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	2^491851+1871453	148062	Enzo Doria	05/2016
2002	(68*10^148060-257)/9	148061	Robert Price	07/2019
2003	(151*10^148020-1)/3	148022	Robert Price	03/2020
2004	39153^6032+6032^39153	148017	Hans Havermann	10/2020
2005	36798^10507+10507^36798	147983	Hans Havermann	12/2020
2006	(26*10^147973-23)/3	147974	Robert Price	12/2019
2007	2^491521-1865323	147963	Enzo Doria	02/2016
2008	(2^491476+7)/71	147948	Lelio R Paula	10/2015
2009	2^491391-7807	147924	Lelio R Paula	01/2013
2010	39736^5279+5279^39736	147920	Hans Havermann	11/2020
2011	2^491370-113297	147918	Enzo Doria	07/2014
2012	(32760^32760+32759^32759)/95546586737133567708319	147900	Robert Price	07/2016
2013	44368^2155+2155^44368	147899	Hans Havermann	12/2020
2014	(17*10^147890+79)/3	147891	Robert Price	04/2019
2015	94*10^147871-3	147873	Robert Price	05/2020
2016	10^147843-50000000001	147843	Robert Price	12/2020
2017	35805^13346+13346^35805	147709	Hans Havermann	11/2020
2018	2^490660-17	147704	Lelio R Paula	12/2017
2019	(229*10^147699-1)/3	147701	Robert Price	07/2020
2020	40656^4289+4289^40656	147678	Hans Havermann	11/2020
2021	2^490550+1179439	147671	Enzo Doria	06/2016
2022	(23*10^147649-59)/9	147650	Robert Price	05/2018
2023	2^490303+2793653	147596	Enzo Doria	03/2016
2024	199^64181-2	147543	Lelio R Paula	11/2017
2025	32849^30958+30958^32849	147518	Hans Havermann	11/2020
2026	2^489871-286987	147466	Enzo Doria	07/2015
2027	2^489864-351899	147464	Enzo Doria	07/2015
2028	175^65724-2	147422	Lelio R Paula	11/2017
2029	2^489712+1874851	147419	Enzo Doria	06/2016
2030	34473^18830+18830^34473	147367	Hans Havermann	11/2020
2031	63^81896-2	147359	Lelio R Paula	10/2017
2032	34580^18237+18237^34580	147344	Hans Havermann	11/2020
2033	(11*10^147313-107)/3	147314	Robert Price	09/2018
2034	2^489305-59815	147296	Enzo Doria	10/2015
2035	(2^489280-7)/6381	147285	Lelio R Paula	09/2015
2036	2*10^147260+29	147261	Robert Price	02/2021
2037	33556^24457+24457^33556	147258	Hans Havermann	11/2020
2038	2^489125+80357	147242	Enzo Doria	06/2016
2039	32835^30452+30452^32835	147220	Hans Havermann	12/2020
2040	(148*10^147139-1)/3	147141	Robert Price	03/2020
2041	34338^19255+19255^34338	147123	Hans Havermann	11/2020
2042	2^488648-112799	147098	Enzo Doria	07/2014
2043	2^488627-350317	147092	Enzo Doria	06/2015
2044	33432^25075+25075^33432	147076	Hans Havermann	12/2020
2045	(2^488441-1)/(61543567*30051203516986199)	147012	Dario Alpern	12/2014
2046	2^488280-2165	146987	Yves Minet	07/2014
2047	2^488278+45	146987	Lelio R Paula	12/2017
2048	2^487927-39	146881	Lelio R Paula	12/2017
2049	(7*10^146860-13)/3	146861	Robert Price	07/2018
2050	(26*10^146856-77)/3	146857	Robert Price	11/2019
2051	32948^28611+28611^32948	146834	Hans Havermann	11/2020
2052	42596^2799+2799^42596	146829	Hans Havermann	12/2020
2053	2^487726-1863341	146821	Enzo Doria	12/2015
2054	43838^2229+2229^43838	146775	Hans Havermann	11/2020
2055	35005^15594+15594^35005	146775	Hans Havermann	11/2020
2056	((10^73362-1)10000/9+6701)10^73362+(10^73362-1)/9	146728	Hans Havermann	09/2019
2057	32963^28234+28234^32963	146711	Hans Havermann	12/2020
2058	(22*10^146661-19)/3	146662	Robert Price	04/2019
2059	33958^20825+20825^33958	146651	Hans Havermann	12/2020
2060	2^487121-39523	146639	Enzo Doria	09/2015
