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	38655^6176+6176^38655	146530	Hans Havermann	11/2020
2002	32820^29059+29059^32820	146485	Hans Havermann	12/2020
2003	37261^8530+8530^37261	146472	Hans Havermann	12/2020
2004	66953^154+154^66953	146462	Hans Havermann	12/2020
2005	96^73877-95^73877	146445	Robert Price	10/2015
2006	8*10^146421+81	146422	Robert Price	08/2019
2007	33153^26090+26090^33153	146420	Hans Havermann	11/2020
2008	(52^85259+1)/53	146304	Paul Bourdelais	09/2017
2009	179^64935+2	146290	Lelio R Paula	10/2017
2010	32595^30758+30758^32595	146285	Hans Havermann	11/2020
2011	34972^15157+15157^34972	146205	Hans Havermann	12/2020
2012	(19*10^146181-49)/3	146182	Robert Price	05/2019
2013	2^485531-114621	146160	Enzo Doria	05/2015
2014	(2^485461-9)/4249	146135	Lelio R Paula	09/2015
2015	2^485389+81887	146117	Enzo Doria	08/2016
2016	32554^30773+30773^32554	146108	Hans Havermann	11/2020
2017	(10^146063+71)/9	146063	Serge Batalov	07/2015
2018	(2^485119+7)/2745	146032	Lelio R Paula	09/2015
2019	(22*10^146029+257)/9	146030	Robert Price	06/2018
2020	7*10^145982-53	145983	Robert Price	06/2020
2021	2^484743+1872923	145923	Enzo Doria	05/2016
2022	33140^25287+25287^33140	145913	Hans Havermann	01/2021
2023	37875^7112+7112^37875	145895	Hans Havermann	01/2021
2024	32862^27473+27473^32862	145872	Hans Havermann	01/2021
2025	32836^27587+27587^32836	145815	Hans Havermann	01/2021
2026	2^484341+1879157	145802	Enzo Doria	08/2016
2027	2*10^145784-91	145785	Robert Price	04/2020
2028	2^484271-51	145781	Lelio R Paula	11/2017
2029	70^78989-69^78989	145743	Robert Price	01/2014
2030	51^85334+2	145714	Robert Price	07/2015
2031	2^483886-1857101	145665	Enzo Doria	10/2015
2032	33350^23307+23307^33350	145656	Hans Havermann	01/2021
2033	(19*10^145585+131)/3	145586	Robert Price	06/2020
2034	2^483563-1863457	145567	Enzo Doria	12/2015
2035	2^483516-1861409	145553	Enzo Doria	11/2015
2036	2^483384-115019	145514	Enzo Doria	06/2015
2037	(259*10^145501-1)/3	145503	Robert Price	12/2020
2038	(19*10^145499-61)/3	145500	Robert Price	05/2019
2039	2^483302-3221	145489	Lelio R Paula	12/2012
2040	35523^12434+12434^35523	145453	Hans Havermann	01/2021
2041	2^483046+1874029	145412	Enzo Doria	06/2016
2042	2^482991-2789317	145395	Enzo Doria	12/2015
2043	2^482978-2789711	145391	Enzo Doria	12/2015
2044	2^482966-2789711	145388	Enzo Doria	12/2015
2045	2^482817-1858843	145343	Enzo Doria	10/2015
2046	2^482751-113635	145323	Enzo Doria	08/2014
2047	2^482705-459763	145309	Enzo Doria	05/2015
2048	(4^241306+11)/3	145281	Robert Price	03/2017
2049	(238*10^145276-1)/3	145278	Robert Price	04/2020
2050	(19*2^482534+1)/7	145258	Lelio R Paula	09/2015
2051	53^84239-52^84239	145252	Robert Price	01/2013
2052	47952^1067+1067^47952	145207	Hans Havermann	01/2021
2053	(2^482333+5)/9287	145193	Lelio R Paula	09/2015
2054	2^482087+72623	145123	Enzo Doria	04/2016
2055	2^482016-286565	145102	Enzo Doria	07/2015
2056	(19*10^145093+101)/3	145094	Robert Price	09/2019
2057	2^481840+15	145049	Robert Price	09/2015
2058	2^481801-481801	145037	Henri Lifchitz	03/2005
2059	2^481775+1869083	145029	Enzo Doria	05/2016
2060	29^99167+2	145022	Ray Chandler	08/2011
2061	2^481663+1875653	144996	Enzo Doria	07/2016
2062	36486^9379+9379^36486	144929	Hans Havermann	12/2020
