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	32820^29059+29059^32820	146485	Hans Havermann	12/2020
2002	37261^8530+8530^37261	146472	Hans Havermann	12/2020
2003	66953^154+154^66953	146462	Hans Havermann	12/2020
2004	96^73877-95^73877	146445	Robert Price	10/2015
2005	8*10^146421+81	146422	Robert Price	08/2019
2006	33153^26090+26090^33153	146420	Hans Havermann	11/2020
2007	(52^85259+1)/53	146304	Paul Bourdelais	09/2017
2008	179^64935+2	146290	Lelio R Paula	10/2017
2009	32595^30758+30758^32595	146285	Hans Havermann	11/2020
2010	34972^15157+15157^34972	146205	Hans Havermann	12/2020
2011	(19*10^146181-49)/3	146182	Robert Price	05/2019
2012	2^485531-114621	146160	Enzo Doria	05/2015
2013	(2^485461-9)/4249	146135	Lelio R Paula	09/2015
2014	2^485389+81887	146117	Enzo Doria	08/2016
2015	32554^30773+30773^32554	146108	Hans Havermann	11/2020
2016	(10^146063+71)/9	146063	Serge Batalov	07/2015
2017	(2^485119+7)/2745	146032	Lelio R Paula	09/2015
2018	(22*10^146029+257)/9	146030	Robert Price	06/2018
2019	7*10^145982-53	145983	Robert Price	06/2020
2020	2^484743+1872923	145923	Enzo Doria	05/2016
2021	37875^7112+7112^37875	145895	Hans Havermann	01/2021
2022	32862^27473+27473^32862	145872	Hans Havermann	01/2021
2023	32836^27587+27587^32836	145815	Hans Havermann	01/2021
2024	2^484341+1879157	145802	Enzo Doria	08/2016
2025	2*10^145784-91	145785	Robert Price	04/2020
2026	2^484271-51	145781	Lelio R Paula	11/2017
2027	70^78989-69^78989	145743	Robert Price	01/2014
2028	51^85334+2	145714	Robert Price	07/2015
2029	2^483886-1857101	145665	Enzo Doria	10/2015
2030	(19*10^145585+131)/3	145586	Robert Price	06/2020
2031	2^483563-1863457	145567	Enzo Doria	12/2015
2032	2^483516-1861409	145553	Enzo Doria	11/2015
2033	2^483384-115019	145514	Enzo Doria	06/2015
2034	(259*10^145501-1)/3	145503	Robert Price	12/2020
2035	(19*10^145499-61)/3	145500	Robert Price	05/2019
2036	2^483302-3221	145489	Lelio R Paula	12/2012
2037	35523^12434+12434^35523	145453	Hans Havermann	01/2021
2038	2^483046+1874029	145412	Enzo Doria	06/2016
2039	2^482991-2789317	145395	Enzo Doria	12/2015
2040	2^482978-2789711	145391	Enzo Doria	12/2015
2041	2^482966-2789711	145388	Enzo Doria	12/2015
2042	2^482817-1858843	145343	Enzo Doria	10/2015
2043	2^482751-113635	145323	Enzo Doria	08/2014
2044	2^482705-459763	145309	Enzo Doria	05/2015
2045	(4^241306+11)/3	145281	Robert Price	03/2017
2046	(238*10^145276-1)/3	145278	Robert Price	04/2020
2047	(19*2^482534+1)/7	145258	Lelio R Paula	09/2015
2048	53^84239-52^84239	145252	Robert Price	01/2013
2049	47952^1067+1067^47952	145207	Hans Havermann	01/2021
2050	(2^482333+5)/9287	145193	Lelio R Paula	09/2015
2051	2^482087+72623	145123	Enzo Doria	04/2016
2052	2^482016-286565	145102	Enzo Doria	07/2015
2053	(19*10^145093+101)/3	145094	Robert Price	09/2019
2054	2^481840+15	145049	Robert Price	09/2015
2055	2^481801-481801	145037	Henri Lifchitz	03/2005
2056	2^481775+1869083	145029	Enzo Doria	05/2016
2057	29^99167+2	145022	Ray Chandler	08/2011
2058	2^481663+1875653	144996	Enzo Doria	07/2016
2059	36486^9379+9379^36486	144929	Hans Havermann	12/2020
2060	35111^13378+13378^35111	144882	Hans Havermann	01/2021
2061	2^481149-459073	144841	Enzo Doria	05/2015
2062	34619^15246+15246^34619	144817	Hans Havermann	01/2021
