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	2^795468-2786249	239460	Enzo Doria	10/2015
2002	2^795442+80779	239452	Enzo Doria	07/2016
2003	2^795075-1852057	239342	Enzo Doria	08/2015
2004	(86^123677+1)/87	239252	Paul Bourdelais	01/2019
2005	2^794043+1875023	239031	Enzo Doria	06/2016
2006	2^793347-69577	238822	Enzo Doria	01/2016
2007	5*2^793288+3	238805	Jon Grantham	07/2023
2008	2^792988-344429	238714	Enzo Doria	08/2015
2009	2^792700-2786369	238627	Enzo Doria	11/2015
2010	2^792663-1844797	238616	Enzo Doria	06/2015
2011	2^792605-291943	238598	Enzo Doria	07/2015
2012	2^792366+218599	238526	Enzo Doria	01/2024
2013	(2^792061-2^396031+1)/5	238434	Thomas Ritschel	03/2014
2014	2^791321+30077	238212	Enzo Doria	03/2024
2015	4*10^238163+21	238164	Robert Price	12/2022
2016	(26*10^238157-77)/3	238158	Robert Price	03/2023
2017	10^237670+9	237671	Robert Price	08/2023
2018	2^789373+1869377	237625	Enzo Doria	05/2016
2019	((10^59387+1)^3(10^59387+1+10^29694)-(10^118774+10^59387)(10^29694-1)+10^178161)/27961	237544	Serge Batalov	04/2015
2020	Phi(1187740M,10)	237544	Anonymous	03/2025
2021	2^789033+218537	237523	Enzo Doria	01/2024
2022	2^788942+1866409	237496	Enzo Doria	02/2016
2023	2^788844-114329	237466	Enzo Doria	01/2015
2024	2^788705-1859713	237424	Enzo Doria	11/2015
2025	2^788325+224789	237310	Enzo Doria	07/2024
2026	15^201475+14	236953	Alfred Reich	10/2023
2027	2^786663+219173	236810	Enzo Doria	02/2024
2028	2^786180+1871971	236664	Enzo Doria	05/2016
2029	11^227092-90	236492	Enzo Doria	11/2012
2030	2^785260+1866361	236387	Enzo Doria	02/2016
2031	2^785220+1880611	236375	Enzo Doria	10/2016
2032	(2^784689-15)/7	236215	Stefano Morozzi	08/2022
2033	19^184650-2	236122	Robert Price	10/2014
2034	10^236059+216513	236060	Patrick De Geest	04/2016
2035	10^236059-20909	236059	Robert Price	09/2015
2036	2^783988+38011	236004	Enzo Doria	10/2024
2037	2^783893-21	235976	Stefano Morozzi	07/2022
2038	(47^140983-1)/2792206142311142462	235719	Paul Vanderveen	06/2025
2039	2^782821+37577	235653	Enzo Doria	10/2024
2040	(87^121487-1)/86	235625	Paul Bourdelais	12/2018
2041	2^782634-113981	235597	Enzo Doria	11/2014
2042	2^782423+1879733	235533	Enzo Doria	09/2016
2043	(10^(2117707+1)+1210^117707-1)/3	235415	Robert Price	10/2023
2044	(2^781970)/(781970^2)	235385	Henri Lifchitz	06/2025
2045	2^781682-2789543	235310	Enzo Doria	12/2015
2046	2^780481+21489	234949	Enzo Doria	05/2024
2047	2^780408-113453	234927	Enzo Doria	08/2014
2048	7*10^234915+9	234916	Robert Price	04/2023
2049	2^780368-1864829	234915	Enzo Doria	01/2016
2050	2^780284+7	234889	Jon Grantham	08/2023
2051	2^779593-1836559	234681	Enzo Doria	05/2015
2052	(8713#+(549391#)/(8713#))/360295171	234487	Makoto Morimoto	11/2017
2053	(5^335429+1)/6	234455	Paul Bourdelais	08/2010
2054	2^778788+22201	234439	Enzo Doria	09/2023
2055	2^778395-113617	234321	Enzo Doria	08/2014
2056	5*2^778090+3	234230	Jon Grantham	07/2023
2057	(21430^54289-1)/(21430^233-1)	234118	Ryan Propper	11/2023
2058	(5*10^234054-101)/3	234055	Robert Price	08/2023
2059	23*10^234025-7	234027	Robert Price	10/2022
2060	2^777170+21489	233952	Enzo Doria	05/2024
2061	Phi(78125,5517)	233857	Anonymous	09/2022
2062	5^334359-3^334359-1	233707	Jon Grantham	08/2023