2063	35111^13378+13378^35111	144882	Hans Havermann	01/2021
2064	2^481149-459073	144841	Enzo Doria	05/2015
2065	34619^15246+15246^34619	144817	Hans Havermann	01/2021
2066	2^481045-113215	144809	Enzo Doria	07/2014
2067	(64*10^144797+287)/9	144798	Robert Price	04/2019
2068	2^480859-113695	144753	Enzo Doria	09/2014
2069	2^480766-2787191	144725	Enzo Doria	11/2015
2070	(21*27^101106-151)/26	144720	Curtis Bright	05/2015
2071	2^480678+1874239	144699	Enzo Doria	06/2016
2072	(8*10^144683+1)/9	144683	Serge Batalov	05/2010
2073	L(692147)	144651	Henri Lifchitz	10/2008
2074	(76*10^144648+77)/9	144649	Robert Price	10/2019
2075	32672^26721+26721^32672	144635	Hans Havermann	01/2021
2076	2^480417+35	144620	Robert Price	11/2015
2077	2^480296-59879	144584	Enzo Doria	10/2015
2078	33157^22878+22878^33157	144546	Hans Havermann	12/2020
2079	45494^1497+1497^45494	144454	Hans Havermann	12/2020
2080	2^479844+3	144448	Donovan Johnson	06/2006
2081	33442^20803+20803^33442	144407	Hans Havermann	01/2021
2082	(27*2^479642+1)/733	144386	Lelio R Paula	08/2015
2083	44917^1638+1638^44917	144378	Hans Havermann	12/2020
2084	(21*2^479605-1)/11	144376	Lelio R Paula	09/2015
2085	2^479348-2792219	144299	Enzo Doria	02/2016
2086	3^302389-6242	144277	Enzo Doria	05/2014
2087	33778^18641+18641^33778	144248	Hans Havermann	01/2021
2088	2*10^144220-3	144221	Robert Price	07/2015
2089	2^478904-109109	144165	Enzo Doria	04/2014
2090	43698^1987+1987^43698	144125	Hans Havermann	12/2020
2091	36128^9723+9723^36128	144072	Hans Havermann	01/2021
2092	32817^24518+24518^32817	144050	Hans Havermann	12/2020
2093	34295^15828+15828^34295	144020	Hans Havermann	01/2021
2094	2^478337-115333	143994	Enzo Doria	07/2015
2095	(7*2^478330-1)/3	143993	Lelio R Paula	08/2015
2096	88^74047-87^74047	143984	Robert Price	05/2015
2097	33242^21441+21441^33242	143980	Hans Havermann	01/2021
2098	(19*10^143963+467)/9	143964	Robert Price	02/2018
2099	(71^77761+1)/72	143954	Paul Bourdelais	09/2017
2100	33490^19859+19859^33490	143939	Hans Havermann	01/2021
2101	2^478088+27	143919	Robert Price	11/2015
2102	7*10^143857-93	143858	Robert Price	08/2020
2103	3*10^143844+61	143845	Robert Price	09/2020
2104	41358^3005+3005^41358	143837	Hans Havermann	01/2021
2105	2^477475-22071	143735	Enzo Doria	07/2013
2106	2^477417-22123	143717	Enzo Doria	07/2013
2107	2^477359-3577	143700	Yves Minet	03/2017
2108	39435^4402+4402^39435	143688	Hans Havermann	01/2021
2109	(14*10^143662-71)/3	143663	Robert Price	12/2018
2110	46371^1252+1252^46371	143640	Hans Havermann	12/2020
2111	34975^12748+12748^34975	143588	Hans Havermann	01/2021
2112	2^476936-396765	143573	Enzo Doria	07/2013
2113	2^476888-2791229	143558	Enzo Doria	01/2016
2114	2^476868-1859939	143552	Enzo Doria	11/2015
2115	40807^3294+3294^40807	143548	Hans Havermann	12/2020
2116	755^49878+49878^755	143547	Norbert Schneider	04/2019
2117	2^476558-113627	143459	Enzo Doria	08/2014
2118	2^476478-45	143435	Lelio R Paula	11/2017
2119	(2^475854+9)/73	143245	Lelio R Paula	08/2015
2120	2^475813-113239	143234	Enzo Doria	07/2014
2121	2^475624-114059	143178	Enzo Doria	11/2014
2122	(11*2^475553-7)/15	143156	Renaud Lifchitz	03/2011
2123	2^475480-2786129	143134	Enzo Doria	10/2015
2124	(19*10^143129-43)/3	143130	Robert Price	05/2019
