PRP Records

Probable Primes Top 10000

(288949 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 ?
7251(6^120946-11)/594114Paul Bourdelais11/2011
7252(2^312622+534)/294109Stefano Morozzi09/2020
7253(10^94096+191)/394096Robert Price11/2017
725423794^9005+9005^2379494093Hans Havermann09/2020
72552^312562-11268594091Enzo Doria06/2014
7256137^44026-294072Lelio R Paula10/2017
7257s(164441)94052Robert Price05/2020
72582^312404-86968810594043Lelio R Paula09/2016
72592^312387+279353394038Enzo Doria03/2016
726110^94016+9194017Robert Price04/2011
7260(15*2^312325-1)/720194017Lelio R Paula02/2014
726210^94016-18896394016Patrick De Geest08/2013
7263(17*2^312315-1)/4594016Lelio R Paula02/2014
7264(401*10^94010+13)/994012Robert Price09/2021
726523866^8691+8691^2386694010Hans Havermann08/2020
72666^120802+766194003Mike Oakes04/2011
7267(67607*2^312254+1)/17794001Lelio R Paula06/2014
7268(2^312245+702)/293995Stefano Morozzi09/2020
7269(56*10^93993+493)/993994Robert Price10/2021
7270(11*2^312207+1)/1993984Lelio R Paula09/2013
72712^312201+5193982Lelio R Paula11/2012
7272(4*6^120749+1)/593961Serge Batalov10/2014
7273(781*10^93942-7)/993944Robert Price12/2021
72743^196892+5893942Lelio R Paula05/2016
72752^312060+1891593940Lelio R Paula03/2016
727642^57867-4193933Norbert Schneider08/2018
72778*10^93921+8393922Robert Price11/2021
72782^311992-1620993919Enzo Doria04/2013
7279(85^48677+1)/8693917Paul Bourdelais08/2017
72802^311965-3993911Lelio R Paula11/2012
72812^311920-11168993898Enzo Doria05/2014
7282130^44414+12993889Norbert Schneider01/2019
7283(2^311892+2730)/293889Stefano Morozzi09/2020
72847*10^93887-4793888Robert Price02/2017
72859*10^93878-3793879Robert Price06/2021
7286(28*10^93874+323)/993875Robert Price10/2021
7287(2^311778+1530)/293855Stefano Morozzi09/2020
728812^86965-1393851Lelio R Paula06/2016
728924862^5953+5953^2486293848Hans Havermann09/2020
729022299^16148+16148^2229993837Hans Havermann08/2020
72912^311705+1609593833Lelio R Paula03/2016
7292(2^311701+3002)/293832Stefano Morozzi09/2020
72942^311665-8193821Lelio R Paula11/2012
7293(2^311665+2654)/293821Stefano Morozzi09/2020
7295(2^311648+3058)/293816Stefano Morozzi09/2020
7296(2^311639+2738)/293813Stefano Morozzi01/2021
7297730^32761+32761^73093806Norbert Schneider09/2017
729811^90073+9293802Lelio R Paula05/2016
72996*10^93792+4193793Robert Price01/2017
730010^93790+6461193791Patrick De Geest04/2020
7303(2^311580+7)/59132993790Lelio R Paula06/2013
730110^93790-12345678993790Robert Price02/2020
730210^93790-15751793790Patrick De Geest04/2020
7304(49*10^93782+293)/993783Robert Price03/2021
730512^86900-7793781Lelio R Paula06/2016
73062^311508-10976993774Enzo Doria04/2014
73072^311486-185962193767Enzo Doria03/2016
7308Phi(93811,10)/968129521/2109997013/3280113810431/63963778254583193765Kurt Beschorner04/2015
7309(10^93811-1)/(9*968129521*2109997013*3280113810431*639637782545831)93765Gord Palameta10/2018
73102^311471+31146993763Renaud Lifchitz01/2003
7311(88*10^93760-1)/393762Robert Price10/2017
73122^311426+7945993749Enzo Doria06/2016
731321537^21634+21634^2153793745Norbert Schneider04/2020
73142^311409+11154643593744Paul Bourdelais10/2021
7315(2^311360+3078)/293729Stefano Morozzi09/2020
7316(2^311341+2186)/293723Stefano Morozzi09/2020
7317(2^311313+774)/293715Stefano Morozzi09/2020
73192^311294+577593709Lelio R Paula03/2016
731825155^5312+5312^2515593709Hans Havermann09/2020
73202^311252-101793697Lelio R Paula03/2016
73212^311247-11204193695Enzo Doria06/2014
73227*10^93692-8393693Robert Price09/2017
73232^311205-10964593683Enzo Doria04/2014
73245^134027-8493681Lelio R Paula04/2016
7325(2^311148-1017)/55793663Lelio R Paula06/2013
7326(2^311027-2^155514+1)/59362811/2006
732726748^3161+3161^2674893614Hans Havermann08/2020
73283^196192-2893608Robert Price12/2013
7329216091#+26143393606Makoto Morimoto12/2015
73305^133917+6893604Lelio R Paula04/2016
73312^310924-170993598Yves Minet03/2013