2063	2^776245-2792353	233674	Enzo Doria	02/2016
2064	49748^49748+49735^49735	233656	Henri Lifchitz	11/2024
2065	2^776060-114029	233618	Enzo Doria	11/2014
2066	2^775987-2789557	233596	Enzo Doria	12/2015
2067	2*10^233564-91	233565	Robert Price	02/2023
2068	2^775865+21489	233559	Enzo Doria	05/2024
2069	2^775672+1866721	233501	Enzo Doria	03/2016
2070	2^775238+57	233370	Stefano Morozzi	05/2021
2071	(11^223999+1)/12	233270	Paul Bourdelais	02/2010
2072	U(1302049)	233238	Serge Batalov	07/2024
2073	2^774118+1885789	233033	Enzo Doria	04/2017
2074	21^176191-20^176191	232964	Jean-Louis Charton	01/2015
2075	2^773723+217523	232914	Enzo Doria	01/2024
2076	2^773679-113425	232901	Enzo Doria	08/2014
2077	11*17^189085+232	232661	Eric Chen	01/2026
2078	(7*10^232620+23)/3	232621	Robert Price	05/2023
2079	10^232599+192489	232600	Patrick De Geest	12/2013
2080	10^232599-3	232599	Markus Tervooren	10/2010
2081	2^772552-458879	232562	Enzo Doria	04/2015
2082	2^772214+1874899	232460	Enzo Doria	06/2016
2083	2^771994-1862771	232394	Enzo Doria	12/2015
2084	2^771889+1876037	232362	Enzo Doria	07/2016
2085	2^771660+1866511	232293	Enzo Doria	02/2016
2086	5^332150-18188	232163	Enzo Doria	06/2014
2087	2^771227+61121	232163	Boyan Hu	05/2024
2088	2^770623+212543	231981	Enzo Doria	09/2023
2089	3^485977-2^485977	231870	Mike Oakes	09/2009
2090	2^770082-114161	231818	Enzo Doria	01/2015
2091	2^769791+25523	231731	Enzo Doria	11/2023
2092	7^274120-2	231659	Paul Bourdelais	08/2023
2093	(20^177967+1)/21	231540	Paul Bourdelais	05/2013
2094	2^769011+81	231496	Henri Lifchitz	01/2025
2095	(71^125029-1)/105024430	231453	Paul Vanderveen	06/2025
2096	(4*10^231254+23)/9	231254	Serge Batalov	11/2022
2097	2^768205+22217	231253	Enzo Doria	09/2023
2098	49262^49262-49247^49247	231163	Henri Lifchitz	11/2024
2099	2^767622-9221	231078	Lelio R Paula	01/2016
2100	2^767344+1880311	230994	Enzo Doria	09/2016
2101	8*10^230921-13	230922	Robert Price	08/2023
2102	(3^483611-1)/2	230741	Paul Bourdelais	02/2010
2103	(10^230706+179)/9	230706	Serge Batalov	12/2014
2104	2^766309+1875257	230682	Enzo Doria	06/2016
2105	(26131^52441-1)/(26131^229-1)	230629	Ryan Propper	11/2023
2106	2^765635+1879883	230480	Enzo Doria	09/2016
2107	43^141090+141090	230467	Kellen Shenton	06/2023
2108	(26*10^230394-119)/3	230395	Robert Price	07/2023
2109	2^764348-113697	230092	Enzo Doria	09/2014
2110	2^764131+78863	230027	Enzo Doria	05/2016
2111	2^763701+60197	229897	Enzo Doria	03/2016
2112	4*10^229836+21	229837	Robert Price	12/2022
2113	2^763362+27799	229795	Enzo Doria	01/2024
2114	2^762841-25905	229639	Enzo Doria	10/2013
2115	2^762659+212633	229584	Enzo Doria	09/2023
2116	77*10^229211+3	229213	Robert Price	11/2023
2117	2^761117-113569	229120	Enzo Doria	08/2014
2118	(29022^51529-1)/(29022^227-1)	228947	Ryan Propper	11/2023
2119	(98^114859+1)/99	228709	Paul Bourdelais	12/2018
2120	5*3^479067-2^479067	228574	Jon Grantham	08/2023
2121	2^758645+216011	228375	Enzo Doria	12/2023
2122	(2^758231+1)/(32714694297653973236839266867)	228223	Gord Palameta	12/2018
2123	10^228208+111	228209	Boyan Hu	10/2024
2124	(298*10^228177-7)/3	228179	Robert Price	02/2023
2125	2^757985-2790013	228177	Enzo Doria	12/2015
2126	34*10^228129-9	228131	Robert Price	05/2023
2127	2^757038-1862081	227892	Enzo Doria	12/2015
