Henri & Renaud Lifchitz's PRP Top records

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 ?
3001	(25*2^385091+1)/27	115924	Lelio R Paula	04/2014
3002	(11*10^115910-131)/3	115911	Robert Price	09/2018
3003	2^384953-111943	115883	Paul Bourdelais	02/2012
3004	43^70942-2	115882	Lelio R Paula	04/2014
3005	(94*10^115879-7)/3	115881	Robert Price	03/2020
3006	7*10^115863+3	115864	Robert Price	08/2015
3007	2^384834+93	115847	Donovan Johnson	07/2008
3008	2^384809+71297	115840	Enzo Doria	04/2016
3009	(7*2^384759-1)/5	115825	Lelio R Paula	04/2014
3010	(71*10^115810-17)/9	115811	Ray Chandler	08/2011
3011	(97*10^115794-1)/3	115796	Serge Batalov	12/2014
3012	2*10^115784-27	115785	Robert Price	05/2018
3013	10^115773+126739	115774	Patrick De Geest	04/2018
3015	10^115773-1000000001	115773	Robert Price	03/2018
3014	10^115773-396221	115773	Patrick De Geest	04/2018
3016	(2^384582+778)/2	115771	Stefano Morozzi	09/2020
3017	2^384530+1874305	115756	Enzo Doria	06/2016
3018	(3*2^384524-1)/7631	115750	Lelio R Paula	03/2014
3019	(44*10^115697-413)/9	115698	Robert Price	03/2019
3020	(2^384317+1026)/2	115691	Stefano Morozzi	09/2020
3021	2^384312+81091	115690	Yves Minet	02/2010
3022	(2^384265+2150)/2	115675	Stefano Morozzi	09/2020
3023	(2^384246+2182)/2	115670	Stefano Morozzi	09/2020
3024	(4*10^115668-79)/3	115669	Robert Price	02/2018
3025	(2^384193+242)/2	115654	Stefano Morozzi	09/2020
3026	(266947#+1267)/(7^2*181)	115647	Makoto Morimoto	06/2019
3027	(266947#+273808)/(2109157)	115646	Makoto Morimoto	10/2017
3028	18^92125-92125^18	115642	Dylan Delgado	08/2019
3029	3^242337-4042	115625	Enzo Doria	05/2014
3030	(2^383931+674)/2	115575	Stefano Morozzi	09/2020
3031	7*10^115561+79	115562	Robert Price	07/2019
3032	(2^383872+3046)/2	115557	Stefano Morozzi	09/2020
3033	(11*2^383859-13)/15	115553	Renaud Lifchitz	03/2011
3034	2^383780-3149	115530	Yves Minet	10/2014
3035	(41*10^115523-383)/9	115524	Robert Price	11/2018
3036	(2^383618+618)/2	115481	Stefano Morozzi	09/2020
3037	2^383560-455	115464	Yves Minet	03/2012
3038	(2^383544+5)/3	115458	Lelio R Paula	03/2014
3039	89^59221-88^59221	115445	Robert Price	06/2015
3040	2^383347+1869413	115399	Enzo Doria	05/2016
3041	(103*10^115366+17)/3	115368	Robert Price	08/2020
3042	(2^383232+750)/2	115365	Stefano Morozzi	09/2020
3043	(2^383130-7)/131793	115329	Lelio R Paula	03/2014
3044	(12^106859+1)/13	115320	Paul Bourdelais	02/2010
3045	2^383039+1869509	115307	Enzo Doria	05/2016
3046	(13*2^382968+1)/7	115286	Lelio R Paula	04/2014
3047	(2^382945+2046)/2	115278	Stefano Morozzi	09/2020
3048	(2^382789+3182)/2	115231	Stefano Morozzi	09/2020
3049	6*10^115211+79	115212	Robert Price	09/2020
3050	(2^382722+3598)/2	115211	Stefano Morozzi	09/2020
3051	(2^382699+2090)/2	115204	Stefano Morozzi	09/2020
3052	2^382633+73697	115185	Enzo Doria	04/2016
3053	2^382509-113593	115147	Enzo Doria	08/2014
3054	2^382502-2791721	115145	Enzo Doria	03/2016
3055	9^120590-120590	115073	Robert Price	03/2014
3056	2^382198+9	115054	Lelio R Paula	03/2013
3057	(89*10^115030-179)/9	115031	Robert Price	12/2019
3058	2^381883-59197	114959	Enzo Doria	10/2015
3059	(2^381820+1626)/2	114939	Stefano Morozzi	09/2020
3061	2^381806-4481	114936	Yves Minet	07/2011
3060	2^381808-1851507	114936	Enzo Doria	08/2015
