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	2^863621-113833	259976	Enzo Doria	10/2014
2002	10^259945-11	259945	Mischa Rodermond	04/2023
2003	2^863433+34877	259920	Enzo Doria	07/2024
2004	(28*10^259897+113)/3	259898	Robert Price	06/2023
2005	2^862837+75767	259740	Enzo Doria	05/2016
2006	2^862637-31	259680	Jorge Menendez	05/2019
2007	2^862088+1874941	259515	Enzo Doria	06/2016
2008	2^861987-134557	259484	Hans Havermann	10/2018
2009	(14*10^259431-143)/3	259432	Robert Price	05/2023
2010	2^861516-1854029	259343	Enzo Doria	09/2015
2011	2^860975-1853977	259180	Enzo Doria	09/2015
2012	3^543128+16	259138	Robert Price	04/2020
2013	2^860625-1858843	259074	Enzo Doria	10/2015
2014	2^860110+77689	258919	Enzo Doria	05/2016
2015	2^859600+1880371	258766	Enzo Doria	10/2016
2016	2^859433+494711	258716	Makoto Morimoto	10/2013
2018	(2^859433-44)/(2^2*3)	258715	Makoto Morimoto	08/2019
2017	(2^859431-11)/3	258715	Stefano Morozzi	08/2022
2019	(13*10^258710-43)/3	258711	Robert Price	08/2023
2020	(2^859433+39899)/(73390746301)	258705	Makoto Morimoto	10/2016
2021	2^859240+1875271	258658	Enzo Doria	06/2016
2022	Tau(971^15738)	258571	Nik Lygeros / Olivier Rozier	05/2015
2023	2^858812+30421	258529	Enzo Doria	03/2024
2024	(23*10^258494-47)/3	258495	Robert Price	09/2023
2025	(144^119671+1)/145	258292	Paul Bourdelais	08/2019
2026	2^857608+105	258166	Stefano Morozzi	05/2021
2027	(11*2^857159-13)/15	258031	Renaud Lifchitz	08/2011
2028	2^857016-633113	257988	Enzo Doria	12/2013
2029	2^855732-113969	257602	Enzo Doria	10/2014
2030	(5*10^257431+91)/3	257432	Robert Price	08/2023
2031	2^853682-3911	256984	Enzo Doria	05/2014
2032	11^246668-90	256879	Enzo Doria	12/2012
2033	2^853181+30287	256834	Enzo Doria	03/2024
2034	5*2^852698+3	256689	Jon Grantham	07/2023
2035	(23*10^256654+7)/3	256655	Robert Price	05/2023
2036	2^851904-113939	256449	Enzo Doria	10/2014
2037	2^851725-851725^2	256395	Henri Lifchitz	03/2019
2038	11^246167-90	256357	Enzo Doria	12/2012
2039	(85*10^256301-1)/3	256303	Robert Price	12/2022
2040	(10^256187+7)/63443/148782853	256175	Alfred Reich	10/2021
2041	2^850700-569049	256087	Enzo Doria	11/2013
2042	2^850675+153	256079	Stefano Morozzi	05/2021
2043	21^193601-20^193601	255983	Jean-Louis Charton	02/2015
2044	(37^163193+1)/38	255918	Paul Bourdelais	07/2019
2045	(14*10^255805-83)/3	255806	Robert Price	11/2022
2046	2^849316+25861	255670	Enzo Doria	12/2023
2047	2^849177-114025	255628	Enzo Doria	12/2014
2048	2*10^255442-21	255443	Robert Price	08/2023
2049	2^848502-3173	255425	Yves Minet	07/2016
2050	2^848178-140291	255328	Enzo Doria	01/2014
2051	7*10^255167+87	255168	Robert Price	11/2022
2052	2^847622-2441	255160	Yves Minet	02/2016
2053	2^847291+182843	255061	Enzo Doria	11/2016
2054	2^847174+1879429	255025	Enzo Doria	09/2016
2055	2^846881+215837	254937	Enzo Doria	12/2023
2056	Phi(475779,2^3)	254889	Henri Lifchitz	12/2025
2057	24*29^174239+13361	254809	Curtis Bright	04/2015
2058	22*10^254639+7	254641	Robert Price	10/2022
2059	2^845633-933075	254561	Paul Bourdelais	11/2021
2060	2^845610-1868591	254554	Enzo Doria	04/2016
2061	2^845484+81931	254517	Enzo Doria	08/2016
2062	2^845402-114761	254492	Enzo Doria	05/2015