2063	2^481045-113215	144809	Enzo Doria	07/2014
2064	(64*10^144797+287)/9	144798	Robert Price	04/2019
2065	2^480859-113695	144753	Enzo Doria	09/2014
2066	2^480766-2787191	144725	Enzo Doria	11/2015
2067	(21*27^101106-151)/26	144720	Curtis Bright	05/2015
2068	2^480678+1874239	144699	Enzo Doria	06/2016
2069	(8*10^144683+1)/9	144683	Serge Batalov	05/2010
2070	L(692147)	144651	Henri Lifchitz	10/2008
2071	(76*10^144648+77)/9	144649	Robert Price	10/2019
2072	32672^26721+26721^32672	144635	Hans Havermann	01/2021
2073	2^480417+35	144620	Robert Price	11/2015
2074	2^480296-59879	144584	Enzo Doria	10/2015
2075	33157^22878+22878^33157	144546	Hans Havermann	12/2020
2076	45494^1497+1497^45494	144454	Hans Havermann	12/2020
2077	2^479844+3	144448	Donovan Johnson	06/2006
2078	33442^20803+20803^33442	144407	Hans Havermann	01/2021
2079	(27*2^479642+1)/733	144386	Lelio R Paula	08/2015
2080	44917^1638+1638^44917	144378	Hans Havermann	12/2020
2081	(21*2^479605-1)/11	144376	Lelio R Paula	09/2015
2082	2^479348-2792219	144299	Enzo Doria	02/2016
2083	3^302389-6242	144277	Enzo Doria	05/2014
2084	33778^18641+18641^33778	144248	Hans Havermann	01/2021
2085	2*10^144220-3	144221	Robert Price	07/2015
2086	2^478904-109109	144165	Enzo Doria	04/2014
2087	43698^1987+1987^43698	144125	Hans Havermann	12/2020
2088	36128^9723+9723^36128	144072	Hans Havermann	01/2021
2089	32817^24518+24518^32817	144050	Hans Havermann	12/2020
2090	2^478337-115333	143994	Enzo Doria	07/2015
2091	(7*2^478330-1)/3	143993	Lelio R Paula	08/2015
2092	88^74047-87^74047	143984	Robert Price	05/2015
2093	33242^21441+21441^33242	143980	Hans Havermann	01/2021
2094	(19*10^143963+467)/9	143964	Robert Price	02/2018
2095	(71^77761+1)/72	143954	Paul Bourdelais	09/2017
2096	33490^19859+19859^33490	143939	Hans Havermann	01/2021
2097	2^478088+27	143919	Robert Price	11/2015
2098	7*10^143857-93	143858	Robert Price	08/2020
2099	3*10^143844+61	143845	Robert Price	09/2020
2100	41358^3005+3005^41358	143837	Hans Havermann	01/2021
2101	2^477475-22071	143735	Enzo Doria	07/2013
2102	2^477417-22123	143717	Enzo Doria	07/2013
2103	2^477359-3577	143700	Yves Minet	03/2017
2104	39435^4402+4402^39435	143688	Hans Havermann	01/2021
2105	(14*10^143662-71)/3	143663	Robert Price	12/2018
2106	46371^1252+1252^46371	143640	Hans Havermann	12/2020
2107	34975^12748+12748^34975	143588	Hans Havermann	01/2021
2108	2^476936-396765	143573	Enzo Doria	07/2013
2109	2^476888-2791229	143558	Enzo Doria	01/2016
2110	2^476868-1859939	143552	Enzo Doria	11/2015
2111	40807^3294+3294^40807	143548	Hans Havermann	12/2020
2112	755^49878+49878^755	143547	Norbert Schneider	04/2019
2113	2^476558-113627	143459	Enzo Doria	08/2014
2114	2^476478-45	143435	Lelio R Paula	11/2017
2115	(2^475854+9)/73	143245	Lelio R Paula	08/2015
2116	2^475813-113239	143234	Enzo Doria	07/2014
2117	2^475624-114059	143178	Enzo Doria	11/2014
2118	(11*2^475553-7)/15	143156	Renaud Lifchitz	03/2011
2119	2^475480-2786129	143134	Enzo Doria	10/2015
2120	(19*10^143129-43)/3	143130	Robert Price	05/2019
2121	(14*10^143097+73)/3	143098	Robert Price	12/2018
2122	2^475299-111937	143080	Enzo Doria	05/2014
2123	2^475160-2797859	143038	Enzo Doria	04/2016
2124	(2^475069+3)/395	143008	Lelio R Paula	08/2015
2125	2^475027-461437	142998	Enzo Doria	07/2015