3062	(2^381792+2502)/2	114931	Stefano Morozzi	09/2020
3063	2^381774-112373	114926	Enzo Doria	06/2014
3064	2^381555-109051	114860	Enzo Doria	04/2014
3065	2^381546-113501	114857	Enzo Doria	08/2014
3066	(2^381436+1182)/2	114824	Stefano Morozzi	09/2020
3067	3^240644+16	114817	Robert Price	04/2020
3068	2^381360-110429	114801	Enzo Doria	05/2014
3069	(17*10^114795+79)/3	114796	Robert Price	04/2019
3070	(66^63079+1)/67	114774	Paul Bourdelais	09/2017
3071	2^381252-115079	114769	Enzo Doria	06/2015
3072	(2^381251+3186)/2	114768	Stefano Morozzi	09/2020
3073	2^381209-29323	114756	Enzo Doria	07/2015
3074	569^41651-568^41651	114754	Jean-Louis Charton	11/2009
3075	2^381201+1873205	114753	Enzo Doria	06/2016
3076	(85*10^114737+293)/9	114738	Robert Price	12/2019
3077	(265*10^114736+17)/3	114738	Robert Price	03/2020
3078	(2^381062+2170)/2	114711	Stefano Morozzi	09/2020
3079	2^380974-112991	114685	Enzo Doria	07/2014
3080	88^58949-87	114626	Norbert Schneider	11/2015
3081	(2^380773+662)/2	114624	Stefano Morozzi	09/2020
3082	2^380700+91	114603	Lelio R Paula	03/2013
3083	(2^380632+2578)/2	114582	Stefano Morozzi	09/2020
3085	10^114575+3^114576	114576	Mike Oakes	09/2010
3084	10^114575+66561	114576	Patrick De Geest	02/2017
3086	10^114575-581081	114575	Patrick De Geest	02/2017
3087	2^380587-115315	114569	Enzo Doria	06/2015
3088	2^380513-216925	114546	Enzo Doria	05/2014
3089	2^380451-1840087	114528	Enzo Doria	06/2015
3090	(2^380426+1510)/2	114520	Stefano Morozzi	09/2020
3091	(15*2^380388-1)/539	114507	Lelio R Paula	04/2014
3092	2^380279-461347	114476	Enzo Doria	07/2015
3093	2^380021+1871147	114398	Enzo Doria	05/2016
3094	2^380005+1869707	114393	Enzo Doria	05/2016
3095	2^379958-113297	114379	Enzo Doria	07/2014
3096	2^379881-109105	114356	Enzo Doria	04/2014
3097	(21*2^379857-1)/13	114349	Lelio R Paula	03/2014
3098	(4*10^114340+83)/3	114341	Robert Price	02/2018
3099	(26*10^114317-77)/3	114318	Robert Price	11/2019
3100	(4*10^114296+149)/9	114296	Robert Price	04/2018
3101	88^58773-87	114284	Norbert Schneider	11/2015
3102	2^379529-2790283	114250	Enzo Doria	03/2016
3103	2^379522+1869115	114248	Enzo Doria	05/2016
3104	(145*10^114226-1)/9	114228	Serge Batalov	12/2014
3105	2^379317-115033	114186	Enzo Doria	06/2015
3106	(17*2^379246-1)/17407	114162	Lelio R Paula	03/2014
3107	(2^379192+226)/2	114148	Stefano Morozzi	09/2020
3108	6*10^114091+23	114092	Robert Price	09/2020
3109	(4*10^114076+143)/3	114077	Robert Price	03/2018
3110	(2^378754+2058)/2	114017	Stefano Morozzi	09/2020
3111	(46*10^113969+683)/9	113970	Robert Price	03/2019
3112	2*10^113941+9	113942	Dmitry Domanov	11/2010
3113	(2^378478+1642)/2	113933	Stefano Morozzi	09/2020
3114	4*10^113905+91	113906	Robert Price	08/2018
3115	10^113894-10000001	113894	Robert Price	09/2020
3116	4*10^113874-21	113875	Robert Price	09/2018
3117	2^378272-16565	113872	Enzo Doria	04/2013
3118	2^378217-109075	113855	Enzo Doria	04/2014
3119	2^378198+67	113849	Lelio R Paula	03/2013
3120	2^378173-3249	113842	Yves Minet	12/2014
3121	(2^378155-5)/6597	113833	Lelio R Paula	03/2014
3122	92941#+(355049#)/(92941#)	113830	Makoto Morimoto	10/2017
3123	2^378128-262977	113828	Enzo Doria	05/2014
3124	2^378123-113215	113827	Enzo Doria	07/2014