2063	Phi(115655,561)	254335	Henri Lifchitz	12/2025
2064	98*10^254173-9	254175	Robert Price	05/2023
2065	2^844334-2792441	254170	Enzo Doria	02/2016
2066	2*10^254162+69	254163	Robert Price	08/2023
2067	(4*10^254107+11)/3	254108	Tyler Busby	02/2023
2068	11^243796-90	253888	Enzo Doria	12/2012
2069	(10^253891+7)/44777/79843/16940711	253875	Alfred Reich	10/2021
2070	30^171733-29^171733	253671	Jean-Louis Charton	10/2018
2071	2^842325+25907	253566	Enzo Doria	11/2023
2072	Sm(52936)/27320754423352	253560	Youcef Lemsafer	06/2026
2073	2^842209+1876037	253531	Enzo Doria	07/2016
2074	2^842123-59197	253505	Enzo Doria	10/2015
2075	(8*10^253313-53)/9	253313	Serge Batalov	11/2022
2076	(28*10^253210+191)/3	253211	Robert Price	07/2023
2077	2^840797-3	253106	Paul Bourdelais	06/2019
2078	2^840716-2969	253081	Yves Minet	05/2016
2079	2^840358-462491	252973	Enzo Doria	08/2015
2080	2^840310+1878379	252959	Enzo Doria	08/2016
2081	2^840203-21	252927	Stefano Morozzi	07/2022
2082	11^242579-60	252620	Enzo Doria	10/2012
2083	45^152659+2	252378	Robert Price	09/2015
2084	(95^127583+1)/96	252322	Paul Bourdelais	07/2019
2085	7*10^252209-17	252210	Robert Price	12/2022
2086	2^837725+1869377	252181	Enzo Doria	05/2016
2087	2^837536-311039	252124	Enzo Doria	06/2015
2088	21^190632-2	252058	Robert Price	07/2015
2089	2^837242+1873297	252035	Enzo Doria	06/2016
2090	2^836995+226575	251961	Enzo Doria	10/2024
2091	2^836656-2787929	251859	Enzo Doria	11/2015
2092	2^836548+219061	251827	Enzo Doria	02/2024
2093	2^836380+1875541	251776	Enzo Doria	07/2016
2094	(359^98327-1)/358	251233	Alexander Zhirkov	11/2017
2095	tau(41^28288)	250924	Nik Lygeros / Olivier Rozier	10/2013
2096	Phi(137951,-100)	250801	Henri Lifchitz	12/2025
2097	406^96126+405	250748	Alfred Reich	05/2026
2098	Phi(74531,11#)	250691	Henri Lifchitz	12/2025
2099	(28*10^250655+113)/3	250656	Robert Price	06/2023
2100	2^832511-461197	250611	Enzo Doria	07/2015
2101	2^832505+1881137	250609	Enzo Doria	11/2016
2102	2^832363+583295	250567	Enzo Doria	12/2016
2103	2^832244-403635	250531	Enzo Doria	01/2014
2104	(14*10^250336-41)/9	250337	Serge Batalov	01/2023
2105	2^831528+24811	250315	Enzo Doria	11/2023
2106	2^831157+1880657	250204	Enzo Doria	11/2016
2107	2^831088-7200899	250183	Enzo Doria	01/2015
2108	2^830956-1349	250143	Yves Minet	07/2015
2109	2^830699+220583	250066	Enzo Doria	03/2024
2110	2^830037+282317	249867	Enzo Doria	09/2016
2111	2^829589-113653	249732	Enzo Doria	09/2014
2112	(4*10^249550-7)/3	249551	Serge Batalov	01/2023
2113	(103*10^249399+17)/3	249401	Robert Price	04/2023
2114	2^828281-3193	249338	Yves Minet	08/2016
2115	(2^828140-19)/3	249295	Stefano Morozzi	08/2022
2116	2^828064-2785619	249273	Enzo Doria	10/2015
2117	2^827602+60409	249134	Enzo Doria	03/2016
2118	2^827306+212419	249044	Enzo Doria	09/2023
2119	10^249010+348861	249011	Patrick De Geest	04/2016
2120	10^249010-21	249010	Serge Batalov	12/2014
2121	2^826733+1882907	248872	Enzo Doria	12/2016
2122	2^825800+22441	248591	Enzo Doria	10/2023
2123	2^825682+1876549	248556	Enzo Doria	07/2016
2124	2^824991-114121	248348	Enzo Doria	12/2014
2125	2^824642-362727	248242	Enzo Doria	12/2013
2126	2^824565-114265	248219	Enzo Doria	01/2015