2125	(14*10^143097+73)/3	143098	Robert Price	12/2018
2126	2^475299-111937	143080	Enzo Doria	05/2014
2127	2^475160-2797859	143038	Enzo Doria	04/2016
2128	(2^475069+3)/395	143008	Lelio R Paula	08/2015
2129	2^475027-461437	142998	Enzo Doria	07/2015
2130	(2^474958+78557)/3	142977	Lelio R Paula	07/2015
2131	(8*10^142932+43)/3	142933	Robert Price	06/2018
2132	(54^82471-1)/53	142871	Paul Bourdelais	09/2017
2133	(11*2^474432-1)/95	142818	Lelio R Paula	09/2015
2134	2^474417-59923	142814	Enzo Doria	10/2015
2135	4*10^142810-21	142811	Robert Price	09/2018
2136	(3*2^474166+1)/7	142738	Lelio R Paula	08/2015
2137	2^474053+2897	142705	Lelio R Paula	08/2012
2138	(10^142699+359)/9	142699	Serge Batalov	12/2014
2139	898^48311-897^48311	142676	Jean-Louis Charton	12/2012
2140	2^473740-1856639	142610	Enzo Doria	09/2015
2141	(25*10^142573-403)/9	142574	Robert Price	12/2020
2142	2^473617-114223	142573	Enzo Doria	12/2014
2143	2^473257+1873217	142465	Enzo Doria	06/2016
2144	(19*2^473242+1)/11	142461	Lelio R Paula	09/2015
2145	(61*10^142446-1)/3	142448	Robert Price	01/2020
2146	(14*10^142440+61)/3	142441	Robert Price	12/2018
2147	(10^142425+359)/9	142425	Serge Batalov	12/2014
2148	2^473101+773027	142418	Enzo Doria	05/2016
2149	(13*2^472838-1)/3	142340	Lelio R Paula	09/2015
2150	(17*2^472789-1)/187347	142320	Lelio R Paula	09/2015
2151	2^472634-109511	142278	Enzo Doria	04/2014
2152	(48^84589+1)/49	142213	Robert Price	01/2014
2153	7*10^142189+87	142190	Robert Price	07/2019
2154	2^472258+7	142164	Lelio R Paula	08/2015
2155	(23*10^142105+91)/3	142106	Robert Price	08/2019
2156	tau(317^10330)	142098	Nik Lygeros / Olivier Rozier / LR team	10/2013
2157	(11*2^471913-1)/21	142060	Lelio R Paula	09/2015
2158	(16*10^142058+197)/3	142059	Robert Price	04/2019
2159	9*10^142037+91	142038	Robert Price	10/2020
2160	2^471792+1880881	142024	Enzo Doria	11/2016
2161	(31*2^471580-1)/135	141960	Lelio R Paula	08/2015
2162	(4*10^141926-79)/3	141927	Robert Price	02/2018
2163	(904*19^110984-1)/3	141924	Curtis Bright	05/2015
2164	(14*10^141853+37)/3	141854	Robert Price	12/2018
2165	(41*10^141836-59)/9	141837	Robert Price	10/2018
2166	4*5^202913-9	141831	Lelio R Paula	04/2015
2167	2*7^167812-3	141818	Lelio R Paula	12/2014
2168	2^471043+35	141799	Robert Price	11/2015
2169	(11*2^470956-1)/7945	141770	Lelio R Paula	08/2015
2170	(11*10^141718-131)/3	141719	Robert Price	09/2018
2171	2^470692+76771	141693	Enzo Doria	05/2016
2172	(21*2^470391+1)/533	141601	Lelio R Paula	09/2015
2173	2^470305-459373	141576	Enzo Doria	05/2015
2174	2^470183+72623	141540	Enzo Doria	04/2016
2175	2^470173-16465	141537	Enzo Doria	04/2013
2176	44*10^141476+9	141478	Robert Price	10/2020
2177	2^469974-1841	141477	Enzo Doria	05/2014
2178	(23*2^469939+1)/25	141466	Lelio R Paula	08/2015
2179	2*10^141448+63	141449	Robert Price	05/2018
2180	2^469824+43	141432	Lelio R Paula	09/2017
2181	2*10^141407-27	141408	Robert Price	05/2018
2182	(214*10^141385-1)/3	141387	Robert Price	01/2021
2183	2^469630-59711	141373	Enzo Doria	10/2015
2184	(25*10^141366-331)/9	141367	Robert Price	08/2018
2185	(2^469564-3)/611	141351	Lelio R Paula	08/2015
2186	197^61601+2	141342	Lelio R Paula	08/2017
2187	2^469372-112949	141296	Enzo Doria	07/2014
2188	3^296115+4	141283	Tyler NeSmith	01/2021
