PRP Records

Probable Primes Top 10000

(280932 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 ?
62512^312404-86968810594043Lelio R Paula09/2016
62522^312387+279353394038Enzo Doria03/2016
625410^94016+9194017Robert Price04/2011
6253(15*2^312325-1)/720194017Lelio R Paula02/2014
625510^94016-18896394016Patrick De Geest08/2013
6256(17*2^312315-1)/4594016Lelio R Paula02/2014
625723866^8691+8691^2386694010Hans Havermann08/2020
62586^120802+766194003Mike Oakes04/2011
6259(67607*2^312254+1)/17794001Lelio R Paula06/2014
6260(2^312245+702)/293995Stefano Morozzi09/2020
6261(11*2^312207+1)/1993984Lelio R Paula09/2013
62622^312201+5193982Lelio R Paula11/2012
6263(4*6^120749+1)/593961Serge Batalov10/2014
62643^196892+5893942Lelio R Paula05/2016
62652^312060+1891593940Lelio R Paula03/2016
626642^57867-4193933Norbert Schneider08/2018
62672^311992-1620993919Enzo Doria04/2013
6268(85^48677+1)/8693917Paul Bourdelais08/2017
62692^311965-3993911Lelio R Paula11/2012
62702^311920-11168993898Enzo Doria05/2014
6272130^44414+12993889Norbert Schneider01/2019
6271(2^311892+2730)/293889Stefano Morozzi09/2020
62737*10^93887-4793888Robert Price02/2017
6274(2^311778+1530)/293855Stefano Morozzi09/2020
627512^86965-1393851Lelio R Paula06/2016
627624862^5953+5953^2486293848Hans Havermann09/2020
627722299^16148+16148^2229993837Hans Havermann08/2020
62782^311705+1609593833Lelio R Paula03/2016
6279(2^311701+3002)/293832Stefano Morozzi09/2020
62812^311665-8193821Lelio R Paula11/2012
6280(2^311665+2654)/293821Stefano Morozzi09/2020
6282(2^311648+3058)/293816Stefano Morozzi09/2020
6283(2^311639+2738)/293813Stefano Morozzi01/2021
6284730^32761+32761^73093806Norbert Schneider09/2017
628511^90073+9293802Lelio R Paula05/2016
62866*10^93792+4193793Robert Price01/2017
628710^93790+6461193791Patrick De Geest04/2020
6290(2^311580+7)/59132993790Lelio R Paula06/2013
628810^93790-12345678993790Robert Price02/2020
628910^93790-15751793790Patrick De Geest04/2020
6291(49*10^93782+293)/993783Robert Price03/2021
629212^86900-7793781Lelio R Paula06/2016
62932^311508-10976993774Enzo Doria04/2014
62942^311486-185962193767Enzo Doria03/2016
6295Phi(93811,10)/968129521/2109997013/3280113810431/63963778254583193765Kurt Beschorner04/2015
6296(10^93811-1)/(9*968129521*2109997013*3280113810431*639637782545831)93765Gord Palameta10/2018
62972^311471+31146993763Renaud Lifchitz01/2003
6298(88*10^93760-1)/393762Robert Price10/2017
62992^311426+7945993749Enzo Doria06/2016
630021537^21634+21634^2153793745Norbert Schneider04/2020
6301(2^311360+3078)/293729Stefano Morozzi09/2020
6302(2^311341+2186)/293723Stefano Morozzi09/2020
6303(2^311313+774)/293715Stefano Morozzi09/2020
63052^311294+577593709Lelio R Paula03/2016
630425155^5312+5312^2515593709Hans Havermann09/2020
63062^311252-101793697Lelio R Paula03/2016
63072^311247-11204193695Enzo Doria06/2014
63087*10^93692-8393693Robert Price09/2017
63092^311205-10964593683Enzo Doria04/2014
63105^134027-8493681Lelio R Paula04/2016
