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	2^545958+1876189	164350	Enzo Doria	07/2016
3002	2^545878-49841	164326	Enzo Doria	10/2015
3003	(10^164284+77)/3	164284	Robert Price	01/2018
3004	2^545668-4019	164263	Yves Minet	04/2017
3005	10^164216+780639	164217	Patrick De Geest	08/2021
3007	10^164216-50000000001	164216	Robert Price	12/2020
3006	10^164216-891051	164216	Patrick De Geest	08/2021
3008	(1353^238539617^9)/10^247183	164151	Hans Havermann	07/2017
3009	(16*10^164122+197)/3	164123	Robert Price	04/2019
3010	2^545185+76757	164118	Enzo Doria	05/2016
3011	2^545076-114329	164085	Enzo Doria	01/2015
3012	(2*10^164043-143)/3	164043	Robert Price	03/2018
3013	(33085^36481-1)/(33085^191-1)	164018	Ryan Propper	11/2023
3014	(29^112153+1)/30	164011	Lelio R Paula	03/2017
3015	2^544757+1874777	163989	Enzo Doria	06/2016
3016	2^544723+211193	163978	Enzo Doria	08/2023
3017	2^544444-457199	163894	Enzo Doria	01/2015
3018	(32804^36481-1)/(32804^191-1)	163883	Ryan Propper	11/2023
3019	2^544264-343529	163840	Enzo Doria	07/2015
3020	7*10^163780+9	163781	Robert Price	09/2015
3021	2^543989+2793047	163758	Enzo Doria	02/2016
3022	(28*10^163709+113)/3	163710	Robert Price	03/2020
3023	(2013^49729-1)/(2013^223-1)	163561	Ryan Propper	11/2023
3024	(23*10^163523+301)/9	163524	Robert Price	06/2021
3025	(68*10^163521-329)/9	163522	Robert Price	03/2021
3026	35820^35899+35899^35820	163489	Norbert Schneider	11/2021
3027	2^542870-69551	163421	Enzo Doria	12/2015
3028	2^542502+24799	163310	Enzo Doria	10/2023
3029	2^542395+72533	163278	Enzo Doria	04/2016
3030	2^542258+216949	163236	Enzo Doria	12/2023
3031	2^542072-3683	163180	Yves Minet	03/2017
3032	fibonacci(780566)-4	163129	Jon Grantham	08/2023
3033	(682*10^163106-7)/9	163108	Robert Price	08/2021
3034	2^541779-1867357	163092	Enzo Doria	04/2016
3035	(29*10^163056+313)/9	163057	Robert Price	04/2021
3036	2^541476+214743	163001	Enzo Doria	11/2023
3037	13^142159+14^142159-2	162933	Harsh Aggarwal	05/2024
3038	8*10^162924+9	162925	Robert Price	12/2015
3039	2^540905+81557	162829	Enzo Doria	08/2016
3040	2^540628-2939	162746	Yves Minet	09/2014
3041	919^54919-918^54919	162743	Jean-Louis Charton	01/2013
3042	(203*10^162689+1)/3	162691	Robert Price	03/2020
3043	3*10^162620-59	162621	Robert Price	09/2018
3044	2^540180+26791	162611	Enzo Doria	12/2023
3045	3^340694-112960	162553	Enzo Doria	07/2014
3046	2^539807-114081	162499	Enzo Doria	12/2014
3047	414^62093+62093^414	162498	Norbert Schneider	03/2022
3048	2^539654-114893	162453	Enzo Doria	05/2015
3049	9*10^162449-71	162450	Robert Price	11/2020
3050	2^539617-1851583	162441	Enzo Doria	08/2015
3051	(509*10^162422+31)/9	162424	Robert Price	08/2022
3052	(91*10^162410+11)/3	162412	Robert Price	02/2020
3053	2^539346+81049	162360	Enzo Doria	07/2016
3054	2^539220-115499	162322	Enzo Doria	07/2015
3055	2^539217-113713	162321	Enzo Doria	09/2014
3056	9^170099-8^170099	162316	Jean-Louis Charton	05/2005
3057	4*10^162263-39	162264	Robert Price	09/2020
3058	31243^36098-36098^31243	162252	Frank Doornink	01/2024
3059	31987^36000-36000^31987	162180	Frank Doornink	01/2024
3060	(115*10^162153-1)/3	162155	Serge Batalov	12/2014
3061	(10^162138+11)/3	162138	Serge Batalov	07/2015
3062	(61*10^162100-403)/9	162101	Robert Price	10/2021