2128	2^756839+95849	227832	Makoto Morimoto	10/2013
2129	(2^756839+6989)/756091	227826	Makoto Morimoto	09/2016
2130	(2^756839-50211)/(137*3203)	227826	Makoto Morimoto	08/2019
2131	2^756773-112723	227812	Enzo Doria	07/2014
2132	(710^(2113887+1)+9*10^113887-7)/9	227775	Robert Price	08/2024
2133	(10^227542)/(227542^10)	227489	Henri Lifchitz	05/2025
2134	524309#+616367	227431	Makoto Morimoto	02/2016
2135	2^755404+226575	227400	Enzo Doria	09/2024
2136	2^755116+81	227313	Henri Lifchitz	11/2024
2137	2^755097-114193	227307	Enzo Doria	12/2014
2138	7*10^227178+39	227179	Robert Price	01/2023
2139	9*10^227153-89	227154	Robert Price	02/2023
2140	2^754473-2791513	227120	Enzo Doria	01/2016
2141	2^754376+25	227090	Stefano Morozzi	05/2021
2142	2^754138+213289	227019	Enzo Doria	09/2023
2143	2^754038+25	226989	Stefano Morozzi	05/2021
2144	2^753263+217133	226755	Enzo Doria	12/2023
2145	7*10^226479-9	226480	Robert Price	02/2023
2146	(10^226381+1)/14973418875371	226368	Alfred Reich	06/2025
2147	2^751655+33893	226271	Enzo Doria	06/2024
2148	2^751426-764321	226202	Enzo Doria	12/2013
2149	(18^180181-1)/17	226176	Andy Steward	04/2007
2150	2^750740-3	225996	Paul Bourdelais	03/2012
2151	2^750725+60227	225991	Enzo Doria	02/2016
2152	2^750525-113743	225931	Enzo Doria	09/2014
2153	(2^750151-1)/(4299340426317590093831289397764574647511836143783478715117383638888678527263)	225744	Dario Alpern	10/2014
2154	2^749444-1861889	225606	Enzo Doria	12/2015
2155	tau(311^16452)	225560	Nik Lygeros / Olivier Rozier / LR team	10/2013
2156	(3^472721+1)/9422189991086734893916	225524	Paul Vanderveen	06/2025
2157	2^749096+1876861	225501	Enzo Doria	07/2016
2158	2^748895+26213	225440	Enzo Doria	12/2023
2159	(519643#+43033)/(2318712706283)	225379	Makoto Morimoto	08/2019
2160	2^748657+79607	225369	Enzo Doria	06/2016
2161	(2^746920-11)/5	224845	Stefano Morozzi	08/2022
2162	2^746653-291583	224765	Enzo Doria	07/2015
2163	2^746461-114043	224708	Enzo Doria	11/2014
2164	2^746302+25	224660	Stefano Morozzi	05/2021
2165	(202*10^224545-1)/3	224547	Robert Price	06/2023
2166	(19*10^224533-37)/9	224534	Alfred Reich	12/2023
2167	2^745674+213949	224471	Enzo Doria	10/2023
2168	2^745098-350471	224297	Enzo Doria	06/2015
2169	2^745039-4897	224280	Yves Minet	03/2021
2170	23*10^224232-7	224234	Robert Price	10/2022
2171	(154*10^224061-1)/9	224063	Serge Batalov	12/2014
2172	2^744211-1845787	224030	Enzo Doria	07/2015
2173	2^743773+37757	223898	Enzo Doria	10/2024
2174	2^743592-134579	223844	Hans Havermann	10/2018
2175	2^742452+3	223501	Paul Bourdelais	06/2019
2176	234178^9+9^234178	223463	Anatoly F. Selevich	07/2011
2177	47747^47747-2512^2512	223406	Henri Lifchitz	10/2024
2178	2^741651-461197	223260	Enzo Doria	07/2015
2179	10^223236-1001	223236	Robert Price	10/2022
2180	2^741362-1845251	223173	Enzo Doria	07/2015
2181	3^467546-5*2^467546	223077	Jon Grantham	08/2023
2182	2^740455-1863877	222900	Enzo Doria	12/2015
2183	2^740274+217519	222845	Enzo Doria	01/2024
2184	(14*10^222718-41)/9	222719	Serge Batalov	01/2023
2185	2^739636-2792219	222653	Enzo Doria	02/2016
2186	11^213654-180	222498	Enzo Doria	01/2013
2187	2^738957-1859743	222449	Enzo Doria	11/2015
2188	4*10^222253-21	222254	Robert Price	12/2022
2189	2^737825+57	222108	Stefano Morozzi	05/2021
