PRP Records

Probable Primes Top 10000

(252538 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 ?
40012^318496-9730595877Lelio R Paula03/2016
40022^318466+1501595868Lelio R Paula03/2016
40036^123187-17312995859Mike Oakes04/2011
40042^318423-48795855Yves Minet03/2012
4005(10223*2^318350+1)/156395834Lelio R Paula07/2014
400645369!2+102495787Robert Price02/2015
40073^200758-8695786Lelio R Paula05/2016
4008(2^318271+1)/(3*46031404238891*654090604244843)95781Gord Palameta12/2018
40093*10^95776-5995777Robert Price10/2017
4010193^41901-295768Lelio R Paula10/2017
40114*10^95752-7195753Robert Price11/2017
4012(509203*2^317881-1)/5280595693Lelio R Paula04/2015
40134*10^95672+9195673Robert Price11/2017
4014(11*10^95641-113)/395642Robert Price01/2017
4015(13*10^95588+11)/395589Robert Price05/2015
4016Phi(191188,10)/19118995587Maksym Voznyy11/2015
40173^200325+7095580Lelio R Paula05/2016
4018(25*10^95574-7)/995575Robert Price12/2014
4019(2^317485-3)/2131395569Lelio R Paula06/2013
40202^317464+3195567Lelio R Paula11/2012
40217^113073+8295558Lelio R Paula04/2016
40222^317251+46595503Lelio R Paula03/2016
402319^74684+5895503Lelio R Paula06/2016
4024(2^317250-7)/33995500Lelio R Paula07/2013
40256^122718-7995494Lelio R Paula05/2016
40262^317141-11049195469Enzo Doria05/2014
40272^317094+7630995455Enzo Doria05/2016
40282^317085+9595453Lelio R Paula11/2012
4029(17*10^95451-377)/995452Robert Price11/2017
40302^317057-10955195444Enzo Doria04/2014
40313^200026+2895437Lelio R Paula05/2016
40322^317024+9395434Donovan Johnson06/2008
40332^316999+160595427Lelio R Paula03/2016
40342^316995-11042795426Enzo Doria05/2014
40362^316937+17795408Lelio R Paula11/2012
40354*10^95407+9195408Robert Price11/2017
40372^316908+191595399Lelio R Paula03/2016
40382^316894+9995395Lelio R Paula11/2012
40396^122547+1195361Lelio R Paula05/2016
40402^316771+8287595358Lelio R Paula03/2016
4042(23*10^95326+1)/395327Serge Batalov05/2009
40411*10^95326+5795327Robert Price03/2011
404310^95326-39368795326Patrick De Geest09/2013
4044(3^199803+4)/47953995325Lelio R Paula04/2013
40452^316654-10948195323Enzo Doria04/2014
40468*10^95316+5195317Robert Price05/2017
4047(50^56099+43^56099)/9395309Serge Batalov12/2016
4048(23*2^316559+1)/392595292Lelio R Paula09/2013
4049(71*10^95277-539)/995278Robert Price11/2017
405019^74503-5695271Lelio R Paula06/2016
405111^91475-438095262Enzo Doria01/2013
4052(62*10^95251-611)/995252Robert Price05/2017
4053(2^316321-509203)/6937795218Lelio R Paula06/2013
4054(79*10^95214-43)/995215Erik Branger11/2013
4055(9*2^316233-1)/175195194Lelio R Paula02/2014
40565*2^316213+995191Lelio R Paula08/2014
40572^316205-184816395188Enzo Doria07/2015
40582^316185-278791395182Enzo Doria04/2016
4059(9787*2^316142-1)/395172Lelio R Paula04/2015
40602^316140-595168Henri Lifchitz02/2006
4061(15185*2^316117-1)/395165Lelio R Paula04/2015
4062(34*10^95153-7)/9/19/1915795149Makoto Morimoto05/2016
40632^316069+7681795147Enzo Doria05/2016
4064(199*10^95134-7)/395136Robert Price02/2017
40652^316027-9730595134Lelio R Paula03/2016
40662^316006-279805195128Enzo Doria04/2016
40672^315921-279760395102Enzo Doria04/2016
40682*10^95095+6395096Robert Price10/2017
40692^315857+129995083Lelio R Paula03/2016
407014^82955-4395078Lelio R Paula06/2016
4071(2*10^95072-17)/395072Robert Price08/2014
40722^315727+6595044Lelio R Paula11/2012
40732^315725+188575795043Enzo Doria03/2017
40741*10^94983+2194984Robert Price03/2011
407510^94983-71794983Patrick De Geest08/2013
407617^77187-8294975Lelio R Paula07/2016
40773*10^94964+3794965Robert Price10/2017
4078(2^315481-1017)/2062728594962Lelio R Paula06/2013
40792^315423-11032994952Enzo Doria05/2014
408011^91169-723094943Enzo Doria02/2013
40817*10^94938+6194939Robert Price02/2017
40822^315351+102594931Lelio R Paula03/2016
40832^315350-11225394930Enzo Doria06/2014
