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	(163*10^183227-1)/9	183229	Serge Batalov	12/2014
3002	2^608541-608541^2	183190	Henri Lifchitz	02/2018
3003	2^608293+143807	183115	Enzo Doria	10/2016
3004	2^608164-462419	183076	Enzo Doria	08/2015
3005	2^607950-1862303	183012	Enzo Doria	12/2015
3006	5*3^383376+2^383376	182918	Jon Grantham	08/2023
3007	(46*10^182896+683)/9	182897	Robert Price	03/2019
3008	(2*10^182787+73)/3	182787	Robert Price	09/2020
3009	2^607101+1871987	182756	Enzo Doria	05/2016
3010	2^606869-69175	182686	Enzo Doria	11/2015
3011	8*10^182671+71	182672	Robert Price	05/2022
3012	(23*10^182666-71)/3	182667	Robert Price	07/2020
3013	3*10^182614-11	182615	Robert Price	07/2018
3014	2^606560-357	182593	Enzo Doria	05/2014
3015	66*10^182420+7	182422	Robert Price	07/2020
3016	2^605687+1866983	182330	Enzo Doria	03/2016
3017	2^605655-114445	182321	Enzo Doria	02/2015
3018	94*10^182291-3	182293	Robert Price	05/2020
3019	(20^140053+1)/21	182212	Paul Bourdelais	04/2010
3020	(14*10^182177-221)/9	182178	Robert Price	04/2018
3021	2^605174-112751	182176	Enzo Doria	06/2014
3022	(905^61609-1)/904	182154	Anonymous	05/2024
3023	2^604761+1874507	182052	Enzo Doria	06/2016
3024	2^604705+1871957	182035	Enzo Doria	05/2016
3025	(14*10^182000+229)/9	182001	Robert Price	03/2018
3026	(10^181996+41)/3	181996	Robert Price	12/2017
3027	(17*10^181979+91)/9	181980	Robert Price	02/2022
3028	(10^181960+3)/7	181960	Jinyuan Wang	11/2024
3029	(5*10^181950-101)/3	181951	Robert Price	04/2018
3030	2^603915+75233	181797	Enzo Doria	04/2016
3031	39470^39537+39537^39470	181723	Norbert Schneider	12/2022
3032	(10^181710+7)/563747/2019847	181698	Alfred Reich	08/2021
3033	7*10^181594-57	181595	Robert Price	06/2020
3034	8*10^181580+29	181581	Robert Price	11/2021
3035	(83*10^181544+61)/9	181545	Serge Batalov	01/2023
3036	(2*10^181457+7)/9	181457	Rytis Slatkevicius	01/2023
3037	3*10^181445+23	181446	Robert Price	03/2022
3038	(194*10^181369-11)/3	181371	Robert Price	09/2020
3039	11^174145-360	181354	Enzo Doria	10/2012
3040	2^602351-396765	181326	Enzo Doria	08/2013
3041	6*10^181306+17	181307	Robert Price	04/2019
3042	(353^71143-1)/352	181254	Anonymous	04/2024
3043	(286*10^181220-1)/3	181222	Robert Price	11/2020
3044	2^601957-113833	181208	Enzo Doria	09/2014
3045	66^99581-65^99581	181193	Robert Price	09/2013
3046	10^181182+383973	181183	Patrick De Geest	04/2016
3047	10^181182-21	181182	Serge Batalov	12/2014
3048	(797*10^181171-41)/9	181173	Robert Price	04/2022
3049	2^601722+74209	181137	Enzo Doria	08/2023
3050	(5*10^181127-29)/3	181128	Robert Price	03/2018
3051	2^601521-29143	181076	Enzo Doria	07/2015
3052	2^601442-2797811	181053	Enzo Doria	04/2016
3053	44*10^181029+3	181031	Robert Price	04/2020
3054	5*10^180992-9	180993	Robert Price	05/2015
3055	10^180979+79477	180980	Patrick De Geest	04/2016
3056	10^180979+107739	180980	Patrick De Geest	04/2016
3057	10^180979-11	180979	Serge Batalov	12/2014
3058	2^601023-113851	180926	Enzo Doria	10/2014
3059	(23*10^180862-143)/3	180863	Robert Price	12/2019
3060	3*10^180852+29	180853	Robert Price	05/2018
3061	(277*10^180782-7)/9	180784	Robert Price	02/2022
3062	2^600412+29851	180743	Enzo Doria	03/2024
3063	(8*10^180725-629)/9	180725	Robert Price	01/2022
3064	(79*10^180710-1)/3	180712	Robert Price	02/2020
