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	2^607950-1862303	183012	Enzo Doria	12/2015
3002	5*3^383376+2^383376	182918	Jon Grantham	08/2023
3003	(46*10^182896+683)/9	182897	Robert Price	03/2019
3004	(2*10^182787+73)/3	182787	Robert Price	09/2020
3005	2^607101+1871987	182756	Enzo Doria	05/2016
3006	2^606869-69175	182686	Enzo Doria	11/2015
3007	8*10^182671+71	182672	Robert Price	05/2022
3008	(23*10^182666-71)/3	182667	Robert Price	07/2020
3009	3*10^182614-11	182615	Robert Price	07/2018
3010	2^606560-357	182593	Enzo Doria	05/2014
3011	66*10^182420+7	182422	Robert Price	07/2020
3012	2^605687+1866983	182330	Enzo Doria	03/2016
3013	2^605655-114445	182321	Enzo Doria	02/2015
3014	94*10^182291-3	182293	Robert Price	05/2020
3015	(20^140053+1)/21	182212	Paul Bourdelais	04/2010
3016	(14*10^182177-221)/9	182178	Robert Price	04/2018
3017	2^605174-112751	182176	Enzo Doria	06/2014
3018	(905^61609-1)/904	182154	Anonymous	05/2024
3019	2^604761+1874507	182052	Enzo Doria	06/2016
3020	2^604705+1871957	182035	Enzo Doria	05/2016
3021	(14*10^182000+229)/9	182001	Robert Price	03/2018
3022	(10^181996+41)/3	181996	Robert Price	12/2017
3023	(17*10^181979+91)/9	181980	Robert Price	02/2022
3024	(10^181960+3)/7	181960	Jinyuan Wang	11/2024
3025	(5*10^181950-101)/3	181951	Robert Price	04/2018
3026	2^603915+75233	181797	Enzo Doria	04/2016
3027	39470^39537+39537^39470	181723	Norbert Schneider	12/2022
3028	(10^181710+7)/563747/2019847	181698	Alfred Reich	08/2021
3029	7*10^181594-57	181595	Robert Price	06/2020
3030	8*10^181580+29	181581	Robert Price	11/2021
3031	(83*10^181544+61)/9	181545	Serge Batalov	01/2023
3032	(2*10^181457+7)/9	181457	Rytis Slatkevicius	01/2023
3033	3*10^181445+23	181446	Robert Price	03/2022
3034	(194*10^181369-11)/3	181371	Robert Price	09/2020
3035	11^174145-360	181354	Enzo Doria	10/2012
3036	2^602351-396765	181326	Enzo Doria	08/2013
3037	6*10^181306+17	181307	Robert Price	04/2019
3038	(353^71143-1)/352	181254	Anonymous	04/2024
3039	(286*10^181220-1)/3	181222	Robert Price	11/2020
3040	2^601957-113833	181208	Enzo Doria	09/2014
3041	66^99581-65^99581	181193	Robert Price	09/2013
3042	10^181182+383973	181183	Patrick De Geest	04/2016
3043	10^181182-21	181182	Serge Batalov	12/2014
3044	(797*10^181171-41)/9	181173	Robert Price	04/2022
3045	2^601722+74209	181137	Enzo Doria	08/2023
3046	(5*10^181127-29)/3	181128	Robert Price	03/2018
3047	2^601521-29143	181076	Enzo Doria	07/2015
3048	2^601442-2797811	181053	Enzo Doria	04/2016
3049	44*10^181029+3	181031	Robert Price	04/2020
3050	5*10^180992-9	180993	Robert Price	05/2015
3051	10^180979+79477	180980	Patrick De Geest	04/2016
3052	10^180979+107739	180980	Patrick De Geest	04/2016
3053	10^180979-11	180979	Serge Batalov	12/2014
3054	2^601023-113851	180926	Enzo Doria	10/2014
3055	(23*10^180862-143)/3	180863	Robert Price	12/2019
3056	3*10^180852+29	180853	Robert Price	05/2018
3057	(277*10^180782-7)/9	180784	Robert Price	02/2022
3058	2^600412+29851	180743	Enzo Doria	03/2024
3059	(8*10^180725-629)/9	180725	Robert Price	01/2022
3060	(79*10^180710-1)/3	180712	Robert Price	02/2020
3061	2^600300-1852559	180709	Enzo Doria	08/2015
3062	(2*10^180706-77)/3	180706	Robert Price	02/2021
3063	(156^82393-1)/155	180696	Anonymous	06/2024
3064	(10^180689+71)/9	180689	Serge Batalov	07/2015
