PRP Records

Probable Primes Top 10000

(193013 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 (> 30000) Who ? When ?
3501(509203*2^317881-1)/5280595693Lelio R Paula04/2015
35024*10^95672+9195673Robert Price11/2017
3503(11*10^95641-113)/395642Robert Price01/2017
3504(13*10^95588+11)/395589Robert Price05/2015
3505Phi(191188,10)/19118995587Maksym Voznyy11/2015
35063^200325+7095580Lelio R Paula05/2016
3507(25*10^95574-7)/995575Robert Price12/2014
3508(2^317485-3)/2131395569Lelio R Paula06/2013
35092^317464+3195567Lelio R Paula11/2012
35107^113073+8295558Lelio R Paula04/2016
35112^317251+46595503Lelio R Paula03/2016
351219^74684+5895503Lelio R Paula06/2016
3513(2^317250-7)/33995500Lelio R Paula07/2013
35146^122718-7995494Lelio R Paula05/2016
35152^317141-11049195469Enzo Doria05/2014
35162^317094+7630995455Enzo Doria05/2016
35172^317085+9595453Lelio R Paula11/2012
3518(17*10^95451-377)/995452Robert Price11/2017
35192^317057-10955195444Enzo Doria04/2014
35203^200026+2895437Lelio R Paula05/2016
35212^317024+9395434Donovan Johnson06/2008
35222^316999+160595427Lelio R Paula03/2016
35232^316995-11042795426Enzo Doria05/2014
35242^316937+17795408Lelio R Paula11/2012
35254*10^95407+9195408Robert Price11/2017
35262^316908+191595399Lelio R Paula03/2016
35272^316894+9995395Lelio R Paula11/2012
35286^122547+1195361Lelio R Paula05/2016
35292^316771+8287595358Lelio R Paula03/2016
3530(23*10^95326+1)/395327Serge Batalov05/2009
35311*10^95326+5795327Robert Price03/2011
353210^95326-39368795326Patrick De Geest09/2013
3533(3^199803+4)/47953995325Lelio R Paula04/2013
35342^316654-10948195323Enzo Doria04/2014
35358*10^95316+5195317Robert Price05/2017
3536(50^56099+43^56099)/9395309Serge Batalov12/2016
3537(23*2^316559+1)/392595292Lelio R Paula09/2013
3538(71*10^95277-539)/995278Robert Price11/2017
353919^74503-5695271Lelio R Paula06/2016
354011^91475-438095262Enzo Doria01/2013
3541(62*10^95251-611)/995252Robert Price05/2017
3542(2^316321-509203)/6937795218Lelio R Paula06/2013
3543(79*10^95214-43)/995215Erik Branger11/2013
3544(9*2^316233-1)/175195194Lelio R Paula02/2014
35455*2^316213+995191Lelio R Paula08/2014
35462^316205-184816395188Enzo Doria07/2015
35472^316185-278791395182Enzo Doria04/2016
3548(9787*2^316142-1)/395172Lelio R Paula04/2015
35492^316140-595168Henri Lifchitz02/2006
3550(15185*2^316117-1)/395165Lelio R Paula04/2015
3551(34*10^95153-7)/9/19/1915795149Makoto Morimoto05/2016
35522^316069+7681795147Enzo Doria05/2016
3553(199*10^95134-7)/395136Robert Price02/2017
35542^316027-9730595134Lelio R Paula03/2016
35552^316006-279805195128Enzo Doria04/2016
35562^315921-279760395102Enzo Doria04/2016
35572*10^95095+6395096Robert Price10/2017
35582^315857+129995083Lelio R Paula03/2016
355914^82955-4395078Lelio R Paula06/2016
3560(2*10^95072-17)/395072Robert Price08/2014
35612^315727+6595044Lelio R Paula11/2012
35622^315725+188575795043Enzo Doria03/2017
35631*10^94983+2194984Robert Price03/2011
356410^94983-71794983Patrick De Geest08/2013
356517^77187-8294975Lelio R Paula07/2016
35663*10^94964+3794965Robert Price10/2017
3567(2^315481-1017)/2062728594962Lelio R Paula06/2013
35682^315423-11032994952Enzo Doria05/2014
356911^91169-723094943Enzo Doria02/2013
35707*10^94938+6194939Robert Price02/2017
35712^315351+102594931Lelio R Paula03/2016
35722^315350-11225394930Enzo Doria06/2014
3575((1001327^(15817)+1)/1001328)94906Faysal YAtim10/2010
35732^315268+794906Lelio R Paula10/2012
357411^91133+6294906Lelio R Paula05/2016
357630^64244+4194897Lelio R Paula08/2012
3577(151*10^94885-7)/994887Robert Price07/2017
35784^157583+2214794875Mike Oakes01/2011
35792^315098+12394854Lelio R Paula11/2012
35803^198791-3494848Robert Price11/2013
35813*2^315067+794846Lelio R Paula08/2014
3582(9*2^315057+1)/7394841Lelio R Paula09/2013
3583(16*10^94822+53)/394823Robert Price12/2016
