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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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	2^804277-417933	242112	Enzo Doria	01/2014
2002	2^803468-269039	241868	Enzo Doria	10/2013
2003	2^803172+80851	241779	Enzo Doria	07/2016
2004	2^803011+220073	241731	Enzo Doria	03/2024
2005	3^506233-2	241535	Robert Price	11/2013
2006	2^802025-25999	241434	Enzo Doria	10/2013
2007	(3^505823+3^252912+1)/7	241339	Serge Batalov	03/2014
2008	2^801575+25073	241299	Enzo Doria	11/2023
2009	2^801303+1872923	241217	Enzo Doria	05/2016
2010	2^801105+216977	241157	Enzo Doria	12/2023
2011	(23*10^241048-143)/3	241049	Robert Price	12/2023
2012	2^800579-1862947	240999	Enzo Doria	12/2015
2013	2^799999+16205	240824	Norman Luhn	09/2023
2014	3^504206+2	240568	Luke W. Richards	03/2018
2015	2^798973-26283	240515	Enzo Doria	10/2013
2016	Phi(114205,3^7)	240470	Henri Lifchitz	12/2025
2017	2^798671-69487	240424	Enzo Doria	12/2015
2018	2^797220+79831	239988	Enzo Doria	06/2016
2019	2^796910-26001	239894	Enzo Doria	10/2013
2020	(97^120721-1)/811245216	239837	Paul Vanderveen	06/2025
2021	2^796598+653119	239800	Enzo Doria	12/2016
2022	2^796432-1859729	239750	Enzo Doria	11/2015
2023	2^796002-1852211	239621	Enzo Doria	08/2015
2024	2^795884+214081	239585	Enzo Doria	10/2023
2025	2^795709+75767	239533	Enzo Doria	04/2016
2026	2^795708+81721	239532	Enzo Doria	08/2016
2027	2^795468-2786249	239460	Enzo Doria	10/2015
2028	2^795442+80779	239452	Enzo Doria	07/2016
2029	2^795075-1852057	239342	Enzo Doria	08/2015
2030	(86^123677+1)/87	239252	Paul Bourdelais	01/2019
2031	2^794043+1875023	239031	Enzo Doria	06/2016
2032	2^793347-69577	238822	Enzo Doria	01/2016
2033	5*2^793288+3	238805	Jon Grantham	07/2023
2034	2^792988-344429	238714	Enzo Doria	08/2015
2035	2^792700-2786369	238627	Enzo Doria	11/2015
2036	2^792663-1844797	238616	Enzo Doria	06/2015
2037	2^792605-291943	238598	Enzo Doria	07/2015
2038	2^792366+218599	238526	Enzo Doria	01/2024
2039	(2^792061-2^396031+1)/5	238434	Thomas Ritschel	03/2014
2040	2^791321+30077	238212	Enzo Doria	03/2024
2041	4*10^238163+21	238164	Robert Price	12/2022
2042	(26*10^238157-77)/3	238158	Robert Price	03/2023
2043	10^237670+9	237671	Robert Price	08/2023
2044	2^789373+1869377	237625	Enzo Doria	05/2016
2045	((10^59387+1)^3(10^59387+1+10^29694)-(10^118774+10^59387)(10^29694-1)+10^178161)/27961	237544	Serge Batalov	04/2015
2046	Phi(1187740M,10)	237544	Anonymous	03/2025
2047	2^789033+218537	237523	Enzo Doria	01/2024
2048	2^788942+1866409	237496	Enzo Doria	02/2016
2049	2^788844-114329	237466	Enzo Doria	01/2015
2050	2^788705-1859713	237424	Enzo Doria	11/2015
2051	2^788325+224789	237310	Enzo Doria	07/2024
2052	15^201475+14	236953	Alfred Reich	10/2023
2053	2^786663+219173	236810	Enzo Doria	02/2024
2054	2^786180+1871971	236664	Enzo Doria	05/2016
2055	11^227092-90	236492	Enzo Doria	11/2012
2056	2^785260+1866361	236387	Enzo Doria	02/2016
2057	2^785220+1880611	236375	Enzo Doria	10/2016
2058	(2^784689-15)/7	236215	Stefano Morozzi	08/2022
2059	19^184650-2	236122	Robert Price	10/2014
2060	10^236059+216513	236060	Patrick De Geest	04/2016
2061	10^236059-20909	236059	Robert Price	09/2015
2062	2^783988+38011	236004	Enzo Doria	10/2024