2061	61063^252+252^61063	146637	Hans Havermann	12/2020
2062	(7*2^486967+1)/39	146591	Lelio R Paula	09/2015
2063	34099^19900+19900^34099	146587	Hans Havermann	11/2020
2064	2^486893-79	146570	Yves Minet	09/2017
2065	36818^9567+9567^36818	146565	Hans Havermann	12/2020
2066	2^486840+1879141	146554	Enzo Doria	08/2016
2067	2^486774-87	146534	Lelio R Paula	12/2017
2068	38655^6176+6176^38655	146530	Hans Havermann	11/2020
2069	8*10^146522-81	146523	Robert Price	02/2021
2070	32820^29059+29059^32820	146485	Hans Havermann	12/2020
2071	37261^8530+8530^37261	146472	Hans Havermann	12/2020
2072	66953^154+154^66953	146462	Hans Havermann	12/2020
2073	96^73877-95^73877	146445	Robert Price	10/2015
2074	8*10^146421+81	146422	Robert Price	08/2019
2075	33153^26090+26090^33153	146420	Hans Havermann	11/2020
2076	(52^85259+1)/53	146304	Paul Bourdelais	09/2017
2077	179^64935+2	146290	Lelio R Paula	10/2017
2078	32595^30758+30758^32595	146285	Hans Havermann	11/2020
2079	34972^15157+15157^34972	146205	Hans Havermann	12/2020
2080	(19*10^146181-49)/3	146182	Robert Price	05/2019
2081	2^485531-114621	146160	Enzo Doria	05/2015
2082	(2^485461-9)/4249	146135	Lelio R Paula	09/2015
2083	2^485389+81887	146117	Enzo Doria	08/2016
2084	32554^30773+30773^32554	146108	Hans Havermann	11/2020
2085	(10^146063+71)/9	146063	Serge Batalov	07/2015
2086	(2^485119+7)/2745	146032	Lelio R Paula	09/2015
2087	(22*10^146029+257)/9	146030	Robert Price	06/2018
2088	7*10^145982-53	145983	Robert Price	06/2020
2089	2^484743+1872923	145923	Enzo Doria	05/2016
2090	33140^25287+25287^33140	145913	Hans Havermann	01/2021
2091	37875^7112+7112^37875	145895	Hans Havermann	01/2021
2092	32862^27473+27473^32862	145872	Hans Havermann	01/2021
2093	32836^27587+27587^32836	145815	Hans Havermann	01/2021
2094	2^484341+1879157	145802	Enzo Doria	08/2016
2095	2*10^145784-91	145785	Robert Price	04/2020
2096	2^484271-51	145781	Lelio R Paula	11/2017
2097	70^78989-69^78989	145743	Robert Price	01/2014
2098	51^85334+2	145714	Robert Price	07/2015
2099	2^483886-1857101	145665	Enzo Doria	10/2015
2100	33350^23307+23307^33350	145656	Hans Havermann	01/2021
2101	(19*10^145585+131)/3	145586	Robert Price	06/2020
2102	2^483563-1863457	145567	Enzo Doria	12/2015
2103	2^483516-1861409	145553	Enzo Doria	11/2015
2104	2^483384-115019	145514	Enzo Doria	06/2015
2105	(259*10^145501-1)/3	145503	Robert Price	12/2020
2106	(19*10^145499-61)/3	145500	Robert Price	05/2019
2107	2^483302-3221	145489	Lelio R Paula	12/2012
2108	35523^12434+12434^35523	145453	Hans Havermann	01/2021
2109	2^483046+1874029	145412	Enzo Doria	06/2016
2110	2^482991-2789317	145395	Enzo Doria	12/2015
2111	2^482978-2789711	145391	Enzo Doria	12/2015
2112	2^482966-2789711	145388	Enzo Doria	12/2015
2113	2^482817-1858843	145343	Enzo Doria	10/2015
2114	2^482751-113635	145323	Enzo Doria	08/2014
2115	2^482705-459763	145309	Enzo Doria	05/2015
2116	(4^241306+11)/3	145281	Robert Price	03/2017
2117	(238*10^145276-1)/3	145278	Robert Price	04/2020
2118	(19*2^482534+1)/7	145258	Lelio R Paula	09/2015
2119	53^84239-52^84239	145252	Robert Price	01/2013
2120	47952^1067+1067^47952	145207	Hans Havermann	01/2021
2121	(2^482333+5)/9287	145193	Lelio R Paula	09/2015
2122	2^482087+72623	145123	Enzo Doria	04/2016
2123	2^482016-286565	145102	Enzo Doria	07/2015
