PRP Records

Probable Primes Top 10000

(172142 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 ?
3251(2^316321-509203)/6937795218Lelio R Paula06/2013
3252(79*10^95214-43)/995215Erik Branger11/2013
3253(9*2^316233-1)/175195194Lelio R Paula02/2014
32545*2^316213+995191Lelio R Paula08/2014
32552^316205-184816395188Enzo Doria07/2015
32562^316185-278791395182Enzo Doria04/2016
3257(9787*2^316142-1)/395172Lelio R Paula04/2015
32582^316140-595168Henri Lifchitz02/2006
3259(15185*2^316117-1)/395165Lelio R Paula04/2015
3260(34*10^95153-7)/9/19/1915795149Makoto Morimoto05/2016
32612^316069+7681795147Enzo Doria05/2016
3262(199*10^95134-7)/395136Robert Price02/2017
32632^316027-9730595134Lelio R Paula03/2016
32642^316006-279805195128Enzo Doria04/2016
32652^315921-279760395102Enzo Doria04/2016
32662^315857+129995083Lelio R Paula03/2016
326714^82955-4395078Lelio R Paula06/2016
3268(2*10^95072-17)/395072Robert Price08/2014
32692^315727+6595044Lelio R Paula11/2012
32701*10^94983+2194984Robert Price03/2011
327110^94983-71794983Patrick De Geest08/2013
327217^77187-8294975Lelio R Paula07/2016
3273(2^315481-1017)/2062728594962Lelio R Paula06/2013
32742^315423-11032994952Enzo Doria05/2014
327511^91169-723094943Enzo Doria02/2013
32767*10^94938+6194939Robert Price02/2017
32772^315351+102594931Lelio R Paula03/2016
32782^315350-11225394930Enzo Doria06/2014
3281((1001327^(15817)+1)/1001328)94906Faysal YAtim10/2010
32802^315268+794906Lelio R Paula10/2012
327911^91133+6294906Lelio R Paula05/2016
328230^64244+4194897Lelio R Paula08/2012
32834^157583+2214794875Mike Oakes01/2011
32842^315098+12394854Lelio R Paula11/2012
32853^198791-3494848Robert Price11/2013
32863*2^315067+794846Lelio R Paula08/2014
3287(9*2^315057+1)/7394841Lelio R Paula09/2013
3288(16*10^94822+53)/394823Robert Price12/2016
32898*6^121849-794818Lelio R Paula10/2014
3290(85*10^94802+473)/994803Robert Price03/2017
32912^314870-10876194786Enzo Doria03/2014
32925*2^314841-394778Lelio R Paula08/2014
32936^121772+11394758Lelio R Paula05/2016
32946^121756-1625394745Enzo Doria02/2013
32952^314718-11279394740Enzo Doria06/2014
32962^314697-184729394734Enzo Doria07/2015
32972^314548-24994689Yves Minet02/2012
32985^135469+4294689Lelio R Paula04/2016
3299gcd(V(1137755),5*F(227551)*(F(227551)-1)+1)94676Serge Batalov04/2015
33003*2^314152+594570Lelio R Paula08/2014
33012*6^121530-594570Lelio R Paula10/2014
33027*10^94563+8794564Robert Price11/2016
33032^314114-10967794558Enzo Doria04/2014
33042^314059+7658394542Enzo Doria05/2016
33052^314041-403594536Lelio R Paula03/2016
3306(7*2^314003-11)/1594524Renaud Lifchitz03/2011
330711^90760-471094517Enzo Doria01/2013
3308(7*2^313926-1)/14882194497Lelio R Paula02/2014
330994*10^94493-394495Robert Price11/2016
3310(1000547^15749+1)/100054894492Faysal YAtim12/2008
33117^111792-3294476Lelio R Paula04/2016
331211^90680-585094434Enzo Doria01/2013
33132^313675-11012594426Enzo Doria04/2014
3314(2999*29^64556-2427)/494410Curtis Bright05/2015
33152^313609-11222594406Enzo Doria06/2014
33162^313584+7290194399Enzo Doria04/2016
33172^313510-11286594376Enzo Doria06/2014
33187*10^94373+8794374Robert Price11/2016
3319(9^98897+8^98897)/1794371Robert Price12/2012
33202^313453-11470394359Enzo Doria04/2015
33212^313344-313344+194326Robert Price10/2014
332220^72481-4994300Lelio R Paula05/2016
332344725!2+12894289Robert Price03/2015
33244*10^94286+994287Robert Price05/2015
332517^76621+2494279Lelio R Paula07/2016
33262^313156-11285994270Enzo Doria06/2014
33276^121130-5994258Lelio R Paula05/2016
33283^197542+2894252Robert Price11/2013
3329(3^197521+2)/5165594237Lelio R Paula04/2013
33302^313045-595594236Lelio R Paula03/2016
3331(67*10^94212+23)/994213Ray Chandler02/2011
33322^312909-186520394195Enzo Doria03/2016
33332^312848-14994177Lelio R Paula11/2012