3065	2^600300-1852559	180709	Enzo Doria	08/2015
3066	(2*10^180706-77)/3	180706	Robert Price	02/2021
3067	(156^82393-1)/155	180696	Anonymous	06/2024
3068	(10^180689+71)/9	180689	Serge Batalov	07/2015
3069	2^600209+76487	180681	Enzo Doria	05/2016
3070	2^599999+378461	180618	Norman Luhn	09/2023
3071	(8*10^180536-269)/9	180536	Robert Price	09/2021
3072	2^599702-369885	180529	Enzo Doria	11/2013
3073	Tau(643^11688)	180524	Nik Lygeros / Olivier Rozier	05/2015
3074	(2951*29^123418-3)/4	180490	Curtis Bright	05/2015
3075	(29*10^180432-17)/3	180433	Robert Price	09/2019
3076	4*10^180360+93	180361	Robert Price	08/2018
3077	2^599035+219323	180328	Enzo Doria	03/2024
3078	2^598942+80779	180300	Enzo Doria	07/2016
3079	(38*10^180296+403)/9	180297	Robert Price	10/2018
3080	(85*10^180241+77)/9	180242	Robert Price	07/2022
3081	2^598591-1844797	180194	Enzo Doria	06/2015
3082	(100^90089+1)/101	180176	Paul Bourdelais	08/2017
3083	2^598301+28517	180107	Enzo Doria	01/2024
3084	(29*10^180072+691)/9	180073	Robert Price	08/2021
3085	(59*10^180038+157)/9	180039	Robert Price	12/2021
3086	95*10^180019-9	180021	Robert Price	01/2022
3087	6*10^179970+91	179971	Robert Price	05/2019
3088	(4*10^179963-79)/3	179964	Robert Price	02/2018
3089	(403*10^179944-43)/9	179946	Robert Price	06/2021
3090	Gamma-Prime(179849)	179849	Eric W. Weisstein	06/2011
3091	2^597424-1859729	179843	Enzo Doria	11/2015
3092	Phi(180683,10)	179760	Maksym Voznyy	09/2015
3093	(10^180683-1)*9/(10^643-1)/(10^281-1)	179760	Robert Price	07/2016
3094	(3^376657-2^376657)/22301107657	179701	Mike Oakes	04/2017
3095	(29*10^179697+223)/9	179698	Robert Price	09/2018
3096	U(1289697)	179687	Serge Batalov	07/2024
3098	2^596884+73	179680	Stefano Morozzi	04/2021
3097	(11*10^179679+13)/3	179680	Robert Price	03/2022
3099	(68*10^179656+7)/3	179658	Robert Price	01/2020
3100	(10^179643+173)/3	179643	Robert Price	05/2021
3101	2^596690-461261	179622	Enzo Doria	07/2015
3102	2^596684-113939	179620	Enzo Doria	10/2014
3103	2^596642+39	179608	Jon Grantham	08/2023
3104	2*10^179602+63	179603	Robert Price	05/2018
3105	32262^39815-39815^32262	179514	Frank Doornink	02/2024
3106	(25*10^179488-403)/9	179489	Robert Price	01/2021
3107	7*10^179460+99	179461	Robert Price	05/2021
3108	2^596127+74333	179453	Enzo Doria	07/2023
3109	3^375887-112696	179344	Enzo Doria	07/2014
3110	4*10^179265-71	179266	Robert Price	12/2018
3111	2*10^179193+83	179194	Robert Price	12/2021
3112	2^595144-1850429	179157	Enzo Doria	08/2015
3113	2^595122-5	179150	Stefano Morozzi	07/2022
3114	3*10^179138+89	179139	Robert Price	10/2018
3115	(52*10^179062-133)/9	179063	Robert Price	09/2021
3116	2^594531+82253	178972	Enzo Doria	09/2016
3117	(664*10^178939-61)/9	178941	Robert Price	09/2021
3118	2^594260-2787899	178891	Enzo Doria	11/2015
3119	(14*10^178822+67)/9	178823	Robert Price	05/2022
3120	(29*10^178732-119)/9	178733	Robert Price	12/2021
3121	2^593631+101381	178701	Jorge Menendez	04/2018
3122	10^178695+136719	178696	Patrick De Geest	05/2016
3123	10^178695-71	178695	Serge Batalov	12/2014
3124	(2*10^178649-161)/3	178649	Robert Price	12/2020
3125	(691^62903-1)/690	178609	Michael Stocker	05/2020
3126	(2^148330+1)^4-2	178608	Cletus Emmanuel	12/2003
3127	2^593242+28309	178584	Enzo Doria	01/2024
3128	2^593222-14145	178578	Jorge Menendez	10/2017
