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 ?
2001	(8*10^180725-629)/9	180725	Robert Price	01/2022
2002	(79*10^180710-1)/3	180712	Robert Price	02/2020
2003	2^600300-1852559	180709	Enzo Doria	08/2015
2004	(2*10^180706-77)/3	180706	Robert Price	02/2021
2005	(10^180689+71)/9	180689	Serge Batalov	07/2015
2006	2^600209+76487	180681	Enzo Doria	05/2016
2007	2^599999+378461	180617	Norman Luhn	09/2023
2008	(8*10^180536-269)/9	180536	Robert Price	09/2021
2009	2^599702-369885	180529	Enzo Doria	11/2013
2010	Tau(643^11688)	180524	Nik Lygeros / Olivier Rozier	05/2015
2011	(2951*29^123418-3)/4	180490	Curtis Bright	05/2015
2012	(29*10^180432-17)/3	180433	Robert Price	09/2019
2013	4*10^180360+93	180361	Robert Price	08/2018
2014	2^598942+80779	180300	Enzo Doria	07/2016
2015	(38*10^180296+403)/9	180297	Robert Price	10/2018
2016	(85*10^180241+77)/9	180242	Robert Price	07/2022
2017	2^598591-1844797	180194	Enzo Doria	06/2015
2018	(100^90089+1)/101	180176	Paul Bourdelais	08/2017
2019	(29*10^180072+691)/9	180073	Robert Price	08/2021
2020	(59*10^180038+157)/9	180039	Robert Price	12/2021
2021	95*10^180019-9	180021	Robert Price	01/2022
2022	6*10^179970+91	179971	Robert Price	05/2019
2023	(4*10^179963-79)/3	179964	Robert Price	02/2018
2024	(403*10^179944-43)/9	179946	Robert Price	06/2021
2025	Gamma-Prime(179849)	179849	Eric W. Weisstein	06/2011
2026	2^597424-1859729	179843	Enzo Doria	11/2015
2027	Phi(180683,10)	179760	Maksym Voznyy	09/2015
2028	(10^180683-1)*9/(10^643-1)/(10^281-1)	179760	Robert Price	07/2016
2029	(3^376657-2^376657)/22301107657	179701	Mike Oakes	04/2017
2030	(29*10^179697+223)/9	179698	Robert Price	09/2018
2031	2^596884+73	179680	Stefano Morozzi	04/2021
2032	(11*10^179679+13)/3	179680	Robert Price	03/2022
2033	(68*10^179656+7)/3	179658	Robert Price	01/2020
2034	(10^179643+173)/3	179643	Robert Price	05/2021
2035	2^596690-461261	179622	Enzo Doria	07/2015
2036	2^596684-113939	179620	Enzo Doria	10/2014
2037	2^596642+39	179608	Jon Grantham	08/2023
2038	2*10^179602+63	179603	Robert Price	05/2018
2039	(25*10^179488-403)/9	179489	Robert Price	01/2021
2040	7*10^179460+99	179461	Robert Price	05/2021
2041	2^596127+74333	179453	Enzo Doria	07/2023
2042	3^375887-112696	179344	Enzo Doria	07/2014
2043	4*10^179265-71	179266	Robert Price	12/2018
2044	2*10^179193+83	179194	Robert Price	12/2021
2045	2^595144-1850429	179157	Enzo Doria	08/2015
2046	2^595122-5	179150	Stefano Morozzi	07/2022
2047	3*10^179138+89	179139	Robert Price	10/2018
2048	(52*10^179062-133)/9	179063	Robert Price	09/2021
2049	2^594531+82253	178972	Enzo Doria	09/2016
2050	(664*10^178939-61)/9	178941	Robert Price	09/2021
2051	2^594260-2787899	178891	Enzo Doria	11/2015
2052	(14*10^178822+67)/9	178823	Robert Price	05/2022
2053	(29*10^178732-119)/9	178733	Robert Price	12/2021
2054	2^593631+101381	178701	Jorge Menendez	04/2018
2055	10^178695+136719	178696	Patrick De Geest	05/2016
2056	10^178695-71	178695	Serge Batalov	12/2014
2057	(2*10^178649-161)/3	178649	Robert Price	12/2020
2058	(691^62903-1)/690	178609	Michael Stocker	05/2020
2059	(2^148330+1)^4-2	178608	Cletus Emmanuel	12/2003
2060	2^593222-14145	178578	Jorge Menendez	10/2017
2061	7*10^178566+33	178567	Robert Price	06/2020
2062	2^593178+1867219	178565	Enzo Doria	03/2016