2190	(54^128189+1)/55	222073	Paul Bourdelais	11/2018
2191	3^232689+1^232689+4^232689+1^232689+5^232689+9^232689	222042	Henri Lifchitz	03/2025
2192	2^737166+220099	221910	Enzo Doria	03/2024
2193	(10^221654+179)/9	221654	Serge Batalov	12/2014
2194	2^736281+79817	221643	Enzo Doria	06/2016
2195	10^221631+247617	221632	Patrick De Geest	10/2013
2196	10^221631-9	221631	Alexander Gramolin	02/2011
2197	10^221628+7	221629	Alfred Reich	04/2021
2198	2^735970-1839821	221550	Enzo Doria	06/2015
2199	2^735367+60293	221368	Enzo Doria	03/2016
2200	77*10^221343+3	221345	Robert Price	11/2023
2201	299^299^299-582	221328	Henri Lifchitz	03/2025
2202	(241^92821-1)/240	221099	Anonymous	04/2024
2203	(202*10^221092-1)/3	221094	Robert Price	06/2023
2204	(5^316297-1)/220142716	221074	Paul Vanderveen	05/2025
2205	(29^151153+1)/30	221045	Paul Bourdelais	09/2017
2206	2^734228+24751	221025	Enzo Doria	10/2023
2207	(28*10^220800+173)/3	220801	Robert Price	07/2024
2208	2^733264-2784089	220735	Enzo Doria	10/2015
2209	2^733114-24555	220690	Enzo Doria	09/2013
2210	2^731891-636259	220322	Enzo Doria	12/2013
2211	98*10^220185-9	220187	Robert Price	05/2023
2212	418319^39164+418318	220161	Alfred Reich	11/2023
2213	2^4^182829+182829^4^2	220149	Henri Lifchitz	03/2025
2214	2^731124-25539	220091	Enzo Doria	09/2013
2215	2^730972-462029	220045	Enzo Doria	07/2015
2216	2^730833+1868627	220003	Enzo Doria	04/2016
2217	2^730645-2787133	219947	Enzo Doria	11/2015
2218	2^730547-25581	219917	Enzo Doria	09/2013
2219	(113*13^197420-5)/12	219916	Anonymous	11/2022
2220	(13^197420*113-5)/12	219916	Eric Chen	10/2023
2221	2^730460+82291	219891	Enzo Doria	09/2016
2222	(5*10^219847-101)/3	219848	Robert Price	08/2023
2223	(2^730339+1)/(3278390620037943469324347)	219831	Gord Palameta	12/2018
2224	L(1051849)	219824	Renaud Lifchitz	03/2009
2225	3*2^730149+5	219798	Jon Grantham	07/2023
2226	8*10^219740-3	219741	Serge Batalov	01/2023
2227	11^210961-240	219694	Enzo Doria	01/2013
2228	(26*10^219639-77)/3	219640	Robert Price	03/2023
2229	2^729611-113437	219635	Enzo Doria	08/2014
2230	7^259710-2	219481	Paul Bourdelais	01/2021
2231	F(1049897)	219416	Henri Lifchitz	10/2008
2232	(1488^69151-1)/1487	219386	Alexander Zhirkov	02/2023
2233	2^728604+1879321	219332	Enzo Doria	10/2016
2234	33^144412+2	219292	Robert Price	04/2015
2235	2^728277-183313	219234	Hans Havermann	10/2018
2236	2^727998-1862711	219150	Enzo Doria	12/2015
2237	(29*10^219124+91)/3	219125	Robert Price	12/2022
2238	2^727729-114073	219069	Enzo Doria	12/2014
2239	2^727496-1851809	218999	Enzo Doria	08/2015
2240	2^727025+25907	218857	Enzo Doria	12/2023
2241	2^726591+2793143	218726	Enzo Doria	02/2016
2242	(7*10^218644+17)/3	218645	Robert Price	06/2023
2243	2^725534-2791931	218408	Enzo Doria	02/2016
2244	Phi(220531,10)/2686456812680882641	217774	Makoto Kamada	10/2020
2245	2^722184+1877821	217400	Enzo Doria	08/2016
2246	(109*10^217360-1)/9	217362	Serge Batalov	12/2014
2247	2^721721-4453	217260	Yves Minet	03/2021
2248	10^216950+49	216951	Robert Price	02/2023
2249	281*499979#/46410-2702372	216849	Robert Smith	08/2016
2250	281*499979#/46410+2400766	216849	Robert Smith	08/2016

Find by discoverer :

PRP Records

Probable Primes Top 10000

(302545 PRPs in the top)