35848*6^121849-794818Lelio R Paula10/2014
3585(85*10^94802+473)/994803Robert Price03/2017
35862^314870-10876194786Enzo Doria03/2014
35875*2^314841-394778Lelio R Paula08/2014
35886^121772+11394758Lelio R Paula05/2016
35896^121756-1625394745Enzo Doria02/2013
35902^314718-11279394740Enzo Doria06/2014
35912^314697-184729394734Enzo Doria07/2015
35922^314548-24994689Yves Minet02/2012
35935^135469+4294689Lelio R Paula04/2016
3594gcd(V(1137755),5*F(227551)*(F(227551)-1)+1)94676Serge Batalov04/2015
3595(2*10^94604+547)/994604Robert Price10/2017
35963*2^314152+594570Lelio R Paula08/2014
35972*6^121530-594570Lelio R Paula10/2014
35987*10^94563+8794564Robert Price11/2016
35992^314114-10967794558Enzo Doria04/2014
3600(218389#+240867)/(3*11*811)94557Makoto Morimoto10/2017
36012^314059+7658394542Enzo Doria05/2016
36022^314041-403594536Lelio R Paula03/2016
3603(7*2^314003-11)/1594524Renaud Lifchitz03/2011
360411^90760-471094517Enzo Doria01/2013
3605(7*2^313926-1)/14882194497Lelio R Paula02/2014
360694*10^94493-394495Robert Price11/2016
3607(1000547^15749+1)/100054894492Faysal YAtim12/2008
3608(F(3*75345)^2+L(3*75345)^2)/494477Henri Lifchitz10/2017
36097^111792-3294476Lelio R Paula04/2016
361011^90680-585094434Enzo Doria01/2013
36112^313675-11012594426Enzo Doria04/2014
3612(2999*29^64556-2427)/494410Curtis Bright05/2015
36132^313609-11222594406Enzo Doria06/2014
36142^313584+7290194399Enzo Doria04/2016
36152^313510-11286594376Enzo Doria06/2014
36167*10^94373+8794374Robert Price11/2016
3617(9^98897+8^98897)/1794371Robert Price12/2012
36182^313453-11470394359Enzo Doria04/2015
36198*10^94357-5194358Robert Price10/2017
3620(379*10^94337-1)/994339Robert Price08/2017
36212^313344-313344+194326Robert Price10/2014
362220^72481-4994300Lelio R Paula05/2016
362344725!2+12894289Robert Price03/2015
36244*10^94286+994287Robert Price05/2015
362517^76621+2494279Lelio R Paula07/2016
36262^313156-11285994270Enzo Doria06/2014
36276^121130-5994258Lelio R Paula05/2016
36283^197542+2894252Robert Price11/2013
3629(3^197521+2)/5165594237Lelio R Paula04/2013
36302^313045-595594236Lelio R Paula03/2016
3631(67*10^94212+23)/994213Ray Chandler02/2011
36322^312909-186520394195Enzo Doria03/2016
36332^312848-14994177Lelio R Paula11/2012
36344^156403-7759794164Mike Oakes04/2011
363518^75004-8594151Lelio R Paula06/2016
363619^73622-4894145Lelio R Paula06/2016
3637(11^90397-3^90397)/894138Robert Price04/2011
3638(3^197287+5)/1694129Lelio R Paula04/2013
363912^87212-3794118Lelio R Paula06/2016
364011^90376+7694117Lelio R Paula05/2016
3641(6^120946-11)/594114Paul Bourdelais11/2011
3642(10^94096+191)/394096Robert Price11/2017
36432^312562-11268594091Enzo Doria06/2014
3644137^44026-294072Lelio R Paula10/2017
36452^312404-86968810594043Lelio R Paula09/2016
36462^312387+279353394038Enzo Doria03/2016
364810^94016+9194017Robert Price04/2011
3647(15*2^312325-1)/720194017Lelio R Paula02/2014
364910^94016-18896394016Patrick De Geest08/2013
3650(17*2^312315-1)/4594016Lelio R Paula02/2014
36516^120802+766194003Mike Oakes04/2011
3652(67607*2^312254+1)/17794001Lelio R Paula06/2014
3653(11*2^312207+1)/1993984Lelio R Paula09/2013
36542^312201+5193982Lelio R Paula11/2012
3655(4*6^120749+1)/593961Serge Batalov10/2014
36563^196892+5893942Lelio R Paula05/2016
36572^312060+1891593940Lelio R Paula03/2016
36582^311992-1620993919Enzo Doria04/2013
3659(85^48677+1)/8693917Paul Bourdelais08/2017
36602^311965-3993911Lelio R Paula11/2012
36612^311920-11168993898Enzo Doria05/2014
36627*10^93887-4793888Robert Price02/2017
366312^86965-1393851Lelio R Paula06/2016
36642^311705+1609593833Lelio R Paula03/2016
36652^311665-8193821Lelio R Paula11/2012
3666730^32761+32761^73093806Norbert Schneider09/2017
366711^90073+9293802Lelio R Paula05/2016
36686*10^93792+4193793Robert Price01/2017