2124	(19*10^145093+101)/3	145094	Robert Price	09/2019
2125	2^481840+15	145049	Robert Price	09/2015
2126	2^481801-481801	145037	Henri Lifchitz	03/2005
2127	2^481775+1869083	145029	Enzo Doria	05/2016
2128	29^99167+2	145022	Ray Chandler	08/2011
2129	2^481663+1875653	144996	Enzo Doria	07/2016
2130	36486^9379+9379^36486	144929	Hans Havermann	12/2020
2131	35111^13378+13378^35111	144882	Hans Havermann	01/2021
2132	2^481149-459073	144841	Enzo Doria	05/2015
2133	34619^15246+15246^34619	144817	Hans Havermann	01/2021
2134	2^481045-113215	144809	Enzo Doria	07/2014
2135	(64*10^144797+287)/9	144798	Robert Price	04/2019
2136	2^480859-113695	144753	Enzo Doria	09/2014
2137	2^480766-2787191	144725	Enzo Doria	11/2015
2138	(21*27^101106-151)/26	144720	Curtis Bright	05/2015
2139	2^480678+1874239	144699	Enzo Doria	06/2016
2140	(8*10^144683+1)/9	144683	Serge Batalov	05/2010
2141	L(692147)	144651	Henri Lifchitz	10/2008
2142	(76*10^144648+77)/9	144649	Robert Price	10/2019
2143	32672^26721+26721^32672	144635	Hans Havermann	01/2021
2144	2^480417+35	144620	Robert Price	11/2015
2145	2^480296-59879	144584	Enzo Doria	10/2015
2146	33157^22878+22878^33157	144546	Hans Havermann	12/2020
2147	45494^1497+1497^45494	144454	Hans Havermann	12/2020
2148	2^479844+3	144448	Donovan Johnson	06/2006
2149	33442^20803+20803^33442	144407	Hans Havermann	01/2021
2150	(27*2^479642+1)/733	144386	Lelio R Paula	08/2015
2151	44917^1638+1638^44917	144378	Hans Havermann	12/2020
2152	(21*2^479605-1)/11	144376	Lelio R Paula	09/2015
2153	2^479348-2792219	144299	Enzo Doria	02/2016
2154	3^302389-6242	144277	Enzo Doria	05/2014
2155	33778^18641+18641^33778	144248	Hans Havermann	01/2021
2156	2*10^144220-3	144221	Robert Price	07/2015
2157	2^478904-109109	144165	Enzo Doria	04/2014
2158	43698^1987+1987^43698	144125	Hans Havermann	12/2020
2159	36128^9723+9723^36128	144072	Hans Havermann	01/2021
2160	32817^24518+24518^32817	144050	Hans Havermann	12/2020
2161	34295^15828+15828^34295	144020	Hans Havermann	01/2021
2162	2^478337-115333	143994	Enzo Doria	07/2015
2163	(7*2^478330-1)/3	143993	Lelio R Paula	08/2015
2164	88^74047-87^74047	143984	Robert Price	05/2015
2165	33242^21441+21441^33242	143980	Hans Havermann	01/2021
2166	(19*10^143963+467)/9	143964	Robert Price	02/2018
2167	(71^77761+1)/72	143954	Paul Bourdelais	09/2017
2168	33490^19859+19859^33490	143939	Hans Havermann	01/2021
2169	2^478088+27	143919	Robert Price	11/2015
2170	7*10^143857-93	143858	Robert Price	08/2020
2171	3*10^143844+61	143845	Robert Price	09/2020
2172	41358^3005+3005^41358	143837	Hans Havermann	01/2021
2173	2^477475-22071	143735	Enzo Doria	07/2013
2174	2^477417-22123	143717	Enzo Doria	07/2013
2175	2^477359-3577	143700	Yves Minet	03/2017
2176	39435^4402+4402^39435	143688	Hans Havermann	01/2021
2177	(14*10^143662-71)/3	143663	Robert Price	12/2018
2178	6^184614+5	143658	Paul Bourdelais	01/2021
2179	46371^1252+1252^46371	143640	Hans Havermann	12/2020
2180	34975^12748+12748^34975	143588	Hans Havermann	01/2021
2181	2^476936-396765	143573	Enzo Doria	07/2013
2182	2^476888-2791229	143558	Enzo Doria	01/2016
2183	2^476868-1859939	143552	Enzo Doria	11/2015
2184	40807^3294+3294^40807	143548	Hans Havermann	12/2020
2185	755^49878+49878^755	143547	Norbert Schneider	04/2019
2186	(19^112247-4^112247)/15	143536	Robert Price	03/2021