3063	2^538473-112723	162097	Enzo Doria	06/2014
3064	2^538157+79337	162002	Enzo Doria	06/2016
3065	2^538136-114749	161996	Enzo Doria	05/2015
3066	2^538104+1531	161986	Lelio R Paula	01/2013
3067	(9*29^110727-1199)/14	161927	Curtis Bright	05/2015
3068	((2^179294-1)^3+2)/11	161918	Serge Batalov	03/2023
3069	31198^36027-36027^31198	161910	Frank Doornink	01/2024
3070	2^537815-22737	161899	Enzo Doria	07/2013
3071	2^537804-39839	161896	Enzo Doria	09/2015
3072	(754*10^161816-7)/9	161818	Robert Price	05/2020
3073	2^537461+29867	161792	Enzo Doria	03/2024
3074	2^537458-59201	161791	Enzo Doria	10/2015
3075	2*10^161766+51	161767	Robert Price	05/2018
3076	(7*10^161760+131)/3	161761	Robert Price	06/2020
3077	2^537209-49849	161717	Enzo Doria	10/2015
3078	(58*10^161691+329)/9	161692	Robert Price	05/2019
3079	23*10^161668-3	161670	Robert Price	10/2021
3080	2^536937+1879397	161635	Enzo Doria	09/2016
3081	3*2^536868-5	161614	Jon Grantham	07/2023
3082	34*10^161593-9	161595	Robert Price	06/2020
3083	(31*10^161582-1)/3	161584	Robert Price	02/2020
3084	24494^36813+36813^24494	161575	Norbert Schneider	11/2023
3085	2^536569-22881	161524	Enzo Doria	07/2013
3086	(46*10^161505+593)/9	161506	Robert Price	04/2022
3087	10^161253+573493	161254	Patrick De Geest	07/2018
3088	10^161253-8001	161253	Robert Price	03/2018
3089	97*10^161247-3	161249	Robert Price	05/2020
3090	7*10^161192-9	161193	Robert Price	10/2015
3091	2^535415-19	161176	Stefano Morozzi	07/2022
3092	2^535269-113803	161133	Enzo Doria	09/2014
3093	2^535205-23295	161113	Enzo Doria	08/2013
3094	(49*10^161105+437)/9	161106	Robert Price	09/2021
3095	(89^82609+1)/90	161036	Paul Bourdelais	10/2017
3096	35385^35385-17692^17692	160960	Henri Lifchitz	10/2024
3097	2^534429-19	160880	Stefano Morozzi	07/2022
3098	2^534359-23229	160859	Enzo Doria	08/2013
3099	10^160836-1001	160836	Robert Price	10/2022
3100	457^60454+60454^457	160803	Norbert Schneider	07/2021
3101	8*10^160782+53	160783	Robert Price	08/2020
3102	67^88037-66^88037	160763	Robert Price	10/2013
3103	(88*10^160761-637)/9	160762	Robert Price	11/2020
3104	2^533948-1852559	160735	Enzo Doria	08/2015
3105	2^533665-23335	160650	Enzo Doria	08/2013
3106	2^533600+217981	160630	Enzo Doria	01/2024
3107	(19*10^160619+77)/3	160620	Robert Price	05/2019
3108	2^533350-5	160555	Stefano Morozzi	07/2022
3109	(38*10^160508+151)/9	160509	Robert Price	03/2022
3110	3^336353-2^336353	160482	Mike Oakes	10/2007
3111	26134^36315-36315^26134	160411	Frank Doornink	03/2024
3112	25821^36358-36358^25821	160411	Frank Doornink	03/2024
3113	2*10^160339-63	160340	Robert Price	01/2022
3114	24419^36532+36532^24419	160293	Norbert Schneider	10/2023
3115	(91*10^160249+11)/3	160251	Robert Price	02/2020
3116	(772*10^160239-7)/9	160241	Robert Price	06/2022
3117	(2*10^160226+187)/9	160226	Robert Price	06/2022
3118	2^532253+1868417	160225	Enzo Doria	04/2016
3119	2^532108-291989	160181	Enzo Doria	07/2015
3120	(28*10^160171-79)/3	160172	Robert Price	02/2021
3121	(26*10^160166-131)/3	160167	Robert Price	10/2019
3122	55*10^160145+9	160147	Robert Price	03/2022
3123	(17*10^160143+67)/3	160144	Robert Price	01/2019
3124	(394^61637-1)/393	159977	Jinyuan Wang	04/2023
3125	(19*10^159921-49)/3	159922	Robert Price	05/2019
3126	2^531110-1853771	159881	Enzo Doria	09/2015