2063	2^783893-21	235976	Stefano Morozzi	07/2022
2064	(47^140983-1)/2792206142311142462	235719	Paul Vanderveen	06/2025
2065	2^782821+37577	235653	Enzo Doria	10/2024
2066	(87^121487-1)/86	235625	Paul Bourdelais	12/2018
2067	2^782634-113981	235597	Enzo Doria	11/2014
2068	2^782423+1879733	235533	Enzo Doria	09/2016
2069	(10^(2117707+1)+1210^117707-1)/3	235415	Robert Price	10/2023
2070	(2^781970)/(781970^2)	235385	Henri Lifchitz	06/2025
2071	2^781682-2789543	235310	Enzo Doria	12/2015
2072	2^780481+21489	234949	Enzo Doria	05/2024
2073	2^780408-113453	234927	Enzo Doria	08/2014
2074	7*10^234915+9	234916	Robert Price	04/2023
2075	2^780368-1864829	234915	Enzo Doria	01/2016
2076	2^780284+7	234889	Jon Grantham	08/2023
2077	2^779593-1836559	234681	Enzo Doria	05/2015
2078	(8713#+(549391#)/(8713#))/360295171	234487	Makoto Morimoto	11/2017
2079	(5^335429+1)/6	234455	Paul Bourdelais	08/2010
2080	2^778788+22201	234439	Enzo Doria	09/2023
2081	2^778395-113617	234321	Enzo Doria	08/2014
2082	5*2^778090+3	234230	Jon Grantham	07/2023
2083	(21430^54289-1)/(21430^233-1)	234118	Ryan Propper	11/2023
2084	(5*10^234054-101)/3	234055	Robert Price	08/2023
2085	23*10^234025-7	234027	Robert Price	10/2022
2086	2^777170+21489	233952	Enzo Doria	05/2024
2087	Phi(78125,5517)	233857	Anonymous	09/2022
2088	5^334359-3^334359-1	233707	Jon Grantham	08/2023
2089	2^776245-2792353	233674	Enzo Doria	02/2016
2090	49748^49748+49735^49735	233656	Henri Lifchitz	11/2024
2091	2^776060-114029	233618	Enzo Doria	11/2014
2092	2^775987-2789557	233596	Enzo Doria	12/2015
2093	2*10^233564-91	233565	Robert Price	02/2023
2094	2^775865+21489	233559	Enzo Doria	05/2024
2095	2^775672+1866721	233501	Enzo Doria	03/2016
2096	2^775238+57	233370	Stefano Morozzi	05/2021
2097	(11^223999+1)/12	233270	Paul Bourdelais	02/2010
2098	U(1302049)	233238	Serge Batalov	07/2024
2099	2^774118+1885789	233033	Enzo Doria	04/2017
2100	21^176191-20^176191	232964	Jean-Louis Charton	01/2015
2101	2^773723+217523	232914	Enzo Doria	01/2024
2102	2^773679-113425	232901	Enzo Doria	08/2014
2103	11*17^189085+232	232661	Eric Chen	01/2026
2104	(7*10^232620+23)/3	232621	Robert Price	05/2023
2105	10^232599+192489	232600	Patrick De Geest	12/2013
2106	10^232599-3	232599	Markus Tervooren	10/2010
2107	2^772552-458879	232562	Enzo Doria	04/2015
2108	2^772214+1874899	232460	Enzo Doria	06/2016
2109	2^771994-1862771	232394	Enzo Doria	12/2015
2110	2^771889+1876037	232362	Enzo Doria	07/2016
2111	2^771660+1866511	232293	Enzo Doria	02/2016
2112	5^332150-18188	232163	Enzo Doria	06/2014
2113	2^771227+61121	232163	Boyan Hu	05/2024
2114	2^770623+212543	231981	Enzo Doria	09/2023
2115	3^485977-2^485977	231870	Mike Oakes	09/2009
2116	2^770082-114161	231818	Enzo Doria	01/2015
2117	2^769791+25523	231731	Enzo Doria	11/2023
2118	7^274120-2	231659	Paul Bourdelais	08/2023
2119	(20^177967+1)/21	231540	Paul Bourdelais	05/2013
2120	2^769011+81	231496	Henri Lifchitz	01/2025
2121	(71^125029-1)/105024430	231453	Paul Vanderveen	06/2025
2122	(4*10^231254+23)/9	231254	Serge Batalov	11/2022
2123	2^768205+22217	231253	Enzo Doria	09/2023
2124	49262^49262-49247^49247	231163	Henri Lifchitz	11/2024
2125	2^767622-9221	231078	Lelio R Paula	01/2016
2126	2^767344+1880311	230994	Enzo Doria	09/2016
2127	8*10^230921-13	230922	Robert Price	08/2023