2127	2^824325-25	248147	Boyan Hu	12/2024
2128	(73*10^248145-1)/9	248146	Robert Price	01/2015
2129	2^823321+219407	247845	Enzo Doria	02/2024
2130	(2^823337+1)/(3*362268281)	247841	Gord Palameta	08/2018
2131	(13*10^247793-43)/3	247794	Robert Price	08/2023
2132	(2^822971-1)/6583769/28211445881/21255852651726486149207	247700	Robert Kinser	09/2016
2133	2^822296+76501	247536	Enzo Doria	05/2016
2134	2^821590-114167	247324	Enzo Doria	12/2014
2135	2^821512-2790659	247300	Enzo Doria	12/2015
2136	(21996^57121-1)/(21996^239-1)	247002	Ryan Propper	11/2023
2137	2^820356+7	246952	Jon Grantham	08/2023
2138	2^820077+382847	246868	Enzo Doria	11/2016
2139	2^820008+81	246848	Henri Lifchitz	01/2025
2140	2^820001+81269	246845	Enzo Doria	07/2016
2141	2^819463-59197	246683	Enzo Doria	10/2015
2142	2^819296+80581	246633	Enzo Doria	07/2016
2143	2^818764+21573	246473	Enzo Doria	11/2023
2144	2^817852+215491	246198	Enzo Doria	11/2023
2145	2^817160-350369	245990	Enzo Doria	06/2015
2146	2^816039-19	245653	Stefano Morozzi	07/2022
2147	2^816029+219407	245650	Enzo Doria	02/2024
2148	(71*10^245558-17)/9	245559	Serge Batalov	01/2023
2149	5*3^514648+2^514648	245551	Jon Grantham	08/2023
2150	88093#+(653879#)/(88093#)	245374	Makoto Morimoto	11/2017
2151	2^815111-113857	245373	Enzo Doria	10/2014
2152	(34555^54289-1)/(34555^233-1)	245334	Ryan Propper	11/2023
2153	2^814914-4001	245314	Yves Minet	05/2017
2154	846^83761-845^83761	245200	Jean-Louis Charton	12/2012
2155	2^814356-2790449	245146	Enzo Doria	12/2015
2156	2^814276-459029	245122	Enzo Doria	04/2015
2157	2^814023+180923	245046	Enzo Doria	07/2016
2158	2^813496+216751	244887	Enzo Doria	12/2023
2159	(3^513059-2^513059)/(1026119*5430216457)	244776	Mike Oakes	03/2017
2160	3^513007+16	244767	Robert Price	04/2020
2161	(46^147197-31^147197)/15	244752	Aurel Gibier	06/2024
2162	(2543*17^198855-15)/16	244684	Eric Chen	01/2026
2163	2^811882+27289	244401	Enzo Doria	12/2023
2164	2^811842-113675	244389	Enzo Doria	09/2014
2165	2^811132-2787929	244176	Enzo Doria	11/2015
2166	(47*21^184501+953)/20	243952	Eric Chen	03/2026
2167	2^809746-2790971	243758	Enzo Doria	01/2016
2168	(14*10^243724-197)/3	243725	Robert Price	03/2023
2169	2^808767-3295	243464	Yves Minet	12/2016
2170	2^808621-113809	243420	Enzo Doria	09/2014
2171	2^808199+29693	243293	Enzo Doria	03/2024
2172	2^807724+1879621	243150	Enzo Doria	09/2016
2173	2^807417+217787	243057	Enzo Doria	01/2024
2174	(23*10^242909+91)/3	242910	Robert Price	03/2023
2175	2^806708+20371	242844	Enzo Doria	08/2023
2176	2*10^242822-91	242823	Robert Price	02/2023
2177	20^186554-3	242713	Paul Bourdelais	12/2020
2178	2^805843-113611	242583	Enzo Doria	08/2014
2179	2^805745-459763	242554	Enzo Doria	05/2015
2180	2^805353+782687	242436	Enzo Doria	11/2016
2181	(19*10^242362-7)/3	242363	Robert Price	12/2023
2182	2^804895+29963	242298	Enzo Doria	03/2024
2183	2^804725+28229	242247	Enzo Doria	01/2024
2184	6^311257+5	242206	Paul Bourdelais	02/2021
2185	(21^242194)%(10^242194)	242194	Henri Lifchitz	06/2025
2186	2^804277-417933	242112	Enzo Doria	01/2014
2187	7(10^(2121002+1)-1)/9-3*10^121002	242005	Robert Price	06/2026
2188	2^803468-269039	241868	Enzo Doria	10/2013