3065	2^600209+76487	180681	Enzo Doria	05/2016
3066	2^599999+378461	180618	Norman Luhn	09/2023
3067	(8*10^180536-269)/9	180536	Robert Price	09/2021
3068	2^599702-369885	180529	Enzo Doria	11/2013
3069	Tau(643^11688)	180524	Nik Lygeros / Olivier Rozier	05/2015
3070	(2951*29^123418-3)/4	180490	Curtis Bright	05/2015
3071	(29*10^180432-17)/3	180433	Robert Price	09/2019
3072	4*10^180360+93	180361	Robert Price	08/2018
3073	2^599035+219323	180328	Enzo Doria	03/2024
3074	2^598942+80779	180300	Enzo Doria	07/2016
3075	(38*10^180296+403)/9	180297	Robert Price	10/2018
3076	(85*10^180241+77)/9	180242	Robert Price	07/2022
3077	2^598591-1844797	180194	Enzo Doria	06/2015
3078	(100^90089+1)/101	180176	Paul Bourdelais	08/2017
3079	2^598301+28517	180107	Enzo Doria	01/2024
3080	(29*10^180072+691)/9	180073	Robert Price	08/2021
3081	(59*10^180038+157)/9	180039	Robert Price	12/2021
3082	95*10^180019-9	180021	Robert Price	01/2022
3083	6*10^179970+91	179971	Robert Price	05/2019
3084	(4*10^179963-79)/3	179964	Robert Price	02/2018
3085	(403*10^179944-43)/9	179946	Robert Price	06/2021
3086	Gamma-Prime(179849)	179849	Eric W. Weisstein	06/2011
3087	2^597424-1859729	179843	Enzo Doria	11/2015
3088	Phi(180683,10)	179760	Maksym Voznyy	09/2015
3089	(10^180683-1)*9/(10^643-1)/(10^281-1)	179760	Robert Price	07/2016
3090	(3^376657-2^376657)/22301107657	179701	Mike Oakes	04/2017
3091	(29*10^179697+223)/9	179698	Robert Price	09/2018
3092	U(1289697)	179687	Serge Batalov	07/2024
3094	2^596884+73	179680	Stefano Morozzi	04/2021
3093	(11*10^179679+13)/3	179680	Robert Price	03/2022
3095	(68*10^179656+7)/3	179658	Robert Price	01/2020
3096	(10^179643+173)/3	179643	Robert Price	05/2021
3097	2^596690-461261	179622	Enzo Doria	07/2015
3098	2^596684-113939	179620	Enzo Doria	10/2014
3099	2^596642+39	179608	Jon Grantham	08/2023
3100	2*10^179602+63	179603	Robert Price	05/2018
3101	32262^39815-39815^32262	179514	Frank Doornink	02/2024
3102	(25*10^179488-403)/9	179489	Robert Price	01/2021
3103	7*10^179460+99	179461	Robert Price	05/2021
3104	2^596127+74333	179453	Enzo Doria	07/2023
3105	3^375887-112696	179344	Enzo Doria	07/2014
3106	4*10^179265-71	179266	Robert Price	12/2018
3107	2*10^179193+83	179194	Robert Price	12/2021
3108	2^595144-1850429	179157	Enzo Doria	08/2015
3109	2^595122-5	179150	Stefano Morozzi	07/2022
3110	3*10^179138+89	179139	Robert Price	10/2018
3111	(52*10^179062-133)/9	179063	Robert Price	09/2021
3112	2^594531+82253	178972	Enzo Doria	09/2016
3113	(664*10^178939-61)/9	178941	Robert Price	09/2021
3114	2^594260-2787899	178891	Enzo Doria	11/2015
3115	(14*10^178822+67)/9	178823	Robert Price	05/2022
3116	(29*10^178732-119)/9	178733	Robert Price	12/2021
3117	2^593631+101381	178701	Jorge Menendez	04/2018
3118	10^178695+136719	178696	Patrick De Geest	05/2016
3119	10^178695-71	178695	Serge Batalov	12/2014
3120	(2*10^178649-161)/3	178649	Robert Price	12/2020
3121	(691^62903-1)/690	178609	Michael Stocker	05/2020
3122	(2^148330+1)^4-2	178608	Cletus Emmanuel	12/2003
3123	2^593242+28309	178584	Enzo Doria	01/2024
3124	2^593222-14145	178578	Jorge Menendez	10/2017
3125	7*10^178566+33	178567	Robert Price	06/2020
3126	2^593178+1867219	178565	Enzo Doria	03/2016
3127	2^593152+22441	178557	Enzo Doria	09/2023
3128	(38*10^178456+151)/9	178457	Robert Price	03/2022