4085((1001327^(15817)+1)/1001328)94906Faysal YAtim10/2010
40842^315268+794906Lelio R Paula10/2012
408611^91133+6294906Lelio R Paula05/2016
408730^64244+4194897Lelio R Paula08/2012
4088(151*10^94885-7)/994887Robert Price07/2017
40894^157583+2214794875Mike Oakes01/2011
40902^315098+12394854Lelio R Paula11/2012
40913^198791-3494848Robert Price11/2013
40923*2^315067+794846Lelio R Paula08/2014
4093(9*2^315057+1)/7394841Lelio R Paula09/2013
4094(16*10^94822+53)/394823Robert Price12/2016
40958*6^121849-794818Lelio R Paula10/2014
4096(85*10^94802+473)/994803Robert Price03/2017
40972^314870-10876194786Enzo Doria03/2014
40985*2^314841-394778Lelio R Paula08/2014
40996^121772+11394758Lelio R Paula05/2016
41006^121756-1625394745Enzo Doria02/2013
41012^314718-11279394740Enzo Doria06/2014
41022^314697-184729394734Enzo Doria07/2015
41042^314548-24994689Yves Minet02/2012
41035^135469+4294689Lelio R Paula04/2016
4105gcd(V(1137755),5*F(227551)*(F(227551)-1)+1)94676Serge Batalov04/2015
4106(2*10^94604+547)/994604Robert Price10/2017
41073*2^314152+594570Lelio R Paula08/2014
41082*6^121530-594570Lelio R Paula10/2014
41097*10^94563+8794564Robert Price11/2016
41102^314114-10967794558Enzo Doria04/2014
4111(218389#+240867)/(3*11*811)94557Makoto Morimoto10/2017
41122^314059+7658394542Enzo Doria05/2016
41132^314041-403594536Lelio R Paula03/2016
4114(7*2^314003-11)/1594524Renaud Lifchitz03/2011
411511^90760-471094517Enzo Doria01/2013
4116(7*2^313926-1)/14882194497Lelio R Paula02/2014
411794*10^94493-394495Robert Price11/2016
4118(1000547^15749+1)/100054894492Faysal YAtim12/2008
4119(F(3*75345)^2+L(3*75345)^2)/494477Henri Lifchitz10/2017
41207^111792-3294476Lelio R Paula04/2016
412111^90680-585094434Enzo Doria01/2013
41222^313675-11012594426Enzo Doria04/2014
4123(2999*29^64556-2427)/494410Curtis Bright05/2015
41242^313609-11222594406Enzo Doria06/2014
41252^313584+7290194399Enzo Doria04/2016
41262^313510-11286594376Enzo Doria06/2014
41277*10^94373+8794374Robert Price11/2016
4128(9^98897+8^98897)/1794371Robert Price12/2012
41292^313453-11470394359Enzo Doria04/2015
41308*10^94357-5194358Robert Price10/2017
4131(379*10^94337-1)/994339Robert Price08/2017
41322^313344-313344+194326Robert Price10/2014
413320^72481-4994300Lelio R Paula05/2016
413444725!2+12894289Robert Price03/2015
41354*10^94286+994287Robert Price05/2015
413617^76621+2494279Lelio R Paula07/2016
41372^313156-11285994270Enzo Doria06/2014
41386^121130-5994258Lelio R Paula05/2016
41393^197542+2894252Robert Price11/2013
4140(3^197521+2)/5165594237Lelio R Paula04/2013
41412^313045-595594236Lelio R Paula03/2016
4142(67*10^94212+23)/994213Ray Chandler02/2011
41432^312909-186520394195Enzo Doria03/2016
41442^312848-14994177Lelio R Paula11/2012
41454^156403-7759794164Mike Oakes04/2011
414618^75004-8594151Lelio R Paula06/2016
414719^73622-4894145Lelio R Paula06/2016
4148(11^90397-3^90397)/894138Robert Price04/2011
4149(3^197287+5)/1694129Lelio R Paula04/2013
415012^87212-3794118Lelio R Paula06/2016
415111^90376+7694117Lelio R Paula05/2016
4152(6^120946-11)/594114Paul Bourdelais11/2011
4153(10^94096+191)/394096Robert Price11/2017
41542^312562-11268594091Enzo Doria06/2014
4155137^44026-294072Lelio R Paula10/2017
41562^312404-86968810594043Lelio R Paula09/2016
41572^312387+279353394038Enzo Doria03/2016
415910^94016+9194017Robert Price04/2011
4158(15*2^312325-1)/720194017Lelio R Paula02/2014
416110^94016-18896394016Patrick De Geest08/2013
4160(17*2^312315-1)/4594016Lelio R Paula02/2014
41626^120802+766194003Mike Oakes04/2011
4163(67607*2^312254+1)/17794001Lelio R Paula06/2014
4164(11*2^312207+1)/1993984Lelio R Paula09/2013
41652^312201+5193982Lelio R Paula11/2012
4166(4*6^120749+1)/593961Serge Batalov10/2014
41673^196892+5893942Lelio R Paula05/2016
41682^312060+1891593940Lelio R Paula03/2016
416942^57867-4193933Norbert Schneider08/2018