733224555^6476+6476^2455593587Hans Havermann08/2020
7333(2^310867+734)/293580Stefano Morozzi09/2020
7334(266*10^93577-11)/393579Robert Price09/2016
7335(16*10^93577+161)/393578Robert Price05/2016
73363^196113-5693570Lelio R Paula04/2016
73372^310806-11034593562Enzo Doria05/2014
73383^196093+8693561Lelio R Paula04/2016
73392^310780-232793555Yves Minet10/2013
734030^63332+4193550Lelio R Paula08/2012
7341(21181*2^310707+1)/2193536Lelio R Paula06/2014
73428*5^133807+793528Lelio R Paula10/2014
73432^310686+819393526Lelio R Paula03/2016
734422681^13282+13282^2268193520Hans Havermann09/2020
73452^310646+6393514Lelio R Paula11/2012
7346(77*10^93508+31)/993509Robert Price10/2015
7347(1000907^15583+1)/100090893499Faysal YAtim04/2009
7348(2*10^93497+7)/993497Erik Branger03/2011
73493^195958-11285293496Enzo Doria07/2014
73502^310583+1638593495Lelio R Paula03/2016
7351(9913*2^310557-1)/3593490Lelio R Paula04/2015
73529*7^110614+293481Lelio R Paula11/2014
7353(19*10^93467+83)/393468Robert Price08/2020
73542^310469-829593461Lelio R Paula03/2016
73552^310459-115993458Yves Minet11/2012
73566^120075-9593437Lelio R Paula05/2016
7357(2^310362+1758)/293428Stefano Morozzi09/2020
7358148^43041-14793411Norbert Schneider05/2019
73592^310289+9832793407Yves Minet11/2010
736021769^19510+19510^2176993395Hans Havermann08/2020
73612^310217-11314393385Enzo Doria07/2014
73627^110494-6893379Lelio R Paula04/2016
73632^310184-11309393375Enzo Doria07/2014
73642^310180-11041793374Enzo Doria05/2014
7365gcd(V(1124905),5*F(224981)*(F(224981)-1)+1)93372Serge Batalov04/2015
7366(2^310173+3150)/293372Stefano Morozzi09/2020
73673^195669+6893358Lelio R Paula04/2016
736810^93356+9193357Robert Price04/2011
736910^93356-2831393356Patrick De Geest08/2013
7370(85*10^93346+23)/993347Robert Price11/2015
7371(3^195648-5)/315827693342Lelio R Paula04/2013
737210^93333-400000193333Robert Price07/2021
73733^195556+868093304Lelio R Paula04/2016
73742^309942-10999193302Enzo Doria04/2014
73752^309926-186730193298Enzo Doria03/2016
73762^309924+8595193297Yves Minet03/2011
73772^309896-422993288Yves Minet08/2018
7378(86*10^93263-77)/993264Robert Price05/2016
73796^119836-12593251Lelio R Paula05/2016
7380(77*10^93249-257)/993250Robert Price10/2017
738121822^18749+18749^2182293245Hans Havermann09/2020
73823^195430-293244Theodore Burton02/2007
7383(13*10^93236+47)/393237Robert Price01/2017
7384(67*10^93226-7)/393228Robert Price10/2017
7385(86*10^93217-221)/993218Robert Price06/2017
73862^309637-1632993211Enzo Doria04/2013
7387(41*10^93207+49)/993208Robert Price04/2016
738814^81312-5793194Lelio R Paula06/2016
738941^57783-4093192Theodore Burton02/2007
73903*10^93179-9793180Robert Price08/2017
73915*7^110252-493175Lelio R Paula11/2014
739222022^16959+16959^2202293140Hans Havermann08/2020
739383061!4-51293137Robert Price11/2019
739425169^5016+5016^2516993135Hans Havermann08/2020
7395(483641^16384+1)/293135Richard Fischer02/2021
73962^309380-2793133Lelio R Paula11/2012
739725653^4268+4268^2565393127Hans Havermann08/2020
7398(2^309355+1826)/293125Stefano Morozzi02/2021
7399(2^309334+2710)/293119Stefano Morozzi09/2020
740023*10^93116-793118Robert Price03/2016
7401(2^309270+3214)/293100Stefano Morozzi09/2020
7402(29*10^93082+1)/393083Robert Price11/2015
7403(2^309198+3738)/293078Stefano Morozzi09/2020
7404(58*10^93062-13)/993063Robert Price09/2015
7405(2^309138+1794)/293060Stefano Morozzi01/2021
74062^309131+186938393058Enzo Doria05/2016
7407(2^309114+3610)/293053Stefano Morozzi09/2020
74082^309066-9393039Lelio R Paula11/2012
74092^309063-11326993038Enzo Doria07/2014
74103^194965+1693022Robert Price10/2013
7411(89*10^93019-737)/993020Robert Price01/2022
74122^308979+186914393012Enzo Doria05/2016
74135^133064+5493008Lelio R Paula04/2016
7414(2^308947+2750)/293003Stefano Morozzi01/2021
7415(2^308905-509203)/11992988Lelio R Paula06/2013
7416(94*10^92981-49)/9992981Ray Chandler07/2011
7417(2*10^92976-17)/392976Robert Price08/2014