3127	(275^65536+53^65536)/2	159864	Kellen Shenton	11/2020
3128	2^530992-1845299	159845	Enzo Doria	07/2015
3129	2^530810+25	159790	Stefano Morozzi	04/2021
3130	25590^36241-36241^25590	159753	Frank Doornink	02/2024
3131	(136*10^159736-1)/9	159738	Serge Batalov	12/2014
3132	2^530417-113833	159672	Enzo Doria	09/2014
3133	2^530406-69701	159669	Enzo Doria	02/2016
3134	5*10^159656+41	159657	Robert Price	03/2019
3135	8*10^159614+29	159615	Robert Price	11/2021
3136	7^188858-188858^7	159604	Norbert Schneider	05/2018
3137	28^110278+27	159590	Alfred Reich	02/2024
3138	7*10^159553-27	159554	Robert Price	11/2022
3139	3^334409-5*2^334409	159554	Jon Grantham	08/2023
3140	(24^115597-1)/23	159547	Paul Bourdelais	09/2017
3141	25472^36209-36209^25472	159540	Frank Doornink	01/2024
3142	(17*10^159438-377)/9	159439	Robert Price	03/2018
3143	(203*10^159381+1)/3	159383	Robert Price	03/2020
3144	32282^35343-35343^32282	159361	Frank Doornink	02/2024
3145	2^529215+219383	159310	Enzo Doria	02/2024
3146	89*10^159258-9	159260	Robert Price	05/2020
3147	2^528944-461315	159229	Enzo Doria	07/2015
3148	(13*10^159147+161)/3	159148	Robert Price	11/2018
3149	2^528620-113879	159131	Enzo Doria	10/2014
3150	32125^35306-35306^32125	159119	Frank Doornink	02/2024
3151	(47*10^159083+259)/9	159084	Robert Price	03/2022
3152	(861^54181-1)/860	159019	Jinyuan Wang	11/2023
3153	2^528000-23307	158944	Enzo Doria	08/2013
3154	(29*10^158909+61)/9	158910	Robert Price	08/2018
3155	2^527817+1876817	158889	Enzo Doria	07/2016
3156	2^527774-49451	158876	Enzo Doria	10/2015
3157	2^527745-291553	158868	Enzo Doria	07/2015
3158	(91*10^158862+11)/3	158864	Robert Price	02/2020
3159	2^527644-1856999	158837	Enzo Doria	10/2015
3160	(37200^37199-37198^37199)/(2^37199)	158822	Henri Lifchitz	06/2013
3161	(17*10^158819+7)/3	158820	Robert Price	06/2023
3162	2^527573-1863253	158816	Enzo Doria	12/2015
3163	2^527553-23401	158810	Enzo Doria	08/2013
3164	(49*10^158783+437)/9	158784	Robert Price	09/2021
3165	10^158755+310207	158756	Patrick De Geest	08/2021
3166	10^158755-50001	158755	Robert Price	08/2020
3167	(61*10^158748-619)/9	158749	Robert Price	03/2022
3168	11^152420-210	158730	Enzo Doria	09/2012
3169	(13*10^158694+401)/9	158695	Robert Price	01/2018
3170	2^527052-69059	158659	Enzo Doria	11/2015
3171	2^526849-113233	158598	Enzo Doria	07/2014
3172	24286^36161+36161^24286	158579	Norbert Schneider	08/2023
3173	(2^526763-lucasV(1,2,526763)+1)/2	158572	Mike Oakes	11/2016
3174	(299*10^158544-17)/3	158546	Robert Price	04/2020
3175	2^526658-3551	158540	Yves Minet	03/2017
3176	7*10^158465-11	158466	Robert Price	06/2019
3177	(7^187507-3^187507)/4	158462	Jon Grantham	08/2023
3178	2^526375-23115	158455	Enzo Doria	08/2013
3179	(77*10^158407-293)/9	158408	Robert Price	09/2019
3180	31209^35242-35242^31209	158388	Frank Doornink	01/2024
3181	32071^35144-35144^32071	158363	Frank Doornink	01/2024
3182	2^526028-112793	158351	Enzo Doria	07/2014
3183	(229*10^158339-1)/3	158341	Robert Price	07/2020
3184	32042^35123-35123^32042	158255	Frank Doornink	01/2024
3185	2^525690-9221	158249	Lelio R Paula	01/2013
3186	2*10^158242-7	158243	Robert Price	10/2015
3187	2^525667-525667^2	158242	Henri Lifchitz	12/2017
3188	(56*10^158230+187)/9	158231	Robert Price	10/2021