3125	6^146274-18893	113824	Enzo Doria	03/2013
3126	2^378078+75	113813	Lelio R Paula	03/2013
3127	2^377940+63	113772	Lelio R Paula	03/2013
3128	2^377941-2785843	113772	Enzo Doria	04/2016
3129	2^377810+1875109	113733	Enzo Doria	09/2016
3130	2^377803-1838635	113731	Enzo Doria	05/2015
3131	2^377799+52223	113729	Yves Minet	08/2010
3132	11^109190-270	113710	Enzo Doria	12/2012
3133	7*10^113693+9	113694	Robert Price	09/2015
3134	(82*10^113681+161)/9	113682	Robert Price	10/2019
3135	4*10^113658+49	113659	Robert Price	01/2019
3136	(2*10^113631+529)/9	113631	Robert Price	01/2018
3137	2^377408-2798279	113612	Enzo Doria	04/2016
3138	5*10^113586+57	113587	Robert Price	12/2018
3139	2^377222+93679	113556	Yves Minet	02/2011
3140	262147#+316847	113552	Makoto Morimoto	02/2016
3141	(2^377131+2018)/2	113528	Stefano Morozzi	09/2020
3142	2^377026-458903	113497	Enzo Doria	04/2015
3143	(2^377014+2202)/2	113493	Stefano Morozzi	09/2020
3144	(2^376967+258)/2	113479	Stefano Morozzi	09/2020
3145	(29*10^113468-17)/3	113469	Robert Price	09/2019
3146	35^73477-34^73477	113454	Robert Price	05/2012
3147	(14*10^113451-89)/3	113452	Robert Price	05/2020
3148	2^376790+27	113426	Lelio R Paula	03/2013
3149	2^376786-112701	113424	Enzo Doria	06/2014
3150	2^376731+21	113408	Lelio R Paula	03/2013
3151	2^376634+1871245	113379	Enzo Doria	05/2016
3152	(4^188318+17)/3	113379	Robert Price	02/2017
3153	2^376576-344369	113361	Enzo Doria	07/2015
3154	2^376549-4543	113353	Yves Minet	03/2019
3155	(17*2^376526-1)/223	113345	Lelio R Paula	03/2014
3156	(27*2^376441-1)/811	113319	Lelio R Paula	03/2014
3157	(2^376350+3538)/2	113293	Stefano Morozzi	09/2020
3158	(2*10^113248+73)/3	113248	Robert Price	09/2020
3159	2^376128-21237	113226	Enzo Doria	06/2013
3160	5*10^113224-81	113225	Robert Price	01/2019
3161	10^113220-1000001	113220	Robert Price	08/2020
3162	(2^376102+1578)/2	113218	Stefano Morozzi	09/2020
3163	(2^375996+3102)/2	113186	Stefano Morozzi	09/2020
3164	(94*10^113176+11)/3	113178	Robert Price	04/2020
3165	(46*10^113162+521)/9	113163	Robert Price	02/2019
3166	(2^375885+3614)/2	113153	Stefano Morozzi	09/2020
3167	(2^375873+2006)/2	113149	Stefano Morozzi	09/2020
3168	(2^375726+694)/2	113105	Stefano Morozzi	09/2020
3169	2^375638-1787171	113079	Enzo Doria	03/2016
3170	(2^375563+2178)/2	113056	Stefano Morozzi	09/2020
3171	2^375537+4847	113048	Yves Minet	02/2011
3172	(17^91837+16^91837)/33	113000	Robert Price	08/2013
3173	5F(270343)(F(270343)+1)+1	112997	Serge Batalov	04/2015
3174	2^375350-3221	112992	Yves Minet	07/2011
3175	(13*2^375306+1)/7	112979	Lelio R Paula	03/2014
3176	2^375305+76757	112979	Enzo Doria	05/2016
3177	2^375258+1874989	112964	Enzo Doria	07/2016
3178	(29^77237-1)/28	112950	Robert Price	04/2012
3179	2^375154+74959	112933	Enzo Doria	04/2016
3180	(266*10^112930-17)/3	112932	Robert Price	07/2020
3181	(2^375134+778)/2	112927	Stefano Morozzi	09/2020
3182	(85*10^112919+293)/9	112920	Robert Price	12/2019
3183	(2^375022+1210)/2	112893	Stefano Morozzi	09/2020
3184	2^374993-2787163	112885	Enzo Doria	11/2015
3185	123^53970+2	112793	Lelio R Paula	06/2013
3186	2^374640-4685	112778	Yves Minet	05/2019
3187	(2^374556+682)/2	112753	Stefano Morozzi	09/2020
3188	p(22852)#/2+512	112745	Robert Price	05/2017
