PRP Records

Probable Primes Top 10000

(252932 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 ?
425111^91133+6294906Lelio R Paula05/2016
425230^64244+4194897Lelio R Paula08/2012
4253(151*10^94885-7)/994887Robert Price07/2017
42544^157583+2214794875Mike Oakes01/2011
42552^315098+12394854Lelio R Paula11/2012
42563^198791-3494848Robert Price11/2013
42573*2^315067+794846Lelio R Paula08/2014
4258(9*2^315057+1)/7394841Lelio R Paula09/2013
4259(16*10^94822+53)/394823Robert Price12/2016
42608*6^121849-794818Lelio R Paula10/2014
4261(85*10^94802+473)/994803Robert Price03/2017
42622^314870-10876194786Enzo Doria03/2014
42635*2^314841-394778Lelio R Paula08/2014
42646^121772+11394758Lelio R Paula05/2016
42656^121756-1625394745Enzo Doria02/2013
42662^314718-11279394740Enzo Doria06/2014
42672^314697-184729394734Enzo Doria07/2015
42682^314548-24994689Yves Minet02/2012
42695^135469+4294689Lelio R Paula04/2016
4270gcd(V(1137755),5*F(227551)*(F(227551)-1)+1)94676Serge Batalov04/2015
4271(2*10^94604+547)/994604Robert Price10/2017
42723*2^314152+594570Lelio R Paula08/2014
42732*6^121530-594570Lelio R Paula10/2014
42747*10^94563+8794564Robert Price11/2016
42752^314114-10967794558Enzo Doria04/2014
4276(218389#+240867)/(3*11*811)94557Makoto Morimoto10/2017
42772^314059+7658394542Enzo Doria05/2016
42782^314041-403594536Lelio R Paula03/2016
4279(7*2^314003-11)/1594524Renaud Lifchitz03/2011
428011^90760-471094517Enzo Doria01/2013
4281(7*2^313926-1)/14882194497Lelio R Paula02/2014
428294*10^94493-394495Robert Price11/2016
4283(1000547^15749+1)/100054894492Faysal YAtim12/2008
4284(F(3*75345)^2+L(3*75345)^2)/494477Henri Lifchitz10/2017
42857^111792-3294476Lelio R Paula04/2016
428611^90680-585094434Enzo Doria01/2013
42872^313675-11012594426Enzo Doria04/2014
4288(2999*29^64556-2427)/494410Curtis Bright05/2015
42892^313609-11222594406Enzo Doria06/2014
42902^313584+7290194399Enzo Doria04/2016
42912^313510-11286594376Enzo Doria06/2014
42927*10^94373+8794374Robert Price11/2016
4293(9^98897+8^98897)/1794371Robert Price12/2012
42942^313453-11470394359Enzo Doria04/2015
42958*10^94357-5194358Robert Price10/2017
4296(379*10^94337-1)/994339Robert Price08/2017
42972^313344-313344+194326Robert Price10/2014
429820^72481-4994300Lelio R Paula05/2016
429944725!2+12894289Robert Price03/2015
43004*10^94286+994287Robert Price05/2015
430117^76621+2494279Lelio R Paula07/2016
43022^313156-11285994270Enzo Doria06/2014
43036^121130-5994258Lelio R Paula05/2016
43043^197542+2894252Robert Price11/2013
4305(3^197521+2)/5165594237Lelio R Paula04/2013
43062^313045-595594236Lelio R Paula03/2016
4307(67*10^94212+23)/994213Ray Chandler02/2011
43082^312909-186520394195Enzo Doria03/2016
43092^312848-14994177Lelio R Paula11/2012
43104^156403-7759794164Mike Oakes04/2011
431118^75004-8594151Lelio R Paula06/2016
431219^73622-4894145Lelio R Paula06/2016
4313(11^90397-3^90397)/894138Robert Price04/2011
4314(3^197287+5)/1694129Lelio R Paula04/2013
431512^87212-3794118Lelio R Paula06/2016
431611^90376+7694117Lelio R Paula05/2016
4317(6^120946-11)/594114Paul Bourdelais11/2011
4318(10^94096+191)/394096Robert Price11/2017
43192^312562-11268594091Enzo Doria06/2014
4320137^44026-294072Lelio R Paula10/2017
43212^312404-86968810594043Lelio R Paula09/2016
43222^312387+279353394038Enzo Doria03/2016
432410^94016+9194017Robert Price04/2011
4323(15*2^312325-1)/720194017Lelio R Paula02/2014
432610^94016-18896394016Patrick De Geest08/2013
4325(17*2^312315-1)/4594016Lelio R Paula02/2014
43276^120802+766194003Mike Oakes04/2011
4328(67607*2^312254+1)/17794001Lelio R Paula06/2014
4329(11*2^312207+1)/1993984Lelio R Paula09/2013
43302^312201+5193982Lelio R Paula11/2012
4331(4*6^120749+1)/593961Serge Batalov10/2014
43323^196892+5893942Lelio R Paula05/2016
43332^312060+1891593940Lelio R Paula03/2016