6311(2^311148-1017)/55793663Lelio R Paula06/2013
6312(2^311027-2^155514+1)/59362811/2006
631326748^3161+3161^2674893614Hans Havermann08/2020
63143^196192-2893608Robert Price12/2013
6315216091#+26143393606Makoto Morimoto12/2015
63165^133917+6893604Lelio R Paula04/2016
63172^310924-170993598Yves Minet03/2013
631824555^6476+6476^2455593587Hans Havermann08/2020
6319(2^310867+734)/293580Stefano Morozzi09/2020
6320(266*10^93577-11)/393579Robert Price09/2016
6321(16*10^93577+161)/393578Robert Price05/2016
63223^196113-5693570Lelio R Paula04/2016
63232^310806-11034593562Enzo Doria05/2014
63243^196093+8693561Lelio R Paula04/2016
63252^310780-232793555Yves Minet10/2013
632630^63332+4193550Lelio R Paula08/2012
6327(21181*2^310707+1)/2193536Lelio R Paula06/2014
63288*5^133807+793528Lelio R Paula10/2014
63292^310686+819393526Lelio R Paula03/2016
633022681^13282+13282^2268193520Hans Havermann09/2020
63312^310646+6393514Lelio R Paula11/2012
6332(77*10^93508+31)/993509Robert Price10/2015
6333(1000907^15583+1)/100090893499Faysal YAtim04/2009
6334(2*10^93497+7)/993497Erik Branger03/2011
63353^195958-11285293496Enzo Doria07/2014
63362^310583+1638593495Lelio R Paula03/2016
6337(9913*2^310557-1)/3593490Lelio R Paula04/2015
63389*7^110614+293481Lelio R Paula11/2014
6339(19*10^93467+83)/393468Robert Price08/2020
63402^310469-829593461Lelio R Paula03/2016
63412^310459-115993458Yves Minet11/2012
63426^120075-9593437Lelio R Paula05/2016
6343(2^310362+1758)/293428Stefano Morozzi09/2020
6344148^43041-14793411Norbert Schneider05/2019
63452^310289+9832793407Yves Minet11/2010
634621769^19510+19510^2176993395Hans Havermann08/2020
63472^310217-11314393385Enzo Doria07/2014
63487^110494-6893379Lelio R Paula04/2016
63492^310184-11309393375Enzo Doria07/2014
63502^310180-11041793374Enzo Doria05/2014
6351gcd(V(1124905),5*F(224981)*(F(224981)-1)+1)93372Serge Batalov04/2015
6352(2^310173+3150)/293372Stefano Morozzi09/2020
63533^195669+6893358Lelio R Paula04/2016
635410^93356+9193357Robert Price04/2011
635510^93356-2831393356Patrick De Geest08/2013
6356(85*10^93346+23)/993347Robert Price11/2015
6357(3^195648-5)/315827693342Lelio R Paula04/2013
63583^195556+868093304Lelio R Paula04/2016
63592^309942-10999193302Enzo Doria04/2014
63602^309926-186730193298Enzo Doria03/2016
63612^309924+8595193297Yves Minet03/2011
63622^309896-422993288Yves Minet08/2018
6363(86*10^93263-77)/993264Robert Price05/2016
63646^119836-12593251Lelio R Paula05/2016
6365(77*10^93249-257)/993250Robert Price10/2017
636621822^18749+18749^2182293245Hans Havermann09/2020
63673^195430-293244Theodore Burton02/2007
6368(13*10^93236+47)/393237Robert Price01/2017
6369(67*10^93226-7)/393228Robert Price10/2017
6370(86*10^93217-221)/993218Robert Price06/2017
63712^309637-1632993211Enzo Doria04/2013
6372(41*10^93207+49)/993208Robert Price04/2016
637314^81312-5793194Lelio R Paula06/2016
637441^57783-4093192Theodore Burton02/2007
63753*10^93179-9793180Robert Price08/2017