3669(2^311580+7)/59132993790Lelio R Paula06/2013
367012^86900-7793781Lelio R Paula06/2016
36712^311508-10976993774Enzo Doria04/2014
36722^311486-185962193767Enzo Doria03/2016
3673Phi(93811,10)/968129521/2109997013/3280113810431/63963778254583193765Kurt Beschorner04/2015
36742^311471+31146993763Renaud Lifchitz01/2003
3675(88*10^93760-1)/393762Robert Price10/2017
36762^311426+7945993749Enzo Doria06/2016
36772^311294+577593709Lelio R Paula03/2016
36782^311252-101793697Lelio R Paula03/2016
36792^311247-11204193695Enzo Doria06/2014
36807*10^93692-8393693Robert Price09/2017
36812^311205-10964593683Enzo Doria04/2014
36825^134027-8493681Lelio R Paula04/2016
3683(2^311148-1017)/55793663Lelio R Paula06/2013
3684(2^311027-2^155514+1)/59362811/2006
36853^196192-2893608Robert Price12/2013
3686216091#+26143393606Makoto Morimoto12/2015
36875^133917+6893604Lelio R Paula04/2016
36882^310924-170993598Yves Minet03/2013
3689(266*10^93577-11)/393579Robert Price09/2016
3690(16*10^93577+161)/393578Robert Price05/2016
36913^196113-5693570Lelio R Paula04/2016
36922^310806-11034593562Enzo Doria05/2014
36933^196093+8693561Lelio R Paula04/2016
36942^310780-232793555Yves Minet10/2013
369530^63332+4193550Lelio R Paula08/2012
3696(21181*2^310707+1)/2193536Lelio R Paula06/2014
36978*5^133807+793528Lelio R Paula10/2014
36982^310686+819393526Lelio R Paula03/2016
36992^310646+6393514Lelio R Paula11/2012
3700(77*10^93508+31)/993509Robert Price10/2015
3701(1000907^15583+1)/100090893499Faysal YAtim04/2009
3702(2*10^93497+7)/993497Erik Branger03/2011
37033^195958-11285293496Enzo Doria07/2014
37042^310583+1638593495Lelio R Paula03/2016
3705(9913*2^310557-1)/3593490Lelio R Paula04/2015
37069*7^110614+293481Lelio R Paula11/2014
37072^310469-829593461Lelio R Paula03/2016
37082^310459-115993458Yves Minet11/2012
37096^120075-9593437Lelio R Paula05/2016
37102^310289+9832793407Yves Minet11/2010
37112^310217-11314393385Enzo Doria07/2014
37127^110494-6893379Lelio R Paula04/2016
37132^310184-11309393375Enzo Doria07/2014
37142^310180-11041793374Enzo Doria05/2014
3715gcd(V(1124905),5*F(224981)*(F(224981)-1)+1)93372Serge Batalov04/2015
37163^195669+6893358Lelio R Paula04/2016
371710^93356+9193357Robert Price04/2011
371810^93356-2831393356Patrick De Geest08/2013
3719(85*10^93346+23)/993347Robert Price11/2015
3720(3^195648-5)/315827693342Lelio R Paula04/2013
37213^195556+868093304Lelio R Paula04/2016
37222^309942-10999193302Enzo Doria04/2014
37232^309926-186730193298Enzo Doria03/2016
37242^309924+8595193297Yves Minet03/2011
3725(86*10^93263-77)/993264Robert Price05/2016
37266^119836-12593251Lelio R Paula05/2016
3727(77*10^93249-257)/993250Robert Price10/2017
37283^195430-293244Theodore Burton02/2007
3729(13*10^93236+47)/393237Robert Price01/2017
3730(67*10^93226-7)/393228Robert Price10/2017
3731(86*10^93217-221)/993218Robert Price06/2017
37322^309637-1632993211Enzo Doria04/2013
3733(41*10^93207+49)/993208Robert Price04/2016
373414^81312-5793194Lelio R Paula06/2016
373541^57783-4093192Theodore Burton02/2007
37363*10^93179-9793180Robert Price08/2017
37375*7^110252-493175Lelio R Paula11/2014
37382^309380-2793133Lelio R Paula11/2012
373923*10^93116-793118Robert Price03/2016
3740(29*10^93082+1)/393083Robert Price11/2015
3741(58*10^93062-13)/993063Robert Price09/2015
37422^309131+186938393058Enzo Doria05/2016
37432^309066-9393039Lelio R Paula11/2012
37442^309063-11326993038Enzo Doria07/2014
37453^194965+1693022Robert Price10/2013
37462^308979+186914393012Enzo Doria05/2016
37475^133064+5493008Lelio R Paula04/2016
3748(2^308905-509203)/11992988Lelio R Paula06/2013
3749(94*10^92981-49)/9992981Ray Chandler07/2011
3750(2*10^92976-17)/392976Robert Price08/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 09 2017 09:21 (Time in France)

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