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	2^707277+28997	212912	Enzo Doria	02/2024
2002	(163*10^212779-1)/9	212781	Serge Batalov	12/2014
2003	2^706838-69041	212780	Enzo Doria	11/2015
2004	2^705653+25907	212423	Enzo Doria	12/2023
2005	22*10^212339+7	212341	Robert Price	10/2022
2006	2^704577-113871	212099	Enzo Doria	10/2014
2007	(2^704548-19)/3	212090	Stefano Morozzi	08/2022
2008	2^704110-2792441	211959	Enzo Doria	02/2016
2009	2^704084+28531	211951	Enzo Doria	02/2024
2010	2^703943-1862947	211908	Enzo Doria	12/2015
2011	(60^119083+1)/61	211746	Paul Bourdelais	10/2018
2012	(184*10^211682-1)/3	211684	Robert Price	12/2022
2013	(10^211610-91)/9	211610	Serge Batalov	12/2014
2014	227^89797+2	211565	Lelio R Paula	08/2012
2015	2^702194-3	211382	Paul Bourdelais	03/2012
2016	2^702064+1874911	211343	Enzo Doria	07/2016
2017	2^701968-113873	211314	Enzo Doria	10/2014
2018	(14*10^211262-41)/9	211263	Serge Batalov	01/2023
2019	2^701713-113779	211237	Enzo Doria	09/2014
2020	2^701616-216803	211208	Enzo Doria	01/2024
2021	2^701449-25201	211158	Enzo Doria	09/2013
2022	2^701403-2786977	211144	Enzo Doria	11/2015
2023	2^701189-25423	211079	Enzo Doria	09/2013
2024	2^701162-459161	211071	Enzo Doria	05/2015
2025	2^700793+219407	210960	Enzo Doria	03/2024
2026	(24^152783-1)/23	210872	Paul Bourdelais	04/2018
2027	2^700400+9385	210842	Lelio R Paula	01/2014
2028	2^700304-17	210813	Stefano Morozzi	07/2022
2029	2^700131+1874693	210761	Enzo Doria	06/2016
2030	(2^700095+225414)/2	210750	Stefano Morozzi	04/2020
2031	(2^700090+278254)/2	210748	Stefano Morozzi	04/2020
2032	(2^700075+303666)/2	210744	Stefano Morozzi	04/2020
2033	(2^700073+75882)/2	210743	Stefano Morozzi	04/2020
2034	(2^700074+328890)/2	210743	Stefano Morozzi	04/2020
2035	(2^700052+79162)/2	210737	Stefano Morozzi	04/2020
2036	(2^700052+304458)/2	210737	Stefano Morozzi	04/2020
2037	(2^700048+376578)/2	210736	Stefano Morozzi	04/2020
2038	11^202357-1140	210734	Enzo Doria	12/2012
2039	(2^700021+25874)/2	210728	Stefano Morozzi	04/2020
2040	(2^700018+377518)/2	210727	Stefano Morozzi	04/2020
2041	2^699999+300729	210721	Norman Luhn	09/2023
2042	(238*10^210712-1)/3	210714	Robert Price	09/2023
2043	2^699740+25	210643	Stefano Morozzi	05/2021
2044	(23*10^210525-143)/3	210526	Robert Price	12/2023
2045	2^698929-2788423	210399	Enzo Doria	11/2015
2046	(5^300893+4^300893)/9	210315	Jean-Louis Charton	11/2011
2047	2^698316+1878601	210215	Enzo Doria	08/2016
2048	34*10^210097-9	210099	Robert Price	05/2023
2049	(19*10^210011-49)/3	210012	Robert Price	06/2023
2050	6*10^209846-91	209847	Robert Price	05/2023
2051	2^697036+1878751	209829	Enzo Doria	08/2016
2052	2^696813+28607	209762	Enzo Doria	02/2024
2053	(238*10^209715-1)/3	209717	Robert Price	09/2023
2054	6^269407+5	209640	Paul Bourdelais	02/2021
2055	(2^696343-1)/11141489/36009913139329	209600	Tony Prest / Never Odd Or Even	02/2014
2056	2^696254-115151	209594	Enzo Doria	06/2015
2057	2^695841+225	209470	Henri Lifchitz	01/2025
2058	(35^135623+1)/36	209410	Paul Bourdelais	07/2018
2059	7*10^209161+39	209162	Robert Price	01/2023
2060	2^694633+1887257	209106	Enzo Doria	05/2017
2061	fibonacci(999790)-4	208944	Jon Grantham	08/2023
2062	2^693959+180923	208903	Enzo Doria	07/2016