2190	143^(2^16)+106^(2^16)	141253	Valeryi Kuryshev	02/2011
2189	143^65536+106^65536	141253	Serge Batalov	03/2018
2191	2^469198+782569	141243	Enzo Doria	10/2016
2192	2^469076-2786939	141206	Enzo Doria	11/2015
2193	2^468804+1874941	141125	Enzo Doria	06/2016
2194	2^468787+81353	141119	Enzo Doria	08/2016
2195	2^468595-350407	141062	Enzo Doria	06/2015
2196	2^468564+87855	141052	Lelio R Paula	01/2016
2197	2^468551-21987	141048	Enzo Doria	07/2013
2198	2^468523-7	141040	Lelio R Paula	08/2015
2199	(25*10^141019-13)/3	141020	Robert Price	09/2019
2200	2^468405+87855	141004	Lelio R Paula	01/2016
2201	2^467978-113051	140876	Enzo Doria	07/2014
2202	2^467780-344429	140816	Enzo Doria	07/2015
2203	9*10^140802-89	140803	Robert Price	04/2020
2204	2^467605-1855603	140764	Enzo Doria	09/2015
2205	5*10^140744-7	140745	Robert Price	09/2015
2206	(5^201359-1)/4	140744	Paul Bourdelais	12/2008
2207	2^467401-1850023	140702	Enzo Doria	08/2015
2208	(266*10^140681-17)/3	140683	Robert Price	07/2020
2209	(2^467270+78557)/23247	140658	Lelio R Paula	07/2015
2210	(29*2^467205+1)/2780517107	140635	Lelio R Paula	08/2015
2211	2^467166-1854941	140631	Enzo Doria	09/2015
2212	(203*10^140615-11)/3	140617	Robert Price	12/2020
2213	(85*10^140609+473)/9	140610	Robert Price	01/2020
2214	2^466866-1840571	140541	Enzo Doria	06/2015
2215	2^466829-459523	140530	Enzo Doria	05/2015
2216	2^466692-113213	140489	Enzo Doria	07/2014
2217	(44*10^140410-503)/9	140411	Robert Price	12/2018
2218	153^64265-2	140400	Lelio R Paula	11/2017
2219	(112*10^140357-1)/3	140359	Serge Batalov	12/2014
2220	(29*10^140337-17)/3	140338	Robert Price	09/2019
2221	2^466181-112735	140335	Enzo Doria	07/2014
2222	(5*10^140281-119)/3	140282	Robert Price	03/2018
2223	(27*2^465872+1)/691	140241	Lelio R Paula	08/2015
2224	2^465803-114817	140221	Enzo Doria	05/2015
2225	floor(Pi*10^140344)%10^140165	140165	Serge Batalov	08/2012
2226	2^465503-112735	140131	Enzo Doria	07/2014
2227	(16*10^140091+167)/3	140092	Robert Price	06/2019
2228	6^179964+179964^6-1	140040	Robert Price	04/2014
2229	(89*10^140008-179)/9	140009	Robert Price	12/2019
2230	(29*2^465077-1)/9	140003	Lelio R Paula	08/2015
2231	2^465072-344789	140001	Enzo Doria	07/2015
2232	5*10^139945+81	139946	Robert Price	03/2019
2233	2^464864-17	139939	Lelio R Paula	09/2017
2234	8*10^139920+51	139921	Robert Price	08/2019
2235	(85*10^139913-1)/3	139915	Robert Price	02/2020
2236	(17^113621+1)/18	139804	Paul Bourdelais	09/2011
2237	2*10^139800-21	139801	Robert Price	09/2020
2238	(13*10^139782+191)/3	139783	Robert Price	11/2018
2239	(19*2^464312-1)/3	139773	Lelio R Paula	08/2015
2240	(74*10^139723+133)/9	139724	Robert Price	06/2019
2241	3*10^139722+13	139723	Robert Price	07/2018
2242	77*10^139692+3	139694	Robert Price	06/2020
2243	(31*2^463970+1)/5	139670	Lelio R Paula	08/2015
2244	(18203^(2^15)+(18201)^(2^15))/2	139597	Robert Price	05/2018
2245	2^463633-2788423	139568	Enzo Doria	11/2015
2246	2^463271-109501	139459	Enzo Doria	04/2014
2247	(5*10^139457+79)/3	139458	Robert Price	03/2018
2248	2^463237-99	139449	Lelio R Paula	09/2017
2249	(49*10^139442+383)/9	139443	Robert Price	04/2019
2250	(7*10^139417-547)/9	139417	Robert Price	01/2018

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