63765*7^110252-493175Lelio R Paula11/2014
637722022^16959+16959^2202293140Hans Havermann08/2020
637883061!4-51293137Robert Price11/2019
637925169^5016+5016^2516993135Hans Havermann08/2020
6380(483641^16384+1)/293135Richard Fischer02/2021
63812^309380-2793133Lelio R Paula11/2012
638225653^4268+4268^2565393127Hans Havermann08/2020
6383(2^309355+1826)/293125Stefano Morozzi02/2021
6384(2^309334+2710)/293119Stefano Morozzi09/2020
638523*10^93116-793118Robert Price03/2016
6386(2^309270+3214)/293100Stefano Morozzi09/2020
6387(29*10^93082+1)/393083Robert Price11/2015
6388(2^309198+3738)/293078Stefano Morozzi09/2020
6389(58*10^93062-13)/993063Robert Price09/2015
6390(2^309138+1794)/293060Stefano Morozzi01/2021
63912^309131+186938393058Enzo Doria05/2016
6392(2^309114+3610)/293053Stefano Morozzi09/2020
63932^309066-9393039Lelio R Paula11/2012
63942^309063-11326993038Enzo Doria07/2014
63953^194965+1693022Robert Price10/2013
63962^308979+186914393012Enzo Doria05/2016
63975^133064+5493008Lelio R Paula04/2016
6398(2^308947+2750)/293003Stefano Morozzi01/2021
6399(2^308905-509203)/11992988Lelio R Paula06/2013
6400(94*10^92981-49)/9992981Ray Chandler07/2011
6401(2*10^92976-17)/392976Robert Price08/2014
640224783^5642+5642^2478392972Hans Havermann08/2020
6403(472489^16384+1)/292969Richard Fischer01/2021
64042^308809+3796792961Phil Moore03/2008
6405(3^194825+5)/1165692952Lelio R Paula04/2013
6406(2^308679+5)/157392919Lelio R Paula06/2013
64072^308650+51392913Lelio R Paula02/2016
64085*7^109936+692908Lelio R Paula10/2014
64092*10^92897+8992898Robert Price07/2016
6410(2^308585+3182)/292894Stefano Morozzi09/2020
6411(467307^16384+1)/292891Richard Fischer01/2021
641212^86073-2992889Lelio R Paula06/2016
64132^308566-11792888Lelio R Paula11/2012
6414(17*10^92869-11)/392870Robert Price07/2015
64152^308459+7543192856Enzo Doria04/2016
64162^308426-186637792846Enzo Doria03/2016
641724810^5521+5521^2481092840Hans Havermann09/2020
6418(96^46831-1)/9592830Paul Bourdelais09/2017
64192^308349-11211192823Enzo Doria06/2014
64209*10^92821+1992822Robert Price05/2016
64212^308337-7592819Lelio R Paula11/2012
64224*3^194508+792805Lelio R Paula08/2014
642322*25^66379-11392796Curtis Bright05/2015
642424538^6047+6047^2453892792Hans Havermann09/2020
642511^89101-108092790Enzo Doria12/2012
64262^308236-186785992789Enzo Doria04/2016
642712^85963+2592770Lelio R Paula06/2016
642823692^8221+8221^2369292753Hans Havermann08/2020
64297^109750-6692750Lelio R Paula04/2016
64309*10^92742+1192743Robert Kinser01/2017
6431(2^308054+778)/292734Stefano Morozzi09/2020
6432(21*2^308046-1)/885792729Lelio R Paula02/2014
64332^307997-11065592717Enzo Doria05/2014
6434L(443609)92709Renaud Lifchitz11/2003
643510^92691+992692Robert Price03/2011
643610^92691-25229192691Patrick De Geest08/2013
6437(2^307883+3506)/292682Stefano Morozzi09/2020
64382^307879-252192681Yves Minet07/2014
643921269^21412+21412^2126992666Norbert Schneider04/2020
6440(2^307780-7)/1995966992644Lelio R Paula06/2013