41702^311992-1620993919Enzo Doria04/2013
4171(85^48677+1)/8693917Paul Bourdelais08/2017
41722^311965-3993911Lelio R Paula11/2012
41732^311920-11168993898Enzo Doria05/2014
4174130^44414+12993889Norbert Schneider01/2019
41757*10^93887-4793888Robert Price02/2017
417612^86965-1393851Lelio R Paula06/2016
41772^311705+1609593833Lelio R Paula03/2016
41782^311665-8193821Lelio R Paula11/2012
4179730^32761+32761^73093806Norbert Schneider09/2017
418011^90073+9293802Lelio R Paula05/2016
41816*10^93792+4193793Robert Price01/2017
4182(2^311580+7)/59132993790Lelio R Paula06/2013
418312^86900-7793781Lelio R Paula06/2016
41842^311508-10976993774Enzo Doria04/2014
41852^311486-185962193767Enzo Doria03/2016
4186Phi(93811,10)/968129521/2109997013/3280113810431/63963778254583193765Kurt Beschorner04/2015
4187(10^93811-1)/(9*968129521*2109997013*3280113810431*639637782545831)93765Gord Palameta10/2018
41882^311471+31146993763Renaud Lifchitz01/2003
4189(88*10^93760-1)/393762Robert Price10/2017
41902^311426+7945993749Enzo Doria06/2016
41912^311294+577593709Lelio R Paula03/2016
41922^311252-101793697Lelio R Paula03/2016
41932^311247-11204193695Enzo Doria06/2014
41947*10^93692-8393693Robert Price09/2017
41952^311205-10964593683Enzo Doria04/2014
41965^134027-8493681Lelio R Paula04/2016
4197(2^311148-1017)/55793663Lelio R Paula06/2013
4198(2^311027-2^155514+1)/59362811/2006
41993^196192-2893608Robert Price12/2013
4200216091#+26143393606Makoto Morimoto12/2015
42015^133917+6893604Lelio R Paula04/2016
42022^310924-170993598Yves Minet03/2013
4203(266*10^93577-11)/393579Robert Price09/2016
4204(16*10^93577+161)/393578Robert Price05/2016
42053^196113-5693570Lelio R Paula04/2016
42062^310806-11034593562Enzo Doria05/2014
42073^196093+8693561Lelio R Paula04/2016
42082^310780-232793555Yves Minet10/2013
420930^63332+4193550Lelio R Paula08/2012
4210(21181*2^310707+1)/2193536Lelio R Paula06/2014
42118*5^133807+793528Lelio R Paula10/2014
42122^310686+819393526Lelio R Paula03/2016
42132^310646+6393514Lelio R Paula11/2012
4214(77*10^93508+31)/993509Robert Price10/2015
4215(1000907^15583+1)/100090893499Faysal YAtim04/2009
4216(2*10^93497+7)/993497Erik Branger03/2011
42173^195958-11285293496Enzo Doria07/2014
42182^310583+1638593495Lelio R Paula03/2016
4219(9913*2^310557-1)/3593490Lelio R Paula04/2015
42209*7^110614+293481Lelio R Paula11/2014
42212^310469-829593461Lelio R Paula03/2016
42222^310459-115993458Yves Minet11/2012
42236^120075-9593437Lelio R Paula05/2016
42242^310289+9832793407Yves Minet11/2010
42252^310217-11314393385Enzo Doria07/2014
42267^110494-6893379Lelio R Paula04/2016
42272^310184-11309393375Enzo Doria07/2014
42282^310180-11041793374Enzo Doria05/2014
4229gcd(V(1124905),5*F(224981)*(F(224981)-1)+1)93372Serge Batalov04/2015
42303^195669+6893358Lelio R Paula04/2016
423110^93356+9193357Robert Price04/2011
423210^93356-2831393356Patrick De Geest08/2013
4233(85*10^93346+23)/993347Robert Price11/2015
4234(3^195648-5)/315827693342Lelio R Paula04/2013
42353^195556+868093304Lelio R Paula04/2016
42362^309942-10999193302Enzo Doria04/2014
42372^309926-186730193298Enzo Doria03/2016
42382^309924+8595193297Yves Minet03/2011
42392^309896-422993288Yves Minet08/2018
4240(86*10^93263-77)/993264Robert Price05/2016
42416^119836-12593251Lelio R Paula05/2016
4242(77*10^93249-257)/993250Robert Price10/2017
42433^195430-293244Theodore Burton02/2007
4244(13*10^93236+47)/393237Robert Price01/2017
4245(67*10^93226-7)/393228Robert Price10/2017
4246(86*10^93217-221)/993218Robert Price06/2017
42472^309637-1632993211Enzo Doria04/2013
4248(41*10^93207+49)/993208Robert Price04/2016
424914^81312-5793194Lelio R Paula06/2016
425041^57783-4093192Theodore Burton02/2007


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 14 2019 10:37 (Time in France)

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