791-3494848Robert Price11/2013
41743*2^315067+794846Lelio R Paula08/2014
4175(9*2^315057+1)/7394841Lelio R Paula09/2013
4176(16*10^94822+53)/394823Robert Price12/2016
41778*6^121849-794818Lelio R Paula10/2014
4178(85*10^94802+473)/994803Robert Price03/2017
41792^314870-10876194786Enzo Doria03/2014
41805*2^314841-394778Lelio R Paula08/2014
41816^121772+11394758Lelio R Paula05/2016
41826^121756-1625394745Enzo Doria02/2013
41832^314718-11279394740Enzo Doria06/2014
41842^314697-184729394734Enzo Doria07/2015
41862^314548-24994689Yves Minet02/2012
41855^135469+4294689Lelio R Paula04/2016
4187gcd(V(1137755),5*F(227551)*(F(227551)-1)+1)94676Serge Batalov04/2015
4188(2*10^94604+547)/994604Robert Price10/2017
41893*2^314152+594570Lelio R Paula08/2014
41902*6^121530-594570Lelio R Paula10/2014
41917*10^94563+8794564Robert Price11/2016
41922^314114-10967794558Enzo Doria04/2014
4193(218389#+240867)/(3*11*811)94557Makoto Morimoto10/2017
41942^314059+7658394542Enzo Doria05/2016
41952^314041-403594536Lelio R Paula03/2016
4196(7*2^314003-11)/1594524Renaud Lifchitz03/2011
419711^90760-471094517Enzo Doria01/2013
4198(7*2^313926-1)/14882194497Lelio R Paula02/2014
419994*10^94493-394495Robert Price11/2016
4200(1000547^15749+1)/100054894492Faysal YAtim12/2008
4201(F(3*75345)^2+L(3*75345)^2)/494477Henri Lifchitz10/2017
42027^111792-3294476Lelio R Paula04/2016
420311^90680-585094434Enzo Doria01/2013
42042^313675-11012594426Enzo Doria04/2014
4205(2999*29^64556-2427)/494410Curtis Bright05/2015
42062^313609-11222594406Enzo Doria06/2014
42072^313584+7290194399Enzo Doria04/2016
42082^313510-11286594376Enzo Doria06/2014
42097*10^94373+8794374Robert Price11/2016
4210(9^98897+8^98897)/1794371Robert Price12/2012
42112^313453-11470394359Enzo Doria04/2015
42128*10^94357-5194358Robert Price10/2017
4213(379*10^94337-1)/994339Robert Price08/2017
42142^313344-313344+194326Robert Price10/2014
421520^72481-4994300Lelio R Paula05/2016
421644725!2+12894289Robert Price03/2015
42174*10^94286+994287Robert Price05/2015
421817^76621+2494279Lelio R Paula07/2016
42192^313156-11285994270Enzo Doria06/2014
42206^121130-5994258Lelio R Paula05/2016
42213^197542+2894252Robert Price11/2013
4222(3^197521+2)/5165594237Lelio R Paula04/2013
42232^313045-595594236Lelio R Paula03/2016
4224(67*10^94212+23)/994213Ray Chandler02/2011
42252^312909-186520394195Enzo Doria03/2016
42262^312848-14994177Lelio R Paula11/2012
42274^156403-7759794164Mike Oakes04/2011
422818^75004-8594151Lelio R Paula06/2016
422919^73622-4894145Lelio R Paula06/2016
4230(11^90397-3^90397)/894138Robert Price04/2011
4231(3^197287+5)/1694129Lelio R Paula04/2013
423212^87212-3794118Lelio R Paula06/2016
423311^90376+7694117Lelio R Paula05/2016
4234(6^120946-11)/594114Paul Bourdelais11/2011
4235(10^94096+191)/394096Robert Price11/2017
42362^312562-11268594091Enzo Doria06/2014
4237137^44026-294072Lelio R Paula10/2017
42382^312404-86968810594043Lelio R Paula09/2016
42392^312387+279353394038Enzo Doria03/2016
424110^94016+9194017Robert Price04/2011
4240(15*2^312325-1)/720194017Lelio R Paula02/2014
424310^94016-18896394016Patrick De Geest08/2013
4242(17*2^312315-1)/4594016Lelio R Paula02/2014
42446^120802+766194003Mike Oakes04/2011
4245(67607*2^312254+1)/17794001Lelio R Paula06/2014
4246(11*2^312207+1)/1993984Lelio R Paula09/2013
42472^312201+5193982Lelio R Paula11/2012
4248(4*6^120749+1)/593961Serge Batalov10/2014
42493^196892+5893942Lelio R Paula05/2016
42502^312060+1891593940Lelio R Paula03/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 20 2019 09:21 (Time in France)

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