2128	(3^483611-1)/2	230741	Paul Bourdelais	02/2010
2129	(10^230706+179)/9	230706	Serge Batalov	12/2014
2130	2^766309+1875257	230682	Enzo Doria	06/2016
2131	(26131^52441-1)/(26131^229-1)	230629	Ryan Propper	11/2023
2132	2^765635+1879883	230480	Enzo Doria	09/2016
2133	43^141090+141090	230467	Kellen Shenton	06/2023
2134	(26*10^230394-119)/3	230395	Robert Price	07/2023
2135	2^764348-113697	230092	Enzo Doria	09/2014
2136	2^764131+78863	230027	Enzo Doria	05/2016
2137	2^763701+60197	229897	Enzo Doria	03/2016
2138	4*10^229836+21	229837	Robert Price	12/2022
2139	2^763362+27799	229795	Enzo Doria	01/2024
2140	2^762841-25905	229639	Enzo Doria	10/2013
2141	2^762659+212633	229584	Enzo Doria	09/2023
2142	77*10^229211+3	229213	Robert Price	11/2023
2143	2^761117-113569	229120	Enzo Doria	08/2014
2144	(29022^51529-1)/(29022^227-1)	228947	Ryan Propper	11/2023
2145	(98^114859+1)/99	228709	Paul Bourdelais	12/2018
2146	5*3^479067-2^479067	228574	Jon Grantham	08/2023
2147	2^758645+216011	228375	Enzo Doria	12/2023
2148	(2^758231+1)/(32714694297653973236839266867)	228223	Gord Palameta	12/2018
2149	10^228208+111	228209	Boyan Hu	10/2024
2150	(298*10^228177-7)/3	228179	Robert Price	02/2023
2151	2^757985-2790013	228177	Enzo Doria	12/2015
2152	34*10^228129-9	228131	Robert Price	05/2023
2153	2^757038-1862081	227892	Enzo Doria	12/2015
2154	2^756839+95849	227832	Makoto Morimoto	10/2013
2156	(2^756839+6989)/756091	227826	Makoto Morimoto	09/2016
2155	(2^756839-50211)/(137*3203)	227826	Makoto Morimoto	08/2019
2157	2^756773-112723	227812	Enzo Doria	07/2014
2158	(710^(2113887+1)+9*10^113887-7)/9	227775	Robert Price	08/2024
2159	(10^227542)/(227542^10)	227489	Henri Lifchitz	05/2025
2160	524309#+616367	227431	Makoto Morimoto	02/2016
2161	2^755404+226575	227400	Enzo Doria	09/2024
2162	2^755116+81	227313	Henri Lifchitz	11/2024
2163	2^755097-114193	227307	Enzo Doria	12/2014
2164	7*10^227178+39	227179	Robert Price	01/2023
2165	9*10^227153-89	227154	Robert Price	02/2023
2166	2^754473-2791513	227120	Enzo Doria	01/2016
2167	2^754376+25	227090	Stefano Morozzi	05/2021
2168	2^754138+213289	227019	Enzo Doria	09/2023
2169	2^754038+25	226989	Stefano Morozzi	05/2021
2170	2^753263+217133	226755	Enzo Doria	12/2023
2171	7*10^226479-9	226480	Robert Price	02/2023
2172	(10^226381+1)/14973418875371	226368	Alfred Reich	06/2025
2173	2^751655+33893	226271	Enzo Doria	06/2024
2174	2^751426-764321	226202	Enzo Doria	12/2013
2175	(18^180181-1)/17	226176	Andy Steward	04/2007
2176	2^750740-3	225996	Paul Bourdelais	03/2012
2177	2^750725+60227	225991	Enzo Doria	02/2016
2178	2^750525-113743	225931	Enzo Doria	09/2014
2179	(2^750151-1)/(4299340426317590093831289397764574647511836143783478715117383638888678527263)	225744	Dario Alpern	10/2014
2180	2^749444-1861889	225606	Enzo Doria	12/2015
2181	tau(311^16452)	225560	Nik Lygeros / Olivier Rozier / LR team	10/2013
2182	(3^472721+1)/9422189991086734893916	225524	Paul Vanderveen	06/2025
2183	2^749096+1876861	225501	Enzo Doria	07/2016
2184	2^748895+26213	225440	Enzo Doria	12/2023
2185	(519643#+43033)/(2318712706283)	225379	Makoto Morimoto	08/2019
2186	2^748657+79607	225369	Enzo Doria	06/2016
2187	(2^746920-11)/5	224845	Stefano Morozzi	08/2022
2188	2^746653-291583	224765	Enzo Doria	07/2015