3189	10^158209-7000000001	158209	Robert Price	12/2021
3190	31050^35207-35207^31050	158153	Frank Doornink	01/2024
3191	2^525186-1857431	158097	Enzo Doria	10/2015
3192	31527^35108-35108^31527	157940	Frank Doornink	01/2024
3193	2^524515-23245	157895	Enzo Doria	08/2013
3194	2^524499-109087	157890	Enzo Doria	04/2014
3195	2^524384-219533	157856	Enzo Doria	03/2024
3197	2^18067*(2^506221+1)-1	157827	Makoto Morimoto	05/2014
3198	2^524288+189093	157827	Makoto Morimoto	01/2016
3196	2^524288-164073	157827	Matthias Baur	03/2020
3199	(2^(2^19)-9333)/(1923463121331973)	157814	Makoto Morimoto	09/2017
3200	(10^157792+359)/9	157792	Serge Batalov	12/2014
3201	2^524154+25	157787	Stefano Morozzi	04/2021
3202	2^523924+1876591	157717	Enzo Doria	07/2016
3203	(17*10^157705+67)/3	157706	Robert Price	01/2019
3204	(46^94841+1)/47	157696	Robert Price	01/2014
3205	2^523774+77839	157672	Enzo Doria	05/2016
3206	2^523587+2799143	157616	Enzo Doria	04/2016
3207	2^523496+220141	157588	Enzo Doria	03/2024
3208	2^523371+1872113	157551	Enzo Doria	05/2016
3209	8*10^157477+27	157478	Robert Price	09/2021
3210	32268^34909-34909^32268	157397	Frank Doornink	02/2024
3211	(8*10^157368+49)/3	157369	Robert Price	05/2020
3212	(82*10^157319+449)/9	157320	Robert Price	11/2019
3213	2^522535-351457	157299	Enzo Doria	07/2015
3214	25401^35704-35704^25401	157271	Frank Doornink	01/2024
3215	2^522226+2799079	157206	Enzo Doria	04/2016
3216	(134*10^157191-11)/3	157193	Robert Price	01/2022
3217	2^522134-1849451	157178	Enzo Doria	08/2015
3218	9*10^157152+71	157153	Robert Price	08/2020
3219	4*10^157150+93	157151	Robert Price	08/2018
3220	31227^34952-34952^31227	157093	Frank Doornink	01/2024
3221	(32^104347+5^104347)/37	157057	Anonymous	12/2023
3222	fibonacci(751442)-2	157042	Jon Grantham	08/2023
3223	2^521401-29593	156958	Enzo Doria	08/2015
3224	7*10^156956+87	156957	Robert Price	07/2019
3225	2^521348-23397	156942	Enzo Doria	08/2013
3226	10^156902+34509	156903	Patrick De Geest	08/2021
3228	10^156902-80000001	156902	Robert Price	04/2021
3227	10^156902-69789	156902	Patrick De Geest	08/2021
3229	(98^78797+1)/99	156901	Paul Bourdelais	12/2017
3230	65^86522+64	156857	Lelio R Paula	04/2016
3231	8^173687-7^173687	156855	Jean-Louis Charton	09/2004
3232	2^520977-1858183	156830	Enzo Doria	10/2015
3233	(8*10^156718-101)/3	156719	Robert Price	08/2018
3234	(10^156640+7)/53	156639	Alfred Reich	07/2021
3235	2^520314-1849481	156631	Enzo Doria	08/2015
3236	(16*10^156563-637)/9	156564	Robert Price	09/2022
3237	(13*10^156522+89)/3	156523	Robert Price	09/2018
3239	(2^(6*86654+1)-5)/3	156513	Kevin Acres	12/2013
3238	(2^519925-5)/3	156513	Stefano Morozzi	08/2022
3240	(4*10^156501+119)/3	156502	Robert Price	12/2021
3241	(83*10^156476-101)/9	156477	Robert Price	08/2021
3242	3*10^156435-97	156436	Robert Price	07/2018
3243	(8*10^156371-77)/3	156372	Robert Price	07/2018
3244	53^90679-52^90679	156356	Robert Price	01/2013
3245	31267^34782-34782^31267	156349	Frank Doornink	01/2024
3246	(418*10^156309-31)/9	156311	Robert Price	05/2022
3247	2^519106-59141	156267	Enzo Doria	10/2015
3248	25929^35404-35404^25929	156266	Frank Doornink	03/2024
3249	2^519053+6077	156251	Enzo Doria	02/2016
3250	31199^34764-34764^31199	156235	Frank Doornink	01/2024

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