3189	(11*10^112742-131)/3	112743	Robert Price	09/2018
3190	2^374441-21049	112718	Enzo Doria	06/2013
3191	4*10^112706-93	112707	Robert Price	07/2020
3192	(2^374321+1)/3	112682	H.&R. Lifchitz	12/2000
3193	(2^374213+1766)/2	112650	Stefano Morozzi	09/2020
3194	(2^374094+2674)/2	112614	Stefano Morozzi	09/2020
3195	(13^101089-1)/12	112607	Paul Bourdelais	03/2010
3196	3^236011-8828	112606	Enzo Doria	05/2014
3197	(2^373748+1090)/2	112510	Stefano Morozzi	09/2020
3198	39^70666+2	112435	Lelio R Paula	11/2013
3199	(134*10^112400+7)/3	112402	Robert Price	02/2020
3200	(2^373365+326)/2	112394	Stefano Morozzi	09/2020
3201	(2^373350-7)/3	112390	Lelio R Paula	03/2014
3202	2^373306-1840931	112377	Enzo Doria	06/2015
3203	(2^373262+270)/2	112363	Stefano Morozzi	09/2020
3204	(142*10^112352-7)/9	112354	Robert Price	12/2019
3205	2^373117+1872107	112320	Enzo Doria	05/2016
3206	2^373040+2792761	112297	Enzo Doria	03/2016
3207	EPrime(112280)	112280	Eric W. Weisstein	10/2010
3208	2^372950+7	112270	Lelio R Paula	03/2013
3209	2^372945+1872167	112268	Enzo Doria	05/2016
3210	(2^372754+3094)/2	112210	Stefano Morozzi	09/2020
3211	6*10^112208+43	112209	Robert Price	07/2020
3212	(2^372728+3058)/2	112203	Stefano Morozzi	09/2020
3213	2^372695+72113	112193	Enzo Doria	04/2016
3214	2^372689-2563	112191	Yves Minet	07/2014
3215	2^372638-1859441	112176	Enzo Doria	03/2016
3216	3^235074-113056	112159	Enzo Doria	07/2014
3217	131^52949-130	112108	Norbert Schneider	02/2019
3218	(91*10^112098-1)/9	112100	Robert Price	04/2015
3219	2^372310-85061	112077	Paul Bourdelais	02/2012
3220	(10^112067+53)/9	112067	Serge Batalov	07/2015
3221	(2^372237+2082)/2	112055	Stefano Morozzi	09/2020
3222	75^59760+2	112054	Lelio R Paula	08/2013
3223	(2^372200+1710)/2	112044	Stefano Morozzi	09/2020
3224	(2^372161+2574)/2	112032	Stefano Morozzi	09/2020
3225	8*10^112018-49	112019	Robert Price	08/2019
3227	2^372108+74221	112016	Enzo Doria	04/2016
3226	(2^372109+2046)/2	112016	Stefano Morozzi	09/2020
3228	(184*10^112007-1)/3	112009	Robert Price	02/2020
3229	5*10^112003+81	112004	Robert Price	03/2019
3230	215^48018+48018^215	112000	Norbert Schneider	10/2018
3231	2^371970-459491	111975	Enzo Doria	05/2015
3232	41^69427-40^69427	111971	Robert Price	07/2012
3233	(10^111902+71)/9	111902	Serge Batalov	07/2015
3234	(2^371625+1610)/2	111870	Stefano Morozzi	09/2020
3235	2^371440-112865	111815	Enzo Doria	06/2014
3236	2^371426-459161	111811	Enzo Doria	05/2015
3237	(94*10^111770+11)/3	111772	Robert Price	04/2020
3238	2^371276-461267	111766	Enzo Doria	07/2015
3239	6*10^111760+43	111761	Robert Price	07/2020
3240	98079!4-1024	111747	Robert Price	11/2019
3241	(2^371186+3162)/2	111738	Stefano Morozzi	09/2020
3242	2^371098-113261	111712	Enzo Doria	07/2014
3243	(7*10^111706-61)/9	111706	Erik Branger	01/2011
3244	2^371044+1869391	111696	Enzo Doria	05/2016
3245	88^57416+87	111645	Norbert Schneider	11/2015
3246	2^370829-109693	111631	Enzo Doria	04/2014
3247	15^94906-2	111619	Lelio R Paula	11/2013
3248	(2^370726+1198)/2	111600	Stefano Morozzi	09/2020
3249	2^370695-4627	111591	Yves Minet	05/2019
3250	7*10^111579-87	111580	Robert Price	06/2020

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Probable Primes Top 10000

(271067 PRPs in the top)