2063	(2^693747-11)/3	208839	Stefano Morozzi	08/2022
2064	2^693462-1847561	208753	Enzo Doria	07/2015
2065	2^690890-59981	207979	Enzo Doria	11/2015
2066	(38^131591+1)/39	207884	Paul Bourdelais	07/2018
2067	3*2^690484+5	207857	Jon Grantham	07/2023
2068	2^690163+1877063	207760	Enzo Doria	07/2016
2069	7^245608-2	207563	Paul Bourdelais	01/2021
2070	(67*10^207556+23)/9	207557	Serge Batalov	01/2023
2071	2^689286-29381	207496	Enzo Doria	08/2015
2072	2^689122-114521	207447	Enzo Doria	04/2015
2073	9*10^207254-89	207255	Robert Price	02/2023
2074	2^688373+6077	207221	Enzo Doria	02/2016
2075	2^688201+1875527	207170	Enzo Doria	07/2016
2076	(42^127609+1)/43	207140	Paul Bourdelais	07/2018
2077	2^687938+213589	207090	Enzo Doria	10/2023
2078	2^687619+81563	206994	Enzo Doria	08/2016
2079	3*10^206927+37	206928	Robert Price	08/2023
2080	2^687383+21803	206923	Enzo Doria	09/2023
2081	(11*10^206688+19)/3	206689	Robert Price	07/2024
2082	2^686572-1845299	206679	Enzo Doria	07/2015
2083	(21^156217-1)/20	206552	Paul Bourdelais	04/2010
2084	2^685970+39415	206498	Enzo Doria	11/2024
2085	(2^685739+1)/(3*87774593)	206420	Gord Palameta	08/2018
2086	2^685578+3	206380	Paul Bourdelais	04/2012
2087	2^685078+218599	206230	Enzo Doria	01/2024
2088	2^684836-49349	206157	Enzo Doria	10/2015
2089	(73^110603-1)/72	206088	Paul Bourdelais	06/2018
2090	2^684163-2790967	205954	Enzo Doria	12/2015
2091	326^81943-325^81943	205941	Jean-Louis Charton	07/2012
2092	(2^684127-1)/23765203727	205933	Jens K. Andersen	04/2009
2093	(68*10^205510+13)/9	205511	Serge Batalov	01/2023
2094	4^341233-3^341233	205443	Jean-Louis Charton	01/2006
2095	2^682414+215029	205428	Enzo Doria	11/2023
2096	(963^68821-1)/962	205334	Jinyuan Wang	01/2024
2097	(43*10^205183-421)/9	205184	Robert Price	10/2023
2098	2^681545+467	205166	Lelio R Paula	11/2013
2099	2^681306+81049	205094	Enzo Doria	07/2016
2100	2^680697+1877057	204911	Enzo Doria	07/2016
2101	2^680415+71783	204826	Enzo Doria	04/2016
2102	10^204764-8001	204764	Robert Price	03/2023
2103	(26*10^204730-77)/3	204731	Robert Price	03/2023
2104	2^679860-459995	204659	Enzo Doria	06/2015
2105	2^679593+1879547	204578	Enzo Doria	09/2016
2106	2^678899+220073	204369	Enzo Doria	03/2024
2107	2^678753+21677	204326	Enzo Doria	08/2023
2108	2^678651+1875023	204295	Enzo Doria	07/2016
2109	2^678561+678561	204268	Henri Lifchitz	05/2006
2110	5*3^427884+2^427884	204154	Jon Grantham	08/2023
2111	2^678101-114043	204129	Enzo Doria	11/2014
2112	2^678028+1875631	204107	Enzo Doria	06/2016
2113	2^677721+28607	204015	Enzo Doria	01/2024
2114	(19*10^203798-7)/3	203799	Robert Price	12/2023
2115	2^676992-59783	203795	Enzo Doria	10/2015
2116	2^676972+1866871	203789	Enzo Doria	03/2016
2117	2^676815+22583	203742	Enzo Doria	09/2023
2118	2^676761-9	203726	Robert Price	01/2017
2119	2^676592-23	203675	Stefano Morozzi	07/2022
2120	2^676563-2792407	203666	Enzo Doria	02/2016
2121	2^676306-114713	203589	Enzo Doria	04/2015
2122	(2^675977-1)/(1686378749257*7171117283326998925471)	203456	Dario Alpern	07/2015
2123	6*10^203365+53	203366	Robert Price	09/2023
2124	10247^50678-50678^10247	203250	Norbert Schneider	03/2022
2125	2^675106-73241	203228	Stefano Morozzi	02/2025
2126	2^675103-188727	203227	Stefano Morozzi	02/2025