2063	(38*10^178456+151)/9	178457	Robert Price	03/2022
2064	(302*10^178369+13)/9	178371	Robert Price	02/2020
2065	(26*10^178296-113)/3	178297	Robert Price	06/2020
2066	(18^142031-1)/17	178287	Paul Bourdelais	03/2010
2067	(13*10^178233+137)/3	178234	Robert Price	06/2021
2068	(5*10^178206+91)/3	178207	Robert Price	04/2018
2069	2^591872-291929	178172	Enzo Doria	07/2015
2070	2^591682-286871	178115	Enzo Doria	07/2015
2071	(7^210761-5^210761)/2	178114	Jon Grantham	08/2023
2072	4*10^178091+9	178092	Robert Price	05/2015
2073	410747#+478483	178007	Makoto Morimoto	02/2016
2074	3*10^177872+73	177873	Robert Price	08/2018
2075	2^590762-396765	177838	Enzo Doria	08/2013
2076	(136*10^177754-1)/9	177756	Serge Batalov	12/2014
2078	ReverseConsecutiveIntegerPrime(37765)	177719	Eric W. Weisstein	04/2010
2077	Smr(37765)	177719	Eric W. Weisstein	12/2021
2079	(266*10^177577-11)/3	177579	Robert Price	04/2020
2080	(11*10^177466-113)/3	177467	Robert Price	10/2018
2081	3*10^177373-97	177374	Robert Price	07/2018
2082	2^589204+1881151	177369	Enzo Doria	11/2016
2083	2^589132-69479	177347	Enzo Doria	01/2016
2084	(101*10^177302-17)/3	177304	Robert Price	02/2020
2085	2^588912-113519	177281	Enzo Doria	08/2014
2086	(682*10^177266-7)/9	177268	Robert Price	08/2021
2087	15^150706+2	177245	Robert Price	06/2015
2088	2^588194-1861001	177065	Enzo Doria	11/2015
2089	5*10^177016-37	177017	Robert Price	11/2021
2090	fibonacci(846926)-4	176997	Jon Grantham	08/2023
2091	(23*10^176964-47)/3	176965	Robert Price	09/2019
2092	20530^41031+41031^20530	176942	Norbert Schneider	07/2022
2093	(19*10^176932+521)/9	176933	Robert Price	05/2018
2094	(8*10^176908+43)/3	176909	Robert Price	06/2018
2095	(85*10^176900+203)/9	176901	Robert Price	09/2020
2096	2^587560-113699	176874	Enzo Doria	09/2014
2097	20596^40995+40995^20596	176844	Norbert Schneider	07/2022
2098	(101*10^176815-17)/3	176817	Robert Price	02/2020
2099	(25*10^176715-37)/3	176716	Robert Price	10/2019
2100	5^252763-12862	176674	Enzo Doria	05/2014
2101	38442^38531+38531^38442	176658	Norbert Schneider	09/2022
2102	2^586804+81721	176646	Enzo Doria	08/2016
2103	(10^176584+77)/3	176584	Robert Price	01/2018
2104	2^586570+1874419	176576	Enzo Doria	06/2016
2105	(157*10^176482-1)/3	176484	Robert Price	01/2022
2106	5*2^586202+3	176466	Jon Grantham	07/2023
2107	2^585994-3311	176402	Yves Minet	12/2014
2108	8*10^176383-81	176384	Robert Price	02/2021
2109	(23*10^176357+61)/3	176358	Robert Price	01/2022
2110	2^585832-112799	176354	Enzo Doria	07/2014
2111	fibonacci(843383)+4	176257	Jon Grantham	08/2023
2112	(29*10^176240+49)/3	176241	Robert Price	09/2021
2113	(2^585387-11)/3	176219	Stefano Morozzi	08/2022
2114	2^585336-461039	176204	Enzo Doria	06/2015
2115	(25*10^176164+143)/3	176165	Robert Price	08/2020
2116	2^585095-1848127	176132	Enzo Doria	08/2015
2117	(5*10^176101-311)/9	176101	Robert Price	12/2021
2118	6*10^176092+77	176093	Robert Price	06/2020
2119	2^584950-115451	176088	Enzo Doria	07/2015
2120	(646*10^176044+11)/9	176046	Robert Price	10/2021
2121	(7^208283-5^208283)/2	176020	Jon Grantham	08/2023
2122	2^584671-3697	176004	Yves Minet	03/2017
2123	(13*10^175965-37)/3	175966	Robert Price	01/2019
2124	2*10^175860-87	175861	Robert Price	04/2018
2125	(86*10^175774-221)/9	175775	Robert Price	09/2019