433442^57867-4193933Norbert Schneider08/2018
43352^311992-1620993919Enzo Doria04/2013
4336(85^48677+1)/8693917Paul Bourdelais08/2017
43372^311965-3993911Lelio R Paula11/2012
43382^311920-11168993898Enzo Doria05/2014
4339130^44414+12993889Norbert Schneider01/2019
43407*10^93887-4793888Robert Price02/2017
434112^86965-1393851Lelio R Paula06/2016
43422^311705+1609593833Lelio R Paula03/2016
43432^311665-8193821Lelio R Paula11/2012
4344730^32761+32761^73093806Norbert Schneider09/2017
434511^90073+9293802Lelio R Paula05/2016
43466*10^93792+4193793Robert Price01/2017
4347(2^311580+7)/59132993790Lelio R Paula06/2013
434812^86900-7793781Lelio R Paula06/2016
43492^311508-10976993774Enzo Doria04/2014
43502^311486-185962193767Enzo Doria03/2016
4351Phi(93811,10)/968129521/2109997013/3280113810431/63963778254583193765Kurt Beschorner04/2015
4352(10^93811-1)/(9*968129521*2109997013*3280113810431*639637782545831)93765Gord Palameta10/2018
43532^311471+31146993763Renaud Lifchitz01/2003
4354(88*10^93760-1)/393762Robert Price10/2017
43552^311426+7945993749Enzo Doria06/2016
43562^311294+577593709Lelio R Paula03/2016
43572^311252-101793697Lelio R Paula03/2016
43582^311247-11204193695Enzo Doria06/2014
43597*10^93692-8393693Robert Price09/2017
43602^311205-10964593683Enzo Doria04/2014
43615^134027-8493681Lelio R Paula04/2016
4362(2^311148-1017)/55793663Lelio R Paula06/2013
4363(2^311027-2^155514+1)/59362811/2006
43643^196192-2893608Robert Price12/2013
4365216091#+26143393606Makoto Morimoto12/2015
43665^133917+6893604Lelio R Paula04/2016
43672^310924-170993598Yves Minet03/2013
4368(266*10^93577-11)/393579Robert Price09/2016
4369(16*10^93577+161)/393578Robert Price05/2016
43703^196113-5693570Lelio R Paula04/2016
43712^310806-11034593562Enzo Doria05/2014
43723^196093+8693561Lelio R Paula04/2016
43732^310780-232793555Yves Minet10/2013
437430^63332+4193550Lelio R Paula08/2012
4375(21181*2^310707+1)/2193536Lelio R Paula06/2014
43768*5^133807+793528Lelio R Paula10/2014
43772^310686+819393526Lelio R Paula03/2016
43782^310646+6393514Lelio R Paula11/2012
4379(77*10^93508+31)/993509Robert Price10/2015
4380(1000907^15583+1)/100090893499Faysal YAtim04/2009
4381(2*10^93497+7)/993497Erik Branger03/2011
43823^195958-11285293496Enzo Doria07/2014
43832^310583+1638593495Lelio R Paula03/2016
4384(9913*2^310557-1)/3593490Lelio R Paula04/2015
43859*7^110614+293481Lelio R Paula11/2014
43862^310469-829593461Lelio R Paula03/2016
43872^310459-115993458Yves Minet11/2012
43886^120075-9593437Lelio R Paula05/2016
4389148^43041-14793411Norbert Schneider05/2019
43902^310289+9832793407Yves Minet11/2010
43912^310217-11314393385Enzo Doria07/2014
43927^110494-6893379Lelio R Paula04/2016
43932^310184-11309393375Enzo Doria07/2014
43942^310180-11041793374Enzo Doria05/2014
4395gcd(V(1124905),5*F(224981)*(F(224981)-1)+1)93372Serge Batalov04/2015
43963^195669+6893358Lelio R Paula04/2016
439710^93356+9193357Robert Price04/2011
439810^93356-2831393356Patrick De Geest08/2013
4399(85*10^93346+23)/993347Robert Price11/2015
4400(3^195648-5)/315827693342Lelio R Paula04/2013
44013^195556+868093304Lelio R Paula04/2016
44022^309942-10999193302Enzo Doria04/2014
44032^309926-186730193298Enzo Doria03/2016
44042^309924+8595193297Yves Minet03/2011
44052^309896-422993288Yves Minet08/2018
4406(86*10^93263-77)/993264Robert Price05/2016
44076^119836-12593251Lelio R Paula05/2016
4408(77*10^93249-257)/993250Robert Price10/2017
44093^195430-293244Theodore Burton02/2007
4410(13*10^93236+47)/393237Robert Price01/2017
4411(67*10^93226-7)/393228Robert Price10/2017
4412(86*10^93217-221)/993218Robert Price06/2017
44132^309637-1632993211Enzo Doria04/2013
4414(41*10^93207+49)/993208Robert Price04/2016
441514^81312-5793194Lelio R Paula06/2016
441641^57783-4093192Theodore Burton02/2007
44173*10^93179-9793180Robert Price08/2017