2127	2^675104-16199	203227	Stefano Morozzi	02/2025
2128	2^675104-195303	203227	Stefano Morozzi	02/2025
2129	2^675105-94521	203227	Stefano Morozzi	02/2025
2130	2^675100-2775	203226	Stefano Morozzi	02/2025
2131	2^675098-170703	203225	Stefano Morozzi	02/2025
2132	2^675093-162123	203224	Stefano Morozzi	02/2025
2133	2^675093-48955	203224	Stefano Morozzi	02/2025
2134	2^675095-73591	203224	Stefano Morozzi	02/2025
2135	2^675095-89937	203224	Stefano Morozzi	02/2025
2136	2^675092-144539	203223	Stefano Morozzi	02/2025
2137	2^675086-186387	203222	Stefano Morozzi	02/2025
2138	2^675088-68505	203222	Stefano Morozzi	02/2025
2139	2^675083-149199	203221	Stefano Morozzi	02/2025
2140	2^675081-91425	203220	Stefano Morozzi	02/2025
2141	2^675082-80213	203220	Stefano Morozzi	02/2025
2142	2^675077-152683	203219	Stefano Morozzi	02/2025
2143	2^675077-79213	203219	Stefano Morozzi	02/2025
2144	2^675073-149065	203218	Stefano Morozzi	02/2025
2145	2^675073-19663	203218	Stefano Morozzi	02/2025
2146	2^675069-147135	203217	Stefano Morozzi	02/2025
2147	2^675069-161461	203217	Stefano Morozzi	02/2025
2148	2^675071-175189	203217	Stefano Morozzi	02/2025
2149	2^675060+119983	203214	Stefano Morozzi	02/2025
2150	2^675060+161301	203214	Stefano Morozzi	02/2025
2151	2^675061-187773	203214	Stefano Morozzi	02/2025
2152	2^675062-92193	203214	Stefano Morozzi	02/2025
2153	2^675058-10403	203213	Stefano Morozzi	01/2025
2154	2^675058-40337	203213	Stefano Morozzi	01/2025
2155	2^675057+123557	203213	Stefano Morozzi	02/2025
2156	2^675057+172475	203213	Stefano Morozzi	02/2025
2157	2^675053-4801	203212	Stefano Morozzi	01/2025
2158	2^675054-174341	203212	Stefano Morozzi	01/2025
2159	2^675054-53697	203212	Stefano Morozzi	01/2025
2160	2^675054+24825	203212	Stefano Morozzi	02/2025
2161	2^675055+160265	203212	Stefano Morozzi	02/2025
2162	2^675050-30015	203211	Stefano Morozzi	01/2025
2163	2^675051-85941	203211	Stefano Morozzi	01/2025
2164	2^675051+30885	203211	Stefano Morozzi	02/2025
2165	2^675052+12537	203211	Stefano Morozzi	02/2025
2166	2^675047-100299	203210	Stefano Morozzi	01/2025
2167	2^675048-97313	203210	Stefano Morozzi	01/2025
2168	2^675046+118119	203210	Stefano Morozzi	02/2025
2169	2^675048+128941	203210	Stefano Morozzi	02/2025
2170	2^675049+136359	203210	Stefano Morozzi	02/2025
2171	2^675044-81087	203209	Stefano Morozzi	01/2025
2172	2^675042-179811	203208	Stefano Morozzi	01/2025
2173	2^675036-192939	203207	Stefano Morozzi	01/2025
2174	2^675037-17853	203207	Stefano Morozzi	01/2025
2175	2^675036+47101	203207	Stefano Morozzi	02/2025
2176	2^675038+189589	203207	Stefano Morozzi	02/2025
2177	2^675034-169727	203206	Stefano Morozzi	01/2025
2178	2^675035-173055	203206	Stefano Morozzi	01/2025
2179	2^675035-73551	203206	Stefano Morozzi	01/2025
2180	2^675033+79109	203206	Stefano Morozzi	02/2025
2181	2^675034+154057	203206	Stefano Morozzi	02/2025
2182	2^675030+109245	203205	Stefano Morozzi	01/2025
2183	2^675030-160047	203205	Stefano Morozzi	01/2025
2184	2^675027+106733	203204	Stefano Morozzi	01/2025
2185	2^675026-67377	203204	Stefano Morozzi	01/2025
2186	2^675021+13335	203202	Stefano Morozzi	01/2025
2187	2^675020-180497	203202	Stefano Morozzi	01/2025
2188	2^675016+174777	203201	Stefano Morozzi	01/2025