2126	9*10^175654+47	175655	Robert Price	01/2022
2127	10^175608+2971	175609	Mike Oakes	05/2010
2128	10^175608-55829	175608	Patrick De Geest	09/2013
2129	2^583051+1879793	175516	Enzo Doria	09/2016
2130	(76*10^175514+491)/9	175515	Robert Price	10/2021
2131	2^582860-23829	175459	Enzo Doria	08/2013
2132	(8*10^175428-53)/9	175428	Serge Batalov	11/2022
2133	(28*10^175417-67)/3	175418	Robert Price	10/2020
2134	2^582670-23913	175402	Enzo Doria	08/2013
2135	2^582573-29563	175372	Enzo Doria	08/2015
2136	2^582435-1862767	175331	Enzo Doria	12/2015
2137	10^175295-40000001	175295	Robert Price	07/2022
2138	(11*10^175250-149)/3	175251	Robert Price	09/2018
2139	(29*10^175236+31)/3	175237	Robert Price	04/2021
2140	2^582072-1848599	175222	Enzo Doria	08/2015
2141	(404267#+465)/(3^45^231)	175208	Makoto Morimoto	06/2019
2142	Phi(262767,10)/259613797	175168	Makoto Kamada	12/2022
2143	(2^581871-15)/7	175160	Stefano Morozzi	08/2022
2144	(5*10^175117-311)/9	175117	Robert Price	12/2021
2145	(220221^32768+1)/2	175075	Serge Batalov	03/2018
2146	2^581560+1874911	175068	Enzo Doria	06/2016
2147	(25*10^174987-97)/9	174988	Robert Price	01/2022
2148	(75^93307-1)/74	174955	Paul Bourdelais	09/2017
2149	(47*10^174790+493)/9	174791	Robert Price	03/2019
2150	2^580528-114035	174757	Enzo Doria	11/2014
2151	(19*10^174754+737)/9	174755	Robert Price	07/2018
2152	(35*10^174704-377)/9	174705	Robert Price	07/2018
2153	(49*10^174681+293)/9	174682	Robert Price	03/2021
2154	6*10^174681+11	174682	Robert Price	07/2022
2155	3*10^174665-97	174666	Robert Price	07/2018
2156	2^580046-459161	174612	Enzo Doria	05/2015
2157	2^579992-39779	174595	Enzo Doria	09/2015
2158	(29*10^174481-149)/3	174482	Robert Price	08/2022
2159	(4*10^174423+101)/3	174424	Robert Price	11/2021
2160	(2^579371-17)/3	174408	Stefano Morozzi	08/2022
2161	(2*10^174301-71)/3	174301	Robert Price	12/2017
2162	14^152048+3	174267	Paul Bourdelais	12/2020
2163	(2^578696+1)/257	174203	Lelio R Paula	09/2015
2164	2^578656-1851809	174193	Enzo Doria	08/2015
2165	2^578583-113917	174171	Enzo Doria	10/2014
2166	2^578434-83	174126	Yves Minet	07/2017
2167	15^148048-2	174118	Robert Price	06/2015
2168	5*10^174101+81	174102	Robert Price	03/2019
2169	2^578346+2794249	174100	Enzo Doria	03/2016
2170	10^173947+1372429	173948	Patrick De Geest	08/2021
2172	10^173947-500000001	173947	Robert Price	12/2020
2171	10^173947-286391	173947	Patrick De Geest	08/2021
2173	5*10^173904-13	173905	Robert Price	01/2019
2174	(8*10^173862-59)/3	173863	Robert Price	08/2021
2175	(71*10^173854-287)/9	173855	Robert Price	09/2019
2176	(43*10^173826+101)/9	173827	Robert Price	11/2018
2177	2*10^173809-87	173810	Robert Price	04/2018
2178	(2^577372-23)/7	173806	Stefano Morozzi	08/2022
2179	(L!41532)/2	173772	Serge Batalov	07/2017
2180	2^577146-49877	173739	Enzo Doria	10/2015
2181	2^576889+49727	173661	Enzo Doria	09/2016
2182	(167*10^173571-17)/3	173573	Robert Price	03/2020
2183	37803^37916+37916^37803	173562	Norbert Schneider	06/2022
2184	5*10^173534+29	173535	Robert Price	12/2020
2185	(2^576551-1)/4612409/64758208321/242584327930759	173528	Dario Alpern	06/2014
2186	4*10^173509+99	173510	Robert Price	12/2020
2187	(13*10^173467-37)/3	173468	Robert Price	01/2019
2188	2^576016-113919	173399	Enzo Doria	11/2014
2189	2^575911-1849387	173367	Enzo Doria	08/2015