741824783^5642+5642^2478392972Hans Havermann08/2020
7419(472489^16384+1)/292969Richard Fischer01/2021
74202^308809+3796792961Phil Moore03/2008
7421(3^194825+5)/1165692952Lelio R Paula04/2013
7422(2^308679+5)/157392919Lelio R Paula06/2013
74232^308650+51392913Lelio R Paula02/2016
74245*7^109936+692908Lelio R Paula10/2014
74252*10^92897+8992898Robert Price07/2016
7426(2^308585+3182)/292894Stefano Morozzi09/2020
7427(467307^16384+1)/292891Richard Fischer01/2021
742812^86073-2992889Lelio R Paula06/2016
74292^308566-11792888Lelio R Paula11/2012
7430(17*10^92869-11)/392870Robert Price07/2015
74312^308459+7543192856Enzo Doria04/2016
74322^308426-186637792846Enzo Doria03/2016
743324810^5521+5521^2481092840Hans Havermann09/2020
7434(96^46831-1)/9592830Paul Bourdelais09/2017
74352^308349-11211192823Enzo Doria06/2014
74369*10^92821+1992822Robert Price05/2016
74372^308337-7592819Lelio R Paula11/2012
74384*3^194508+792805Lelio R Paula08/2014
743922*25^66379-11392796Curtis Bright05/2015
744024538^6047+6047^2453892792Hans Havermann09/2020
744111^89101-108092790Enzo Doria12/2012
74422^308236-186785992789Enzo Doria04/2016
744312^85963+2592770Lelio R Paula06/2016
744423692^8221+8221^2369292753Hans Havermann08/2020
74457^109750-6692750Lelio R Paula04/2016
74469*10^92742+1192743Robert Kinser01/2017
7447(2^308054+778)/292734Stefano Morozzi09/2020
7448(21*2^308046-1)/885792729Lelio R Paula02/2014
74492^307997-11065592717Enzo Doria05/2014
7450L(443609)92709Renaud Lifchitz11/2003
745110^92691+992692Robert Price03/2011
745210^92691-25229192691Patrick De Geest08/2013
7453(2^307883+3506)/292682Stefano Morozzi09/2020
74542^307879-252192681Yves Minet07/2014
745521269^21412+21412^2126992666Norbert Schneider04/2020
7456(2^307780-7)/1995966992644Lelio R Paula06/2013
745714^80831+4792643Lelio R Paula06/2016
745815^78744+9292611Lelio R Paula07/2016
745965^51083-6492610Norbert Schneider11/2014
7460(2^307639+506)/292609Stefano Morozzi09/2020
7461131^43737-13092604Norbert Schneider02/2019
74626^118996-1694392597Enzo Doria02/2013
7463(16*10^92591+41)/392592Robert Price10/2017
7464(2^307566+3094)/292587Stefano Morozzi09/2020
7465(2^307528+1578)/292575Stefano Morozzi09/2020
74669*10^92573+8392574Robert Price11/2020
7467(3^194014-7)/292568Lelio R Paula04/2013
7468(2^307498+570)/292566Stefano Morozzi09/2020
7469(63^51439+1)/6492555Paul Bourdelais08/2017
7470(26*10^92546-77)/392547Robert Price02/2017
74713^193954+34092540Lelio R Paula04/2016
74722^307407-307407^292539Henri Lifchitz05/2005
747324299^6430+6430^2429992536Hans Havermann08/2020
7474(17*10^92513-11)/392514Robert Price07/2015
74752^307318-421192512Yves Minet06/2011
74762^307280+19392501Lelio R Paula11/2012
747720^71075-3392471Lelio R Paula05/2016
74782^307126-7879592455Lelio R Paula02/2016
74792^307125-4978992454Henri Lifchitz08/2005
74802^307099+2392447Lelio R Paula11/2012
7481129^43798+12892440Norbert Schneider01/2019
748221826^17181+17181^2182692435Hans Havermann09/2020
7483Phi(277314,10)/332776992430Makoto Kamada05/2019
7484(2^307022+1038)/292423Stefano Morozzi09/2020
74857*10^92414-6992415Robert Price01/2017
7486(9787*2^306975-1)/212915592407Lelio R Paula04/2015
748722280^14037+14037^2228092402Hans Havermann09/2020
74882^306915+187337392391Enzo Doria06/2016
74892^306908+1291592389Lelio R Paula02/2016
749021620^18759+18759^2162092387Hans Havermann09/2020
7491(2^306897+1142)/292385Stefano Morozzi09/2020
749219^72244-8092383Lelio R Paula06/2016
74942^306849+7592371Lelio R Paula11/2012
7493(397*10^92369+53)/992371Robert Price11/2017
74952^306813-86968810592360Lelio R Paula08/2016
7496(2^306797+2694)/292355Stefano Morozzi09/2020
749721713^17914+17914^2171392350Hans Havermann09/2020
74982^306672-10905992318Enzo Doria04/2014
7499(430463^16384+1)/292307Richard Fischer09/2020
75006^118604-1706392292Enzo Doria02/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 19 2022 17:15 (Time in France)

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