2189	2^675017+128379	203201	Stefano Morozzi	01/2025
2190	2^675017+171249	203201	Stefano Morozzi	01/2025
2191	2^675018+86517	203201	Stefano Morozzi	01/2025
2192	2^675019+125891	203201	Stefano Morozzi	01/2025
2193	2^675019+163251	203201	Stefano Morozzi	01/2025
2194	2^675016-170847	203201	Stefano Morozzi	01/2025
2195	2^675019-44755	203201	Stefano Morozzi	01/2025
2196	2^675015+120225	203200	Stefano Morozzi	01/2025
2197	2^675013-69831	203200	Stefano Morozzi	01/2025
2198	2^675014-3897	203200	Stefano Morozzi	01/2025
2199	2^675006+75357	203198	Stefano Morozzi	01/2025
2200	2^675008+112231	203198	Stefano Morozzi	01/2025
2201	2^675007-123309	203198	Stefano Morozzi	01/2025
2202	2^675003+52529	203197	Stefano Morozzi	01/2025
2203	2^675002+50595	203196	Stefano Morozzi	01/2025
2204	2^674627-25161	203083	Enzo Doria	09/2013
2205	2^674603-69337	203076	Enzo Doria	12/2015
2206	(182*10^203048+1)/3	203050	Robert Price	09/2023
2207	2^674459+74213	203033	Enzo Doria	04/2016
2208	2^674116-458879	202930	Enzo Doria	04/2015
2209	2^674076-114755	202918	Enzo Doria	04/2015
2210	5^289937-4^289937	202658	Jean-Louis Charton	03/2013
2211	5^289926-289926^5	202650	Henri Lifchitz	07/2024
2212	(2^673184-7)/3	202649	Stefano Morozzi	08/2022
2213	(467617#+14534)/(2^21343)	202603	Makoto Morimoto	06/2019
2214	(155^92479-1)/154	202558	Anonymous	06/2024
2215	2^672773+219407	202525	Enzo Doria	03/2024
2216	1374^64531-64531^1374	202498	Henri Lifchitz	10/2024
2217	2^672556-1835519	202460	Enzo Doria	04/2015
2218	(7*10^202267+179)/3	202268	Robert Price	02/2023
2219	2^671446-351401	202126	Enzo Doria	07/2015
2220	2^671373+77747	202104	Enzo Doria	05/2016
2221	(2*10^202059+7)/9	202059	Rytis Slatkevicius	01/2023
2222	98*10^202021-9	202023	Robert Price	05/2023
2223	2^670726-114845	201909	Enzo Doria	05/2015
2224	2^670539-25045	201853	Enzo Doria	09/2013
2225	10^201801-93	201801	Robert Price	02/2023
2226	43284^43519-43519^43284	201769	Norbert Schneider	08/2018
2227	2^670213+282317	201755	Enzo Doria	09/2016
2228	2^670133+89	201731	Stefano Morozzi	05/2021
2229	2^669854-113501	201647	Enzo Doria	08/2014
2230	2^669718+81619	201606	Enzo Doria	08/2016
2231	(299*10^201547-17)/3	201549	Robert Price	02/2023
2232	(145*10^201504-1)/9	201506	Serge Batalov	12/2014
2233	2^668938-1839821	201371	Enzo Doria	06/2015
2234	(198^87623-1)/197	201239	Anonymous	06/2024
2235	2^668492+1879303	201237	Enzo Doria	08/2016
2236	7*10^201140-87	201141	Robert Price	03/2023
2237	6^258413-5^258413	201085	Jean-Louis Charton	03/2013
2238	10194^50161-50161^10194	201063	Norbert Schneider	09/2020
2239	2^667894+1875589	201057	Enzo Doria	06/2016
2240	2^667569-1836559	200959	Enzo Doria	05/2015
2241	(172*10^200746-1)/9	200748	Serge Batalov	12/2014
2242	(166^90407-1)/165	200712	Anonymous	06/2024
2243	2^666430+782569	200616	Enzo Doria	10/2016
2244	(13*10^200610-43)/3	200611	Robert Price	08/2023
2245	(8*10^200408-11)/3	200409	Robert Price	07/2023
2246	p(38635)#-p(38635+1)	200356	Henri Lifchitz	11/2024
2247	(19*10^200260+101)/3	200261	Robert Price	06/2023
2248	43183^43183+4^4	200167	Serge Batalov	04/2024
2249	(86^103471+1)/87	200163	Paul Bourdelais	05/2018
2250	(10^(2100072+1)+3610^100072-1)/9	200145	Robert Price	09/2023

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