44185*7^110252-493175Lelio R Paula11/2014
44192^309380-2793133Lelio R Paula11/2012
442023*10^93116-793118Robert Price03/2016
4421(29*10^93082+1)/393083Robert Price11/2015
4422(58*10^93062-13)/993063Robert Price09/2015
44232^309131+186938393058Enzo Doria05/2016
44242^309066-9393039Lelio R Paula11/2012
44252^309063-11326993038Enzo Doria07/2014
44263^194965+1693022Robert Price10/2013
44272^308979+186914393012Enzo Doria05/2016
44285^133064+5493008Lelio R Paula04/2016
4429(2^308905-509203)/11992988Lelio R Paula06/2013
4430(94*10^92981-49)/9992981Ray Chandler07/2011
4431(2*10^92976-17)/392976Robert Price08/2014
44322^308809+3796792961Phil Moore03/2008
4433(3^194825+5)/1165692952Lelio R Paula04/2013
4434(2^308679+5)/157392919Lelio R Paula06/2013
44352^308650+51392913Lelio R Paula02/2016
44365*7^109936+692908Lelio R Paula10/2014
44372*10^92897+8992898Robert Price07/2016
443812^86073-2992889Lelio R Paula06/2016
44392^308566-11792888Lelio R Paula11/2012
4440(17*10^92869-11)/392870Robert Price07/2015
44412^308459+7543192856Enzo Doria04/2016
44422^308426-186637792846Enzo Doria03/2016
4443(96^46831-1)/9592830Paul Bourdelais09/2017
44442^308349-11211192823Enzo Doria06/2014
44459*10^92821+1992822Robert Price05/2016
44462^308337-7592819Lelio R Paula11/2012
44474*3^194508+792805Lelio R Paula08/2014
444822*25^66379-11392796Curtis Bright05/2015
444911^89101-108092790Enzo Doria12/2012
44502^308236-186785992789Enzo Doria04/2016
445112^85963+2592770Lelio R Paula06/2016
44527^109750-6692750Lelio R Paula04/2016
44539*10^92742+1192743Robert Kinser01/2017
4454(21*2^308046-1)/885792729Lelio R Paula02/2014
44552^307997-11065592717Enzo Doria05/2014
4456L(443609)92709Renaud Lifchitz11/2003
445710^92691+992692Robert Price03/2011
445810^92691-25229192691Patrick De Geest08/2013
44592^307879-252192681Yves Minet07/2014
4460(2^307780-7)/1995966992644Lelio R Paula06/2013
446114^80831+4792643Lelio R Paula06/2016
446215^78744+9292611Lelio R Paula07/2016
446365^51083-6492610Norbert Schneider11/2014
4464131^43737-13092604Norbert Schneider02/2019
44656^118996-1694392597Enzo Doria02/2013
4466(16*10^92591+41)/392592Robert Price10/2017
4467(3^194014-7)/292568Lelio R Paula04/2013
4468(63^51439+1)/6492555Paul Bourdelais08/2017
4469(26*10^92546-77)/392547Robert Price02/2017
44703^193954+34092540Lelio R Paula04/2016
44712^307407-307407^292539Henri Lifchitz05/2005
4472(17*10^92513-11)/392514Robert Price07/2015
44732^307318-421192512Yves Minet06/2011
44742^307280+19392501Lelio R Paula11/2012
447520^71075-3392471Lelio R Paula05/2016
44762^307126-7879592455Lelio R Paula02/2016
44772^307125-4978992454Henri Lifchitz08/2005
44782^307099+2392447Lelio R Paula11/2012
4479129^43798+12892440Norbert Schneider01/2019
4480Phi(277314,10)/332776992430Makoto Kamada05/2019
44817*10^92414-6992415Robert Price01/2017
4482(9787*2^306975-1)/212915592407Lelio R Paula04/2015
44832^306915+187337392391Enzo Doria06/2016
44842^306908+1291592389Lelio R Paula02/2016
448519^72244-8092383Lelio R Paula06/2016
44872^306849+7592371Lelio R Paula11/2012
4486(397*10^92369+53)/992371Robert Price11/2017
44882^306813-86968810592360Lelio R Paula08/2016
44892^306672-10905992318Enzo Doria04/2014
44906^118604-1706392292Enzo Doria02/2013
4491(31*2^306487-1)/229192260Lelio R Paula02/2014
44922^306467-183561192256Enzo Doria04/2015
44932^306433+7642792246Enzo Doria05/2016
44952^306430-11331392245Enzo Doria07/2014
4494(23*10^92244-59)/992245Robert Price03/2017
4496(47*2^306398+1)/138480392231Lelio R Paula04/2015
4497(25*10^92186+59)/392187Robert Price05/2016
44982^306213-28618392180Enzo Doria06/2015
449910^92178+6192179Robert Price04/2011
450010^92178-17550992178Patrick De Geest07/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2019 07:14 (Time in France)

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