33344^156403-7759794164Mike Oakes04/2011
333518^75004-8594151Lelio R Paula06/2016
333619^73622-4894145Lelio R Paula06/2016
3337(11^90397-3^90397)/894138Robert Price04/2011
3338(3^197287+5)/1694129Lelio R Paula04/2013
333912^87212-3794118Lelio R Paula06/2016
334011^90376+7694117Lelio R Paula05/2016
3341(6^120946-11)/594114Paul Bourdelais11/2011
33422^312562-11268594091Enzo Doria06/2014
33432^312404-86968810594043Lelio R Paula09/2016
33442^312387+279353394038Enzo Doria03/2016
334610^94016+9194017Robert Price04/2011
3345(15*2^312325-1)/720194017Lelio R Paula02/2014
334810^94016-18896394016Patrick De Geest08/2013
3347(17*2^312315-1)/4594016Lelio R Paula02/2014
33496^120802+766194003Mike Oakes04/2011
3350(67607*2^312254+1)/17794001Lelio R Paula06/2014
3351(11*2^312207+1)/1993984Lelio R Paula09/2013
33522^312201+5193982Lelio R Paula11/2012
3353(4*6^120749+1)/593961Serge Batalov10/2014
33543^196892+5893942Lelio R Paula05/2016
33552^312060+1891593940Lelio R Paula03/2016
33562^311992-1620993919Enzo Doria04/2013
33572^311965-3993911Lelio R Paula11/2012
33582^311920-11168993898Enzo Doria05/2014
33597*10^93887-4793888Robert Price02/2017
336012^86965-1393851Lelio R Paula06/2016
33612^311705+1609593833Lelio R Paula03/2016
33622^311665-8193821Lelio R Paula11/2012
336311^90073+9293802Lelio R Paula05/2016
33646*10^93792+4193793Robert Price01/2017
3365(2^311580+7)/59132993790Lelio R Paula06/2013
336612^86900-7793781Lelio R Paula06/2016
33672^311508-10976993774Enzo Doria04/2014
33682^311486-185962193767Enzo Doria03/2016
3369Phi(93811,10)/968129521/2109997013/3280113810431/63963778254583193765Kurt Beschorner04/2015
33702^311471+31146993763Renaud Lifchitz01/2003
33712^311426+7945993749Enzo Doria06/2016
33722^311294+577593709Lelio R Paula03/2016
33732^311252-101793697Lelio R Paula03/2016
33742^311247-11204193695Enzo Doria06/2014
33752^311205-10964593683Enzo Doria04/2014
33765^134027-8493681Lelio R Paula04/2016
3377(2^311148-1017)/55793663Lelio R Paula06/2013
3378(2^311027-2^155514+1)/59362811/2006
33793^196192-2893608Robert Price12/2013
3380216091#+26143393606Makoto Morimoto12/2015
33815^133917+6893604Lelio R Paula04/2016
33822^310924-170993598Yves Minet03/2013
3383(266*10^93577-11)/393579Robert Price09/2016
3384(16*10^93577+161)/393578Robert Price05/2016
33853^196113-5693570Lelio R Paula04/2016
33862^310806-11034593562Enzo Doria05/2014
33873^196093+8693561Lelio R Paula04/2016
33882^310780-232793555Yves Minet10/2013
338930^63332+4193550Lelio R Paula08/2012
3390(21181*2^310707+1)/2193536Lelio R Paula06/2014
33918*5^133807+793528Lelio R Paula10/2014
33922^310686+819393526Lelio R Paula03/2016
33932^310646+6393514Lelio R Paula11/2012
3394(77*10^93508+31)/993509Robert Price10/2015
3395(1000907^15583+1)/100090893499Faysal YAtim04/2009
3396(2*10^93497+7)/993497Erik Branger03/2011
33973^195958-11285293496Enzo Doria07/2014
33982^310583+1638593495Lelio R Paula03/2016
3399(9913*2^310557-1)/3593490Lelio R Paula04/2015
34009*7^110614+293481Lelio R Paula11/2014
34012^310469-829593461Lelio R Paula03/2016
34022^310459-115993458Yves Minet11/2012
34036^120075-9593437Lelio R Paula05/2016
34042^310289+9832793407Yves Minet11/2010
34052^310217-11314393385Enzo Doria07/2014
34067^110494-6893379Lelio R Paula04/2016
34072^310184-11309393375Enzo Doria07/2014
34082^310180-11041793374Enzo Doria05/2014
3409gcd(V(1124905),5*F(224981)*(F(224981)-1)+1)93372Serge Batalov04/2015
34103^195669+6893358Lelio R Paula04/2016
341110^93356+9193357Robert Price04/2011
341210^93356-2831393356Patrick De Geest08/2013
3413(85*10^93346+23)/993347Robert Price11/2015
3414(3^195648-5)/315827693342Lelio R Paula04/2013
34153^195556+868093304Lelio R Paula04/2016
34162^309942-10999193302Enzo Doria04/2014
34172^309926-186730193298Enzo Doria03/2016