2190	515^63898+63898^515	173280	Norbert Schneider	12/2022
2191	2^575614+9	173278	Stefano Morozzi	04/2021
2192	(16*10^173251+107)/3	173252	Robert Price	03/2019
2193	2^575196-114053	173152	Enzo Doria	11/2014
2194	7*10^173135-53	173136	Robert Price	06/2020
2195	(301*10^173047+23)/9	173049	Robert Price	06/2021
2196	2^574591-115387	172970	Enzo Doria	07/2015
2197	(202*10^172940-13)/9	172942	Robert Price	01/2020
2198	45^104608+104608^45	172940	Norbert Schneider	06/2021
2199	2^574328+81121	172890	Enzo Doria	07/2016
2200	(115*10^172862-1)/3	172864	Serge Batalov	12/2014
2201	3*10^172812+13	172813	Robert Price	07/2018
2202	4*5^247217-9	172798	Lelio R Paula	10/2015
2203	6*10^172772-31	172773	Robert Price	07/2020
2204	69061#+(467617#)/(69061#)	172766	Makoto Morimoto	10/2017
2205	(34*10^172693-547)/9	172694	Robert Price	03/2021
2206	5*10^172692+57	172693	Robert Price	12/2018
2207	2^573668-2782319	172692	Enzo Doria	09/2015
2208	2^573444-1855109	172624	Enzo Doria	09/2015
2209	(14*10^172532-29)/3	172533	Robert Price	09/2021
2210	3^361608+2	172531	Robert Price	08/2014
2211	(54^99563+1)/55	172481	Paul Bourdelais	11/2017
2212	2^572592-114893	172368	Enzo Doria	05/2015
2213	4*10^172354-39	172355	Robert Price	09/2020
2214	37535^37674+37674^37535	172338	Norbert Schneider	05/2022
2215	(11*10^172322-119)/9	172323	Robert Price	11/2021
2216	5^246497-4^246497	172295	Jean-Louis Charton	11/2008
2217	(38^109037-1)/37	172254	Paul Bourdelais	10/2017
2218	(4*10^172241+89)/3	172242	Robert Price	08/2021
2219	3*10^172219+73	172220	Robert Price	08/2018
2220	A352736(15)	172032	Kellen Shenton	05/2022
2221	(36^110503+1)/37	171975	Lelio R Paula	04/2017
2222	8*10^171934+71	171935	Robert Price	05/2022
2223	(11*10^171933+601)/9	171934	Robert Price	02/2022
2224	(22*10^171929-73)/3	171930	Robert Price	04/2019
2225	(49*10^171892-319)/9	171893	Robert Price	10/2021
2226	4*10^171891-63	171892	Robert Price	10/2018
2227	67*10^171882-9	171884	Robert Price	03/2021
2228	2^570980-2782289	171883	Enzo Doria	09/2015
2229	(25*10^171849-37)/3	171850	Robert Price	10/2019
2230	10^171832+387909	171833	Patrick De Geest	08/2021
2231	10^171832-10001	171832	Robert Price	02/2021
2233	(2^(12*47563+13)-9)/7	171818	Kevin Acres	11/2013
2232	(2^570769-9)/7	171818	Stefano Morozzi	08/2022
2234	(74*10^171651-29)/9	171652	Robert Price	06/2022
2235	(536*10^171601-23)/9	171603	Robert Price	02/2020
2236	7*10^171535-99	171536	Robert Price	06/2019
2237	(28*10^171534+101)/3	171535	Robert Price	09/2020
2238	2^569563-1854607	171456	Enzo Doria	09/2015
2239	3*10^171391+59	171392	Robert Price	08/2018
2240	(13*10^171306-37)/3	171307	Robert Price	01/2019
2241	8*10^171296+87	171297	Robert Price	10/2019
2242	(55^98419-1)/54	171284	Paul Bourdelais	12/2017
2243	(29*10^171275+67)/3	171276	Robert Price	12/2019
2244	(457*10^171248-7)/9	171250	Robert Price	09/2022
2245	(194*10^171193+1)/3	171195	Robert Price	01/2022
2246	2^568642+1876129	171179	Enzo Doria	07/2016
2247	4*10^171146-47	171147	Robert Price	10/2021
2248	(19*10^170970+131)/3	170971	Robert Price	06/2020
2249	(46*10^170932+143)/9	170933	Robert Price	01/2019
2250	(79*10^170901-1)/3	170903	Robert Price	02/2020

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Probable Primes Top 10000

(293510 PRPs in the top)