PRP Records

Probable Primes Top 10000

(253476 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 ?
4251(22699*2^318527+1)/2195890Lelio R Paula07/2014
42522^318496-9730595877Lelio R Paula03/2016
42532^318466+1501595868Lelio R Paula03/2016
42546^123187-17312995859Mike Oakes04/2011
42552^318423-48795855Yves Minet03/2012
4256(10223*2^318350+1)/156395834Lelio R Paula07/2014
425745369!2+102495787Robert Price02/2015
42583^200758-8695786Lelio R Paula05/2016
4259(2^318271+1)/(3*46031404238891*654090604244843)95781Gord Palameta12/2018
42603*10^95776-5995777Robert Price10/2017
4261193^41901-295768Lelio R Paula10/2017
42624*10^95752-7195753Robert Price11/2017
4263((10^47850-1)*10000/9+6421)*10^47850+(10^47850-1)/995704Hans Havermann05/2019
4264(509203*2^317881-1)/5280595693Lelio R Paula04/2015
42654*10^95672+9195673Robert Price11/2017
4266(11*10^95641-113)/395642Robert Price01/2017
4267(13*10^95588+11)/395589Robert Price05/2015
4268Phi(191188,10)/19118995587Maksym Voznyy11/2015
42693^200325+7095580Lelio R Paula05/2016
4270(25*10^95574-7)/995575Robert Price12/2014
4271(2^317485-3)/2131395569Lelio R Paula06/2013
42722^317464+3195567Lelio R Paula11/2012
42737^113073+8295558Lelio R Paula04/2016
42742^317251+46595503Lelio R Paula03/2016
427519^74684+5895503Lelio R Paula06/2016
4276(2^317250-7)/33995500Lelio R Paula07/2013
42776^122718-7995494Lelio R Paula05/2016
42782^317141-11049195469Enzo Doria05/2014
42792^317094+7630995455Enzo Doria05/2016
42802^317085+9595453Lelio R Paula11/2012
4281(17*10^95451-377)/995452Robert Price11/2017
42822^317057-10955195444Enzo Doria04/2014
42833^200026+2895437Lelio R Paula05/2016
42842^317024+9395434Donovan Johnson06/2008
42852^316999+160595427Lelio R Paula03/2016
42862^316995-11042795426Enzo Doria05/2014
42882^316937+17795408Lelio R Paula11/2012
42874*10^95407+9195408Robert Price11/2017
42892^316908+191595399Lelio R Paula03/2016
42902^316894+9995395Lelio R Paula11/2012
42916^122547+1195361Lelio R Paula05/2016
42922^316771+8287595358Lelio R Paula03/2016
4294(23*10^95326+1)/395327Serge Batalov05/2009
42931*10^95326+5795327Robert Price03/2011
429510^95326-39368795326Patrick De Geest09/2013
4296(3^199803+4)/47953995325Lelio R Paula04/2013
42972^316654-10948195323Enzo Doria04/2014
42988*10^95316+5195317Robert Price05/2017
4299(50^56099+43^56099)/9395309Serge Batalov12/2016
4300(23*2^316559+1)/392595292Lelio R Paula09/2013
4301(71*10^95277-539)/995278Robert Price11/2017
430219^74503-5695271Lelio R Paula06/2016
430311^91475-438095262Enzo Doria01/2013
4304(62*10^95251-611)/995252Robert Price05/2017
4305(2^316321-509203)/6937795218Lelio R Paula06/2013
4306(79*10^95214-43)/995215Erik Branger11/2013
4307(9*2^316233-1)/175195194Lelio R Paula02/2014
43085*2^316213+995191Lelio R Paula08/2014
43092^316205-184816395188Enzo Doria07/2015
43102^316185-278791395182Enzo Doria04/2016
4311(9787*2^316142-1)/395172Lelio R Paula04/2015
43122^316140-595168Henri Lifchitz02/2006
4313(15185*2^316117-1)/395165Lelio R Paula04/2015
4314(34*10^95153-7)/9/19/1915795149Makoto Morimoto05/2016
43152^316069+7681795147Enzo Doria05/2016
4316(199*10^95134-7)/395136Robert Price02/2017
43172^316027-9730595134Lelio R Paula03/2016
43182^316006-279805195128Enzo Doria04/2016
43192^315921-279760395102Enzo Doria04/2016
43202*10^95095+6395096Robert Price10/2017
43212^315857+129995083Lelio R Paula03/2016
432214^82955-4395078Lelio R Paula06/2016
4323(2*10^95072-17)/395072Robert Price08/2014
43242^315727+6595044Lelio R Paula11/2012
43252^315725+188575795043Enzo Doria03/2017
43261*10^94983+2194984Robert Price03/2011
432710^94983-71794983Patrick De Geest08/2013
432817^77187-8294975Lelio R Paula07/2016
43293*10^94964+3794965Robert Price10/2017
4330(2^315481-1017)/2062728594962Lelio R Paula06/2013
43312^315423-11032994952Enzo Doria05/2014
433211^91169-723094943Enzo Doria02/2013