3129	7*10^178566+33	178567	Robert Price	06/2020
3130	2^593178+1867219	178565	Enzo Doria	03/2016
3131	2^593152+22441	178557	Enzo Doria	09/2023
3132	(38*10^178456+151)/9	178457	Robert Price	03/2022
3133	(302*10^178369+13)/9	178371	Robert Price	02/2020
3134	(26*10^178296-113)/3	178297	Robert Price	06/2020
3135	(18^142031-1)/17	178287	Paul Bourdelais	03/2010
3136	(13*10^178233+137)/3	178234	Robert Price	06/2021
3137	(5*10^178206+91)/3	178207	Robert Price	04/2018
3138	2^591872-291929	178172	Enzo Doria	07/2015
3139	2^591682-286871	178115	Enzo Doria	07/2015
3140	(7^210761-5^210761)/2	178114	Jon Grantham	08/2023
3141	4*10^178091+9	178092	Robert Price	05/2015
3142	2^591435+335931	178040	Enzo Doria	09/2024
3143	410747#+478483	178007	Makoto Morimoto	02/2016
3144	3*10^177872+73	177873	Robert Price	08/2018
3145	2^590762-396765	177838	Enzo Doria	08/2013
3146	(136*10^177754-1)/9	177756	Serge Batalov	12/2014
3147	ReverseConsecutiveIntegerPrime(37765)	177719	Eric W. Weisstein	04/2010
3148	Smr(37765)	177719	Eric W. Weisstein	12/2021
3149	598^128^209+209^128^598	177594	Henri Lifchitz	03/2025
3150	(266*10^177577-11)/3	177579	Robert Price	04/2020
3151	(11*10^177466-113)/3	177467	Robert Price	10/2018
3152	3*10^177373-97	177374	Robert Price	07/2018
3153	2^589204+1881151	177369	Enzo Doria	11/2016
3154	2^589132-69479	177347	Enzo Doria	01/2016
3155	(3^371666)/(371666^3)	177314	Henri Lifchitz	05/2025
3156	(101*10^177302-17)/3	177304	Robert Price	02/2020
3157	2^588912-113519	177281	Enzo Doria	08/2014
3158	(682*10^177266-7)/9	177268	Robert Price	08/2021
3159	15^150706+2	177245	Robert Price	06/2015
3160	2^588403+335931	177127	Enzo Doria	09/2024
3161	(31208^39601-1)/(31208^199-1)	177084	Ryan Propper	11/2023
3162	2^588194-1861001	177065	Enzo Doria	11/2015
3163	5*10^177016-37	177017	Robert Price	11/2021
3164	fibonacci(846926)-4	176997	Jon Grantham	08/2023
3165	(23*10^176964-47)/3	176965	Robert Price	09/2019
3166	20530^41031+41031^20530	176942	Norbert Schneider	07/2022
3167	(19*10^176932+521)/9	176933	Robert Price	05/2018
3168	(8*10^176908+43)/3	176909	Robert Price	06/2018
3169	(85*10^176900+203)/9	176901	Robert Price	09/2020
3170	2^587560-113699	176874	Enzo Doria	09/2014
3171	20596^40995+40995^20596	176844	Norbert Schneider	07/2022
3172	(101*10^176815-17)/3	176817	Robert Price	02/2020
3173	(25*10^176715-37)/3	176716	Robert Price	10/2019
3174	5^252763-12862	176674	Enzo Doria	05/2014
3175	38442^38531+38531^38442	176658	Norbert Schneider	09/2022
3176	2^586829+23961	176654	Enzo Doria	10/2023
3177	2^586804+81721	176646	Enzo Doria	08/2016
3178	(10^176584+77)/3	176584	Robert Price	01/2018
3179	2^586570+1874419	176576	Enzo Doria	06/2016
3180	(157*10^176482-1)/3	176484	Robert Price	01/2022
3181	5*2^586202+3	176466	Jon Grantham	07/2023
3182	27122^39799-39799^27122	176442	Frank Doornink	01/2024
3183	2^585994-3311	176402	Yves Minet	12/2014
3184	8*10^176383-81	176384	Robert Price	02/2021
3185	(23*10^176357+61)/3	176358	Robert Price	01/2022
3186	2^585832-112799	176354	Enzo Doria	07/2014
3187	fibonacci(843383)+4	176257	Jon Grantham	08/2023
3188	(29*10^176240+49)/3	176241	Robert Price	09/2021
3189	(2^585387-11)/3	176219	Stefano Morozzi	08/2022
3190	2^585336-461039	176204	Enzo Doria	06/2015