2189	2^746461-114043	224708	Enzo Doria	11/2014
2190	2^746302+25	224660	Stefano Morozzi	05/2021
2191	(202*10^224545-1)/3	224547	Robert Price	06/2023
2192	(19*10^224533-37)/9	224534	Alfred Reich	12/2023
2193	2^745674+213949	224471	Enzo Doria	10/2023
2194	2^745098-350471	224297	Enzo Doria	06/2015
2195	2^745039-4897	224280	Yves Minet	03/2021
2196	23*10^224232-7	224234	Robert Price	10/2022
2197	(154*10^224061-1)/9	224063	Serge Batalov	12/2014
2198	2^744211-1845787	224030	Enzo Doria	07/2015
2199	2^743773+37757	223898	Enzo Doria	10/2024
2200	2^743592-134579	223844	Hans Havermann	10/2018
2201	2^742452+3	223501	Paul Bourdelais	06/2019
2202	234178^9+9^234178	223463	Anatoly F. Selevich	07/2011
2203	47747^47747-2512^2512	223406	Henri Lifchitz	10/2024
2204	2^741651-461197	223260	Enzo Doria	07/2015
2205	10^223236-1001	223236	Robert Price	10/2022
2206	2^741362-1845251	223173	Enzo Doria	07/2015
2207	3^467546-5*2^467546	223077	Jon Grantham	08/2023
2208	2^740455-1863877	222900	Enzo Doria	12/2015
2209	2^740274+217519	222845	Enzo Doria	01/2024
2210	(14*10^222718-41)/9	222719	Serge Batalov	01/2023
2211	2^739636-2792219	222653	Enzo Doria	02/2016
2212	11^213654-180	222498	Enzo Doria	01/2013
2213	2^738957-1859743	222449	Enzo Doria	11/2015
2214	4*10^222253-21	222254	Robert Price	12/2022
2215	2^737825+57	222108	Stefano Morozzi	05/2021
2216	(54^128189+1)/55	222073	Paul Bourdelais	11/2018
2217	3^232689+1^232689+4^232689+1^232689+5^232689+9^232689	222042	Henri Lifchitz	03/2025
2218	2^737166+220099	221910	Enzo Doria	03/2024
2219	(10^221654+179)/9	221654	Serge Batalov	12/2014
2220	2^736281+79817	221643	Enzo Doria	06/2016
2221	10^221631+247617	221632	Patrick De Geest	10/2013
2222	10^221631-9	221631	Alexander Gramolin	02/2011
2223	10^221628+7	221629	Alfred Reich	04/2021
2224	2^735970-1839821	221550	Enzo Doria	06/2015
2225	2^735367+60293	221368	Enzo Doria	03/2016
2226	77*10^221343+3	221345	Robert Price	11/2023
2227	299^299^299-582	221328	Henri Lifchitz	03/2025
2228	(241^92821-1)/240	221099	Anonymous	04/2024
2229	(202*10^221092-1)/3	221094	Robert Price	06/2023
2230	(5^316297-1)/220142716	221074	Paul Vanderveen	05/2025
2231	(29^151153+1)/30	221045	Paul Bourdelais	09/2017
2232	2^734228+24751	221025	Enzo Doria	10/2023
2233	(28*10^220800+173)/3	220801	Robert Price	07/2024
2234	2^733264-2784089	220735	Enzo Doria	10/2015
2235	2^733114-24555	220690	Enzo Doria	09/2013
2236	2^731891-636259	220322	Enzo Doria	12/2013
2237	98*10^220185-9	220187	Robert Price	05/2023
2238	418319^39164+418318	220161	Alfred Reich	11/2023
2239	2^4^182829+182829^4^2	220149	Henri Lifchitz	03/2025
2240	2^731124-25539	220091	Enzo Doria	09/2013
2241	2^730972-462029	220045	Enzo Doria	07/2015
2242	2^730833+1868627	220003	Enzo Doria	04/2016
2243	2^730645-2787133	219947	Enzo Doria	11/2015
2244	2^730547-25581	219917	Enzo Doria	09/2013
2245	(113*13^197420-5)/12	219916	Anonymous	11/2022
2246	(13^197420*113-5)/12	219916	Eric Chen	10/2023
2247	2^730460+82291	219891	Enzo Doria	09/2016
2248	(5*10^219847-101)/3	219848	Robert Price	08/2023
2249	(2^730339+1)/(3278390620037943469324347)	219831	Gord Palameta	12/2018
2250	L(1051849)	219824	Renaud Lifchitz	03/2009

Find by discoverer :

PRP Records

Probable Primes Top 10000

(302601 PRPs in the top)