2187	2^476558-113627	143459	Enzo Doria	08/2014
2188	2^476478-45	143435	Lelio R Paula	11/2017
2189	(2^475854+9)/73	143245	Lelio R Paula	08/2015
2190	2^475813-113239	143234	Enzo Doria	07/2014
2191	2^475624-114059	143178	Enzo Doria	11/2014
2192	(11*2^475553-7)/15	143156	Renaud Lifchitz	03/2011
2193	2^475480-2786129	143134	Enzo Doria	10/2015
2194	(19*10^143129-43)/3	143130	Robert Price	05/2019
2195	(14*10^143097+73)/3	143098	Robert Price	12/2018
2196	2^475299-111937	143080	Enzo Doria	05/2014
2197	2^475160-2797859	143038	Enzo Doria	04/2016
2198	(2^475069+3)/395	143008	Lelio R Paula	08/2015
2199	2^475027-461437	142998	Enzo Doria	07/2015
2200	(2^474958+78557)/3	142977	Lelio R Paula	07/2015
2201	(8*10^142932+43)/3	142933	Robert Price	06/2018
2202	(54^82471-1)/53	142871	Paul Bourdelais	09/2017
2203	(11*2^474432-1)/95	142818	Lelio R Paula	09/2015
2204	2^474417-59923	142814	Enzo Doria	10/2015
2205	4*10^142810-21	142811	Robert Price	09/2018
2206	(3*2^474166+1)/7	142738	Lelio R Paula	08/2015
2207	2^474053+2897	142705	Lelio R Paula	08/2012
2208	(10^142699+359)/9	142699	Serge Batalov	12/2014
2209	898^48311-897^48311	142676	Jean-Louis Charton	12/2012
2210	2^473740-1856639	142610	Enzo Doria	09/2015
2211	(25*10^142573-403)/9	142574	Robert Price	12/2020
2212	2^473617-114223	142573	Enzo Doria	12/2014
2213	2^473257+1873217	142465	Enzo Doria	06/2016
2214	(19*2^473242+1)/11	142461	Lelio R Paula	09/2015
2215	(61*10^142446-1)/3	142448	Robert Price	01/2020
2216	(14*10^142440+61)/3	142441	Robert Price	12/2018
2217	(10^142425+359)/9	142425	Serge Batalov	12/2014
2218	2^473101+773027	142418	Enzo Doria	05/2016
2219	(13*2^472838-1)/3	142340	Lelio R Paula	09/2015
2220	(17*2^472789-1)/187347	142320	Lelio R Paula	09/2015
2221	2^472634-109511	142278	Enzo Doria	04/2014
2222	(48^84589+1)/49	142213	Robert Price	01/2014
2223	7*10^142189+87	142190	Robert Price	07/2019
2224	2^472258+7	142164	Lelio R Paula	08/2015
2225	(23*10^142105+91)/3	142106	Robert Price	08/2019
2226	tau(317^10330)	142098	Nik Lygeros / Olivier Rozier / LR team	10/2013
2227	(11*2^471913-1)/21	142060	Lelio R Paula	09/2015
2228	(16*10^142058+197)/3	142059	Robert Price	04/2019
2229	9*10^142037+91	142038	Robert Price	10/2020
2230	2^471792+1880881	142024	Enzo Doria	11/2016
2231	(31*2^471580-1)/135	141960	Lelio R Paula	08/2015
2232	(4*10^141926-79)/3	141927	Robert Price	02/2018
2233	(904*19^110984-1)/3	141924	Curtis Bright	05/2015
2234	(14*10^141853+37)/3	141854	Robert Price	12/2018
2235	(41*10^141836-59)/9	141837	Robert Price	10/2018
2236	4*5^202913-9	141831	Lelio R Paula	04/2015
2237	2*7^167812-3	141818	Lelio R Paula	12/2014
2238	2^471043+35	141799	Robert Price	11/2015
2239	(11*2^470956-1)/7945	141770	Lelio R Paula	08/2015
2240	(11*10^141718-131)/3	141719	Robert Price	09/2018
2241	2^470692+76771	141693	Enzo Doria	05/2016
2242	(21*2^470391+1)/533	141601	Lelio R Paula	09/2015
2243	2^470305-459373	141576	Enzo Doria	05/2015
2244	2^470183+72623	141540	Enzo Doria	04/2016
2245	2^470173-16465	141537	Enzo Doria	04/2013
2246	44*10^141476+9	141478	Robert Price	10/2020
2247	2^469974-1841	141477	Enzo Doria	05/2014
2248	(23*2^469939+1)/25	141466	Lelio R Paula	08/2015
2249	2*10^141448+63	141449	Robert Price	05/2018
2250	2^469824+43	141432	Lelio R Paula	09/2017

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