3191	(25*10^176164+143)/3	176165	Robert Price	08/2020
3192	2^585095-1848127	176132	Enzo Doria	08/2015
3193	(5*10^176101-311)/9	176101	Robert Price	12/2021
3194	6*10^176092+77	176093	Robert Price	06/2020
3195	2^584950-115451	176088	Enzo Doria	07/2015
3196	(646*10^176044+11)/9	176046	Robert Price	10/2021
3197	(7^208283-5^208283)/2	176020	Jon Grantham	08/2023
3198	2^584671-3697	176004	Yves Minet	03/2017
3199	(13*10^175965-37)/3	175966	Robert Price	01/2019
3200	31728^39089-39089^31728	175957	Frank Doornink	01/2024
3201	2*10^175860-87	175861	Robert Price	04/2018
3202	27009^39670-39670^27009	175798	Frank Doornink	01/2024
3203	(86*10^175774-221)/9	175775	Robert Price	09/2019
3204	2^583614+216037	175686	Enzo Doria	11/2023
3205	9*10^175654+47	175655	Robert Price	01/2022
3206	25430^39869-39869^25430	175637	Frank Doornink	01/2024
3207	10^175608+2971	175609	Mike Oakes	05/2010
3208	10^175608-55829	175608	Patrick De Geest	09/2013
3209	2^583051+1879793	175516	Enzo Doria	09/2016
3210	(76*10^175514+491)/9	175515	Robert Price	10/2021
3212	2^582860-23829	175459	Enzo Doria	08/2013
3211	(200^76253-1)/199	175459	Anonymous	06/2024
3213	(8*10^175428-53)/9	175428	Serge Batalov	11/2022
3214	(28*10^175417-67)/3	175418	Robert Price	10/2020
3215	2^582670-23913	175402	Enzo Doria	08/2013
3216	2^582573-29563	175372	Enzo Doria	08/2015
3217	2^582435-1862767	175331	Enzo Doria	12/2015
3218	10^175295-40000001	175295	Robert Price	07/2022
3219	31093^39018-39018^31093	175295	Frank Doornink	01/2024
3220	(11*10^175250-149)/3	175251	Robert Price	09/2018
3221	(29*10^175236+31)/3	175237	Robert Price	04/2021
3222	2^582072-1848599	175222	Enzo Doria	08/2015
3223	(404267#+465)/(3^45^231)	175208	Makoto Morimoto	06/2019
3224	Phi(262767,10)/259613797	175168	Makoto Kamada	12/2022
3225	(2^581871-15)/7	175160	Stefano Morozzi	08/2022
3226	(5*10^175117-311)/9	175117	Robert Price	12/2021
3227	31193^38966-38966^31193	175116	Frank Doornink	01/2024
3228	2^581695+225893	175108	Enzo Doria	08/2024
3229	10^175093-89	175093	Riley Fisher	10/2023
3230	(220221^32768+1)/2	175075	Serge Batalov	03/2018
3231	2^581560+1874911	175068	Enzo Doria	06/2016
3232	(25*10^174987-97)/9	174988	Robert Price	01/2022
3233	(75^93307-1)/74	174955	Paul Bourdelais	09/2017
3234	26446^39555-39555^26446	174927	Frank Doornink	03/2024
3235	31522^38883-38883^31522	174920	Frank Doornink	01/2024
3236	(27398^39601-1)/(27398^199-1)	174855	Ryan Propper	11/2023
3237	(861^59557-1)/860	174798	Jinyuan Wang	11/2023
3238	31492^38859-38859^31492	174796	Frank Doornink	01/2024
3239	(47*10^174790+493)/9	174791	Robert Price	03/2019
3240	2^580528-114035	174757	Enzo Doria	11/2014
3241	(19*10^174754+737)/9	174755	Robert Price	07/2018
3242	V(1045270)/4181081/12543241/81333115129561	174730	Serge Batalov	07/2024
3243	(35*10^174704-377)/9	174705	Robert Price	07/2018
3245	(49*10^174681+293)/9	174682	Robert Price	03/2021
3244	6*10^174681+11	174682	Robert Price	07/2022
3246	3*10^174665-97	174666	Robert Price	07/2018
3247	2^580046-459161	174612	Enzo Doria	05/2015
3248	2^579992-39779	174595	Enzo Doria	09/2015
3249	25613^39582-39582^25613	174496	Frank Doornink	02/2024
3250	(29*10^174481-149)/3	174482	Robert Price	08/2022

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PRP Records

Probable Primes Top 10000

(301737 PRPs in the top)