2189	2^803172+80851	241779	Enzo Doria	07/2016
2190	2^803011+220073	241731	Enzo Doria	03/2024
2191	3^506233-2	241535	Robert Price	11/2013
2192	2^802025-25999	241434	Enzo Doria	10/2013
2193	(3^505823+3^252912+1)/7	241339	Serge Batalov	03/2014
2194	2^801575+25073	241299	Enzo Doria	11/2023
2195	2^801303+1872923	241217	Enzo Doria	05/2016
2196	2^801105+216977	241157	Enzo Doria	12/2023
2197	(23*10^241048-143)/3	241049	Robert Price	12/2023
2198	2^800579-1862947	240999	Enzo Doria	12/2015
2199	2^799999+16205	240824	Norman Luhn	09/2023
2200	3^504206+2	240568	Luke W. Richards	03/2018
2201	2^798973-26283	240515	Enzo Doria	10/2013
2202	Phi(114205,3^7)	240470	Henri Lifchitz	12/2025
2203	2^798671-69487	240424	Enzo Doria	12/2015
2204	2^797220+79831	239988	Enzo Doria	06/2016
2205	2^796910-26001	239894	Enzo Doria	10/2013
2206	(97^120721-1)/811245216	239837	Paul Vanderveen	06/2025
2207	2^796598+653119	239800	Enzo Doria	12/2016
2208	2^796432-1859729	239750	Enzo Doria	11/2015
2209	2^796002-1852211	239621	Enzo Doria	08/2015
2210	2^795884+214081	239585	Enzo Doria	10/2023
2211	2^795709+75767	239533	Enzo Doria	04/2016
2212	2^795708+81721	239532	Enzo Doria	08/2016
2213	2^795468-2786249	239460	Enzo Doria	10/2015
2214	2^795442+80779	239452	Enzo Doria	07/2016
2215	2^795075-1852057	239342	Enzo Doria	08/2015
2216	(86^123677+1)/87	239252	Paul Bourdelais	01/2019
2217	2^794043+1875023	239031	Enzo Doria	06/2016
2218	2^793347-69577	238822	Enzo Doria	01/2016
2219	5*2^793288+3	238805	Jon Grantham	07/2023
2220	2^792988-344429	238714	Enzo Doria	08/2015
2221	2^792700-2786369	238627	Enzo Doria	11/2015
2222	2^792663-1844797	238616	Enzo Doria	06/2015
2223	2^792605-291943	238598	Enzo Doria	07/2015
2224	2^792366+218599	238526	Enzo Doria	01/2024
2225	(2^792061-2^396031+1)/5	238434	Thomas Ritschel	03/2014
2226	2^791321+30077	238212	Enzo Doria	03/2024
2227	4*10^238163+21	238164	Robert Price	12/2022
2228	(26*10^238157-77)/3	238158	Robert Price	03/2023
2229	10^237670+9	237671	Robert Price	08/2023
2230	2^789373+1869377	237625	Enzo Doria	05/2016
2231	((10^59387+1)^3(10^59387+1+10^29694)-(10^118774+10^59387)(10^29694-1)+10^178161)/27961	237544	Serge Batalov	04/2015
2232	Phi(1187740M,10)	237544	Anonymous	03/2025
2233	2^789033+218537	237523	Enzo Doria	01/2024
2234	2^788942+1866409	237496	Enzo Doria	02/2016
2235	2^788844-114329	237466	Enzo Doria	01/2015
2236	2^788705-1859713	237424	Enzo Doria	11/2015
2237	2^788325+224789	237310	Enzo Doria	07/2024
2238	15^201475+14	236953	Alfred Reich	10/2023
2239	2^786663+219173	236810	Enzo Doria	02/2024
2240	2^786180+1871971	236664	Enzo Doria	05/2016
2241	11^227092-90	236492	Enzo Doria	11/2012
2242	2^785260+1866361	236387	Enzo Doria	02/2016
2243	(309*21^178772+71)/20	236377	Eric Chen	03/2026
2244	2^785220+1880611	236375	Enzo Doria	10/2016
2245	(2^784689-15)/7	236215	Stefano Morozzi	08/2022
2246	19^184650-2	236122	Robert Price	10/2014
2247	10^236059+216513	236060	Patrick De Geest	04/2016
2248	10^236059-20909	236059	Robert Price	09/2015
2249	2^783988+38011	236004	Enzo Doria	10/2024
2250	2^783893-21	235976	Stefano Morozzi	07/2022

Find by discoverer :

PRP Records

Probable Primes Top 10000

(303412 PRPs in the top)