3129	(302*10^178369+13)/9	178371	Robert Price	02/2020
3130	(26*10^178296-113)/3	178297	Robert Price	06/2020
3131	(18^142031-1)/17	178287	Paul Bourdelais	03/2010
3132	(13*10^178233+137)/3	178234	Robert Price	06/2021
3133	(5*10^178206+91)/3	178207	Robert Price	04/2018
3134	2^591872-291929	178172	Enzo Doria	07/2015
3135	2^591682-286871	178115	Enzo Doria	07/2015
3136	(7^210761-5^210761)/2	178114	Jon Grantham	08/2023
3137	4*10^178091+9	178092	Robert Price	05/2015
3138	2^591435+335931	178040	Enzo Doria	09/2024
3139	410747#+478483	178007	Makoto Morimoto	02/2016
3140	3*10^177872+73	177873	Robert Price	08/2018
3141	2^590762-396765	177838	Enzo Doria	08/2013
3142	(136*10^177754-1)/9	177756	Serge Batalov	12/2014
3143	ReverseConsecutiveIntegerPrime(37765)	177719	Eric W. Weisstein	04/2010
3144	Smr(37765)	177719	Eric W. Weisstein	12/2021
3145	598^128^209+209^128^598	177594	Henri Lifchitz	03/2025
3146	(266*10^177577-11)/3	177579	Robert Price	04/2020
3147	(11*10^177466-113)/3	177467	Robert Price	10/2018
3148	3*10^177373-97	177374	Robert Price	07/2018
3149	2^589204+1881151	177369	Enzo Doria	11/2016
3150	2^589132-69479	177347	Enzo Doria	01/2016
3151	(3^371666)/(371666^3)	177314	Henri Lifchitz	05/2025
3152	(101*10^177302-17)/3	177304	Robert Price	02/2020
3153	2^588912-113519	177281	Enzo Doria	08/2014
3154	(682*10^177266-7)/9	177268	Robert Price	08/2021
3155	15^150706+2	177245	Robert Price	06/2015
3156	2^588403+335931	177127	Enzo Doria	09/2024
3157	(31208^39601-1)/(31208^199-1)	177084	Ryan Propper	11/2023
3158	2^588194-1861001	177065	Enzo Doria	11/2015
3159	5*10^177016-37	177017	Robert Price	11/2021
3160	fibonacci(846926)-4	176997	Jon Grantham	08/2023
3161	(23*10^176964-47)/3	176965	Robert Price	09/2019
3162	20530^41031+41031^20530	176942	Norbert Schneider	07/2022
3163	(19*10^176932+521)/9	176933	Robert Price	05/2018
3164	(8*10^176908+43)/3	176909	Robert Price	06/2018
3165	(85*10^176900+203)/9	176901	Robert Price	09/2020
3166	2^587560-113699	176874	Enzo Doria	09/2014
3167	20596^40995+40995^20596	176844	Norbert Schneider	07/2022
3168	(101*10^176815-17)/3	176817	Robert Price	02/2020
3169	(25*10^176715-37)/3	176716	Robert Price	10/2019
3170	5^252763-12862	176674	Enzo Doria	05/2014
3171	38442^38531+38531^38442	176658	Norbert Schneider	09/2022
3172	2^586829+23961	176654	Enzo Doria	10/2023
3173	2^586804+81721	176646	Enzo Doria	08/2016
3174	(10^176584+77)/3	176584	Robert Price	01/2018
3175	2^586570+1874419	176576	Enzo Doria	06/2016
3176	(157*10^176482-1)/3	176484	Robert Price	01/2022
3177	5*2^586202+3	176466	Jon Grantham	07/2023
3178	27122^39799-39799^27122	176442	Frank Doornink	01/2024
3179	2^585994-3311	176402	Yves Minet	12/2014
3180	8*10^176383-81	176384	Robert Price	02/2021
3181	(23*10^176357+61)/3	176358	Robert Price	01/2022
3182	2^585832-112799	176354	Enzo Doria	07/2014
3183	fibonacci(843383)+4	176257	Jon Grantham	08/2023
3184	(29*10^176240+49)/3	176241	Robert Price	09/2021
3185	(2^585387-11)/3	176219	Stefano Morozzi	08/2022
3186	2^585336-461039	176204	Enzo Doria	06/2015
3187	(25*10^176164+143)/3	176165	Robert Price	08/2020
3188	2^585095-1848127	176132	Enzo Doria	08/2015
3189	(5*10^176101-311)/9	176101	Robert Price	12/2021
3190	6*10^176092+77	176093	Robert Price	06/2020