43337*10^94938+6194939Robert Price02/2017
43342^315351+102594931Lelio R Paula03/2016
43352^315350-11225394930Enzo Doria06/2014
4337((1001327^(15817)+1)/1001328)94906Faysal YAtim10/2010
43362^315268+794906Lelio R Paula10/2012
433811^91133+6294906Lelio R Paula05/2016
433930^64244+4194897Lelio R Paula08/2012
4340(151*10^94885-7)/994887Robert Price07/2017
43414^157583+2214794875Mike Oakes01/2011
43422^315098+12394854Lelio R Paula11/2012
43433^198791-3494848Robert Price11/2013
43443*2^315067+794846Lelio R Paula08/2014
4345(9*2^315057+1)/7394841Lelio R Paula09/2013
4346(16*10^94822+53)/394823Robert Price12/2016
43478*6^121849-794818Lelio R Paula10/2014
4348(85*10^94802+473)/994803Robert Price03/2017
43492^314870-10876194786Enzo Doria03/2014
43505*2^314841-394778Lelio R Paula08/2014
43516^121772+11394758Lelio R Paula05/2016
43526^121756-1625394745Enzo Doria02/2013
43532^314718-11279394740Enzo Doria06/2014
43542^314697-184729394734Enzo Doria07/2015
43552^314548-24994689Yves Minet02/2012
43565^135469+4294689Lelio R Paula04/2016
4357gcd(V(1137755),5*F(227551)*(F(227551)-1)+1)94676Serge Batalov04/2015
4358(2*10^94604+547)/994604Robert Price10/2017
43593*2^314152+594570Lelio R Paula08/2014
43602*6^121530-594570Lelio R Paula10/2014
43617*10^94563+8794564Robert Price11/2016
43622^314114-10967794558Enzo Doria04/2014
4363(218389#+240867)/(3*11*811)94557Makoto Morimoto10/2017
43642^314059+7658394542Enzo Doria05/2016
43652^314041-403594536Lelio R Paula03/2016
4366(7*2^314003-11)/1594524Renaud Lifchitz03/2011
436711^90760-471094517Enzo Doria01/2013
4368(7*2^313926-1)/14882194497Lelio R Paula02/2014
436994*10^94493-394495Robert Price11/2016
4370(1000547^15749+1)/100054894492Faysal YAtim12/2008
4371(F(3*75345)^2+L(3*75345)^2)/494477Henri Lifchitz10/2017
43727^111792-3294476Lelio R Paula04/2016
437311^90680-585094434Enzo Doria01/2013
43742^313675-11012594426Enzo Doria04/2014
4375(2999*29^64556-2427)/494410Curtis Bright05/2015
43762^313609-11222594406Enzo Doria06/2014
43772^313584+7290194399Enzo Doria04/2016
43782^313510-11286594376Enzo Doria06/2014
43797*10^94373+8794374Robert Price11/2016
4380(9^98897+8^98897)/1794371Robert Price12/2012
43812^313453-11470394359Enzo Doria04/2015
43828*10^94357-5194358Robert Price10/2017
4383(379*10^94337-1)/994339Robert Price08/2017
43842^313344-313344+194326Robert Price10/2014
438520^72481-4994300Lelio R Paula05/2016
438644725!2+12894289Robert Price03/2015
43874*10^94286+994287Robert Price05/2015
438817^76621+2494279Lelio R Paula07/2016
43892^313156-11285994270Enzo Doria06/2014
43906^121130-5994258Lelio R Paula05/2016
43913^197542+2894252Robert Price11/2013
4392(3^197521+2)/5165594237Lelio R Paula04/2013
43932^313045-595594236Lelio R Paula03/2016
4394(67*10^94212+23)/994213Ray Chandler02/2011
43952^312909-186520394195Enzo Doria03/2016
43962^312848-14994177Lelio R Paula11/2012
43974^156403-7759794164Mike Oakes04/2011
439818^75004-8594151Lelio R Paula06/2016
439919^73622-4894145Lelio R Paula06/2016
4400(11^90397-3^90397)/894138Robert Price04/2011
4401(3^197287+5)/1694129Lelio R Paula04/2013
440212^87212-3794118Lelio R Paula06/2016
440311^90376+7694117Lelio R Paula05/2016
4404(6^120946-11)/594114Paul Bourdelais11/2011
4405(10^94096+191)/394096Robert Price11/2017
44062^312562-11268594091Enzo Doria06/2014
4407137^44026-294072Lelio R Paula10/2017
44082^312404-86968810594043Lelio R Paula09/2016
44092^312387+279353394038Enzo Doria03/2016
441110^94016+9194017Robert Price04/2011
4410(15*2^312325-1)/720194017Lelio R Paula02/2014
441310^94016-18896394016Patrick De Geest08/2013
4412(17*2^312315-1)/4594016Lelio R Paula02/2014
44146^120802+766194003Mike Oakes04/2011
4415(67607*2^312254+1)/17794001Lelio R Paula06/2014
4416(11*2^312207+1)/1993984Lelio R Paula09/2013
44172^312201+5193982Lelio R Paula11/2012
4418(4*6^120749+1)/593961Serge Batalov10/2014