34182^309924+8595193297Yves Minet03/2011
3419(86*10^93263-77)/993264Robert Price05/2016
34206^119836-12593251Lelio R Paula05/2016
34213^195430-293244Theodore Burton02/2007
3422(13*10^93236+47)/393237Robert Price01/2017
34232^309637-1632993211Enzo Doria04/2013
3424(41*10^93207+49)/993208Robert Price04/2016
342514^81312-5793194Lelio R Paula06/2016
342641^57783-4093192Theodore Burton02/2007
34275*7^110252-493175Lelio R Paula11/2014
34282^309380-2793133Lelio R Paula11/2012
342923*10^93116-793118Robert Price03/2016
3430(29*10^93082+1)/393083Robert Price11/2015
3431(58*10^93062-13)/993063Robert Price09/2015
34322^309131+186938393058Enzo Doria05/2016
34332^309066-9393039Lelio R Paula11/2012
34342^309063-11326993038Enzo Doria07/2014
34353^194965+1693022Robert Price10/2013
34362^308979+186914393012Enzo Doria05/2016
34375^133064+5493008Lelio R Paula04/2016
3438(2^308905-509203)/11992988Lelio R Paula06/2013
3439(94*10^92981-49)/9992981Ray Chandler07/2011
3440(2*10^92976-17)/392976Robert Price08/2014
34412^308809+3796792961Phil Moore03/2008
3442(3^194825+5)/1165692952Lelio R Paula04/2013
3443(2^308679+5)/157392919Lelio R Paula06/2013
34442^308650+51392913Lelio R Paula02/2016
34455*7^109936+692908Lelio R Paula10/2014
34462*10^92897+8992898Robert Price07/2016
344712^86073-2992889Lelio R Paula06/2016
34482^308566-11792888Lelio R Paula11/2012
3449(17*10^92869-11)/392870Robert Price07/2015
34502^308459+7543192856Enzo Doria04/2016
34512^308426-186637792846Enzo Doria03/2016
34522^308349-11211192823Enzo Doria06/2014
34539*10^92821+1992822Robert Price05/2016
34542^308337-7592819Lelio R Paula11/2012
34554*3^194508+792805Lelio R Paula08/2014
345622*25^66379-11392796Curtis Bright05/2015
345711^89101-108092790Enzo Doria12/2012
34582^308236-186785992789Enzo Doria04/2016
345912^85963+2592770Lelio R Paula06/2016
34607^109750-6692750Lelio R Paula04/2016
34619*10^92742+1192743Robert Kinser01/2017
3462(21*2^308046-1)/885792729Lelio R Paula02/2014
34632^307997-11065592717Enzo Doria05/2014
3464L(443609)92709Renaud Lifchitz11/2003
346510^92691+992692Robert Price03/2011
346610^92691-25229192691Patrick De Geest08/2013
34672^307879-252192681Yves Minet07/2014
3468(2^307780-7)/1995966992644Lelio R Paula06/2013
346914^80831+4792643Lelio R Paula06/2016
347015^78744+9292611Lelio R Paula07/2016
347165^51083-6492610Norbert Schneider11/2014
34726^118996-1694392597Enzo Doria02/2013
3473(3^194014-7)/292568Lelio R Paula04/2013
3474(26*10^92546-77)/392547Robert Price02/2017
34753^193954+34092540Lelio R Paula04/2016
34762^307407-307407^292539Henri Lifchitz05/2005
3477(17*10^92513-11)/392514Robert Price07/2015
34782^307318-421192512Yves Minet06/2011
34792^307280+19392501Lelio R Paula11/2012
348020^71075-3392471Lelio R Paula05/2016
34812^307126-7879592455Lelio R Paula02/2016
34822^307125-4978992454Henri Lifchitz08/2005
34832^307099+2392447Lelio R Paula11/2012
34847*10^92414-6992415Robert Price01/2017
3485(9787*2^306975-1)/212915592407Lelio R Paula04/2015
34862^306915+187337392391Enzo Doria06/2016
34872^306908+1291592389Lelio R Paula02/2016
348819^72244-8092383Lelio R Paula06/2016
34892^306849+7592371Lelio R Paula11/2012
34902^306813-86968810592360Lelio R Paula08/2016
34912^306672-10905992318Enzo Doria04/2014
34926^118604-1706392292Enzo Doria02/2013
3493(31*2^306487-1)/229192260Lelio R Paula02/2014
34942^306467-183561192256Enzo Doria04/2015
34952^306433+7642792246Enzo Doria05/2016
34972^306430-11331392245Enzo Doria07/2014
3496(23*10^92244-59)/992245Robert Price03/2017
3498(47*2^306398+1)/138480392231Lelio R Paula04/2015
3499(25*10^92186+59)/392187Robert Price05/2016
35002^306213-28618392180Enzo Doria06/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 18 2017 12:02 (Time in France)

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