3191	2^584950-115451	176088	Enzo Doria	07/2015
3192	(646*10^176044+11)/9	176046	Robert Price	10/2021
3193	(7^208283-5^208283)/2	176020	Jon Grantham	08/2023
3194	2^584671-3697	176004	Yves Minet	03/2017
3195	(13*10^175965-37)/3	175966	Robert Price	01/2019
3196	31728^39089-39089^31728	175957	Frank Doornink	01/2024
3197	2*10^175860-87	175861	Robert Price	04/2018
3198	27009^39670-39670^27009	175798	Frank Doornink	01/2024
3199	(86*10^175774-221)/9	175775	Robert Price	09/2019
3200	2^583614+216037	175686	Enzo Doria	11/2023
3201	9*10^175654+47	175655	Robert Price	01/2022
3202	25430^39869-39869^25430	175637	Frank Doornink	01/2024
3203	10^175608+2971	175609	Mike Oakes	05/2010
3204	10^175608-55829	175608	Patrick De Geest	09/2013
3205	2^583051+1879793	175516	Enzo Doria	09/2016
3206	(76*10^175514+491)/9	175515	Robert Price	10/2021
3208	2^582860-23829	175459	Enzo Doria	08/2013
3207	(200^76253-1)/199	175459	Anonymous	06/2024
3209	(8*10^175428-53)/9	175428	Serge Batalov	11/2022
3210	(28*10^175417-67)/3	175418	Robert Price	10/2020
3211	2^582670-23913	175402	Enzo Doria	08/2013
3212	2^582573-29563	175372	Enzo Doria	08/2015
3213	2^582435-1862767	175331	Enzo Doria	12/2015
3214	10^175295-40000001	175295	Robert Price	07/2022
3215	31093^39018-39018^31093	175295	Frank Doornink	01/2024
3216	(11*10^175250-149)/3	175251	Robert Price	09/2018
3217	(29*10^175236+31)/3	175237	Robert Price	04/2021
3218	2^582072-1848599	175222	Enzo Doria	08/2015
3219	(404267#+465)/(3^45^231)	175208	Makoto Morimoto	06/2019
3220	Phi(262767,10)/259613797	175168	Makoto Kamada	12/2022
3221	(2^581871-15)/7	175160	Stefano Morozzi	08/2022
3222	(5*10^175117-311)/9	175117	Robert Price	12/2021
3223	31193^38966-38966^31193	175116	Frank Doornink	01/2024
3224	2^581695+225893	175108	Enzo Doria	08/2024
3225	10^175093-89	175093	Riley Fisher	10/2023
3226	(220221^32768+1)/2	175075	Serge Batalov	03/2018
3227	2^581560+1874911	175068	Enzo Doria	06/2016
3228	(25*10^174987-97)/9	174988	Robert Price	01/2022
3229	(75^93307-1)/74	174955	Paul Bourdelais	09/2017
3230	26446^39555-39555^26446	174927	Frank Doornink	03/2024
3231	31522^38883-38883^31522	174920	Frank Doornink	01/2024
3232	(27398^39601-1)/(27398^199-1)	174855	Ryan Propper	11/2023
3233	(861^59557-1)/860	174798	Jinyuan Wang	11/2023
3234	31492^38859-38859^31492	174796	Frank Doornink	01/2024
3235	(47*10^174790+493)/9	174791	Robert Price	03/2019
3236	2^580528-114035	174757	Enzo Doria	11/2014
3237	(19*10^174754+737)/9	174755	Robert Price	07/2018
3238	V(1045270)/4181081/12543241/81333115129561	174730	Serge Batalov	07/2024
3239	(35*10^174704-377)/9	174705	Robert Price	07/2018
3241	(49*10^174681+293)/9	174682	Robert Price	03/2021
3240	6*10^174681+11	174682	Robert Price	07/2022
3242	3*10^174665-97	174666	Robert Price	07/2018
3243	2^580046-459161	174612	Enzo Doria	05/2015
3244	2^579992-39779	174595	Enzo Doria	09/2015
3245	25613^39582-39582^25613	174496	Frank Doornink	02/2024
3246	(29*10^174481-149)/3	174482	Robert Price	08/2022
3247	(4*10^174423+101)/3	174424	Robert Price	11/2021
3248	(2^579371-17)/3	174408	Stefano Morozzi	08/2022
3249	(2*10^174301-71)/3	174301	Robert Price	12/2017
3250	14^152048+3	174267	Paul Bourdelais	12/2020

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Probable Primes Top 10000

(301723 PRPs in the top)