44193^196892+5893942Lelio R Paula05/2016
44202^312060+1891593940Lelio R Paula03/2016
442142^57867-4193933Norbert Schneider08/2018
44222^311992-1620993919Enzo Doria04/2013
4423(85^48677+1)/8693917Paul Bourdelais08/2017
44242^311965-3993911Lelio R Paula11/2012
44252^311920-11168993898Enzo Doria05/2014
4426130^44414+12993889Norbert Schneider01/2019
44277*10^93887-4793888Robert Price02/2017
442812^86965-1393851Lelio R Paula06/2016
44292^311705+1609593833Lelio R Paula03/2016
44302^311665-8193821Lelio R Paula11/2012
4431730^32761+32761^73093806Norbert Schneider09/2017
443211^90073+9293802Lelio R Paula05/2016
44336*10^93792+4193793Robert Price01/2017
4434(2^311580+7)/59132993790Lelio R Paula06/2013
443512^86900-7793781Lelio R Paula06/2016
44362^311508-10976993774Enzo Doria04/2014
44372^311486-185962193767Enzo Doria03/2016
4438Phi(93811,10)/968129521/2109997013/3280113810431/63963778254583193765Kurt Beschorner04/2015
4439(10^93811-1)/(9*968129521*2109997013*3280113810431*639637782545831)93765Gord Palameta10/2018
44402^311471+31146993763Renaud Lifchitz01/2003
4441(88*10^93760-1)/393762Robert Price10/2017
44422^311426+7945993749Enzo Doria06/2016
44432^311294+577593709Lelio R Paula03/2016
44442^311252-101793697Lelio R Paula03/2016
44452^311247-11204193695Enzo Doria06/2014
44467*10^93692-8393693Robert Price09/2017
44472^311205-10964593683Enzo Doria04/2014
44485^134027-8493681Lelio R Paula04/2016
4449(2^311148-1017)/55793663Lelio R Paula06/2013
4450(2^311027-2^155514+1)/59362811/2006
44513^196192-2893608Robert Price12/2013
4452216091#+26143393606Makoto Morimoto12/2015
44535^133917+6893604Lelio R Paula04/2016
44542^310924-170993598Yves Minet03/2013
4455(266*10^93577-11)/393579Robert Price09/2016
4456(16*10^93577+161)/393578Robert Price05/2016
44573^196113-5693570Lelio R Paula04/2016
44582^310806-11034593562Enzo Doria05/2014
44593^196093+8693561Lelio R Paula04/2016
44602^310780-232793555Yves Minet10/2013
446130^63332+4193550Lelio R Paula08/2012
4462(21181*2^310707+1)/2193536Lelio R Paula06/2014
44638*5^133807+793528Lelio R Paula10/2014
44642^310686+819393526Lelio R Paula03/2016
44652^310646+6393514Lelio R Paula11/2012
4466(77*10^93508+31)/993509Robert Price10/2015
4467(1000907^15583+1)/100090893499Faysal YAtim04/2009
4468(2*10^93497+7)/993497Erik Branger03/2011
44693^195958-11285293496Enzo Doria07/2014
44702^310583+1638593495Lelio R Paula03/2016
4471(9913*2^310557-1)/3593490Lelio R Paula04/2015
44729*7^110614+293481Lelio R Paula11/2014
44732^310469-829593461Lelio R Paula03/2016
44742^310459-115993458Yves Minet11/2012
44756^120075-9593437Lelio R Paula05/2016
4476148^43041-14793411Norbert Schneider05/2019
44772^310289+9832793407Yves Minet11/2010
44782^310217-11314393385Enzo Doria07/2014
44797^110494-6893379Lelio R Paula04/2016
44802^310184-11309393375Enzo Doria07/2014
44812^310180-11041793374Enzo Doria05/2014
4482gcd(V(1124905),5*F(224981)*(F(224981)-1)+1)93372Serge Batalov04/2015
44833^195669+6893358Lelio R Paula04/2016
448410^93356+9193357Robert Price04/2011
448510^93356-2831393356Patrick De Geest08/2013
4486(85*10^93346+23)/993347Robert Price11/2015
4487(3^195648-5)/315827693342Lelio R Paula04/2013
44883^195556+868093304Lelio R Paula04/2016
44892^309942-10999193302Enzo Doria04/2014
44902^309926-186730193298Enzo Doria03/2016
44912^309924+8595193297Yves Minet03/2011
44922^309896-422993288Yves Minet08/2018
4493(86*10^93263-77)/993264Robert Price05/2016
44946^119836-12593251Lelio R Paula05/2016
4495(77*10^93249-257)/993250Robert Price10/2017
44963^195430-293244Theodore Burton02/2007
4497(13*10^93236+47)/393237Robert Price01/2017
4498(67*10^93226-7)/393228Robert Price10/2017
4499(86*10^93217-221)/993218Robert Price06/2017
45002^309637-1632993211Enzo Doria04/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 25 2019 15:53 (Time in France)

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