644114^80831+4792643Lelio R Paula06/2016
644215^78744+9292611Lelio R Paula07/2016
644365^51083-6492610Norbert Schneider11/2014
6444(2^307639+506)/292609Stefano Morozzi09/2020
6445131^43737-13092604Norbert Schneider02/2019
64466^118996-1694392597Enzo Doria02/2013
6447(16*10^92591+41)/392592Robert Price10/2017
6448(2^307566+3094)/292587Stefano Morozzi09/2020
6449(2^307528+1578)/292575Stefano Morozzi09/2020
64509*10^92573+8392574Robert Price11/2020
6451(3^194014-7)/292568Lelio R Paula04/2013
6452(2^307498+570)/292566Stefano Morozzi09/2020
6453(63^51439+1)/6492555Paul Bourdelais08/2017
6454(26*10^92546-77)/392547Robert Price02/2017
64553^193954+34092540Lelio R Paula04/2016
64562^307407-307407^292539Henri Lifchitz05/2005
645724299^6430+6430^2429992536Hans Havermann08/2020
6458(17*10^92513-11)/392514Robert Price07/2015
64592^307318-421192512Yves Minet06/2011
64602^307280+19392501Lelio R Paula11/2012
646120^71075-3392471Lelio R Paula05/2016
64622^307126-7879592455Lelio R Paula02/2016
64632^307125-4978992454Henri Lifchitz08/2005
64642^307099+2392447Lelio R Paula11/2012
6465129^43798+12892440Norbert Schneider01/2019
646621826^17181+17181^2182692435Hans Havermann09/2020
6467Phi(277314,10)/332776992430Makoto Kamada05/2019
6468(2^307022+1038)/292423Stefano Morozzi09/2020
64697*10^92414-6992415Robert Price01/2017
6470(9787*2^306975-1)/212915592407Lelio R Paula04/2015
647122280^14037+14037^2228092402Hans Havermann09/2020
64722^306915+187337392391Enzo Doria06/2016
64732^306908+1291592389Lelio R Paula02/2016
647421620^18759+18759^2162092387Hans Havermann09/2020
6475(2^306897+1142)/292385Stefano Morozzi09/2020
647619^72244-8092383Lelio R Paula06/2016
64782^306849+7592371Lelio R Paula11/2012
6477(397*10^92369+53)/992371Robert Price11/2017
64792^306813-86968810592360Lelio R Paula08/2016
6480(2^306797+2694)/292355Stefano Morozzi09/2020
648121713^17914+17914^2171392350Hans Havermann09/2020
64822^306672-10905992318Enzo Doria04/2014
6483(430463^16384+1)/292307Richard Fischer09/2020
64846^118604-1706392292Enzo Doria02/2013
648521969^15878+15878^2196992288Hans Havermann08/2020
648621690^17959+17959^2169092276Hans Havermann08/2020
6487(7613^23773-1)/761292273Serge Batalov08/2020
6488(31*2^306487-1)/229192260Lelio R Paula02/2014
64892^306467-183561192256Enzo Doria04/2015
64902^306433+7642792246Enzo Doria05/2016
64922^306430-11331392245Enzo Doria07/2014
6491(23*10^92244-59)/992245Robert Price03/2017
6493(47*2^306398+1)/138480392231Lelio R Paula04/2015
649421436^20043+20043^2143692217Hans Havermann09/2020
6495(25*10^92186+59)/392187Robert Price05/2016
64962^306213-28618392180Enzo Doria06/2015
649710^92178+6192179Robert Price04/2011
649810^92178-17550992178Patrick De Geest07/2013
64992^306200+118592176Lelio R Paula02/2016
6500(2^306171+1514)/292167Stefano Morozzi09/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 13 2021 12:02 (Time in France)

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