2126	(2^474958+78557)/3	142977	Lelio R Paula	07/2015
2127	(8*10^142932+43)/3	142933	Robert Price	06/2018
2128	(54^82471-1)/53	142871	Paul Bourdelais	09/2017
2129	(11*2^474432-1)/95	142818	Lelio R Paula	09/2015
2130	2^474417-59923	142814	Enzo Doria	10/2015
2131	4*10^142810-21	142811	Robert Price	09/2018
2132	(3*2^474166+1)/7	142738	Lelio R Paula	08/2015
2133	2^474053+2897	142705	Lelio R Paula	08/2012
2134	(10^142699+359)/9	142699	Serge Batalov	12/2014
2135	898^48311-897^48311	142676	Jean-Louis Charton	12/2012
2136	2^473740-1856639	142610	Enzo Doria	09/2015
2137	(25*10^142573-403)/9	142574	Robert Price	12/2020
2138	2^473617-114223	142573	Enzo Doria	12/2014
2139	2^473257+1873217	142465	Enzo Doria	06/2016
2140	(19*2^473242+1)/11	142461	Lelio R Paula	09/2015
2141	(61*10^142446-1)/3	142448	Robert Price	01/2020
2142	(14*10^142440+61)/3	142441	Robert Price	12/2018
2143	(10^142425+359)/9	142425	Serge Batalov	12/2014
2144	2^473101+773027	142418	Enzo Doria	05/2016
2145	(13*2^472838-1)/3	142340	Lelio R Paula	09/2015
2146	(17*2^472789-1)/187347	142320	Lelio R Paula	09/2015
2147	2^472634-109511	142278	Enzo Doria	04/2014
2148	(48^84589+1)/49	142213	Robert Price	01/2014
2149	7*10^142189+87	142190	Robert Price	07/2019
2150	2^472258+7	142164	Lelio R Paula	08/2015
2151	(23*10^142105+91)/3	142106	Robert Price	08/2019
2152	tau(317^10330)	142098	Nik Lygeros / Olivier Rozier / LR team	10/2013
2153	(11*2^471913-1)/21	142060	Lelio R Paula	09/2015
2154	(16*10^142058+197)/3	142059	Robert Price	04/2019
2155	9*10^142037+91	142038	Robert Price	10/2020
2156	2^471792+1880881	142024	Enzo Doria	11/2016
2157	(31*2^471580-1)/135	141960	Lelio R Paula	08/2015
2158	(4*10^141926-79)/3	141927	Robert Price	02/2018
2159	(904*19^110984-1)/3	141924	Curtis Bright	05/2015
2160	(14*10^141853+37)/3	141854	Robert Price	12/2018
2161	(41*10^141836-59)/9	141837	Robert Price	10/2018
2162	4*5^202913-9	141831	Lelio R Paula	04/2015
2163	2*7^167812-3	141818	Lelio R Paula	12/2014
2164	2^471043+35	141799	Robert Price	11/2015
2165	(11*2^470956-1)/7945	141770	Lelio R Paula	08/2015
2166	(11*10^141718-131)/3	141719	Robert Price	09/2018
2167	2^470692+76771	141693	Enzo Doria	05/2016
2168	(21*2^470391+1)/533	141601	Lelio R Paula	09/2015
2169	2^470305-459373	141576	Enzo Doria	05/2015
2170	2^470183+72623	141540	Enzo Doria	04/2016
2171	2^470173-16465	141537	Enzo Doria	04/2013
2172	44*10^141476+9	141478	Robert Price	10/2020
2173	2^469974-1841	141477	Enzo Doria	05/2014
2174	(23*2^469939+1)/25	141466	Lelio R Paula	08/2015
2175	2*10^141448+63	141449	Robert Price	05/2018
2176	2^469824+43	141432	Lelio R Paula	09/2017
2177	2*10^141407-27	141408	Robert Price	05/2018
2178	(214*10^141385-1)/3	141387	Robert Price	01/2021
2179	2^469630-59711	141373	Enzo Doria	10/2015
2180	(25*10^141366-331)/9	141367	Robert Price	08/2018
2181	(2^469564-3)/611	141351	Lelio R Paula	08/2015
2182	197^61601+2	141342	Lelio R Paula	08/2017
2183	2^469372-112949	141296	Enzo Doria	07/2014
2185	143^(2^16)+106^(2^16)	141253	Valeryi Kuryshev	02/2011
2184	143^65536+106^65536	141253	Serge Batalov	03/2018
2186	2^469198+782569	141243	Enzo Doria	10/2016
2187	2^469076-2786939	141206	Enzo Doria	11/2015
2188	2^468804+1874941	141125	Enzo Doria	06/2016
2189	2^468787+81353	141119	Enzo Doria	08/2016
2190	2^468595-350407	141062	Enzo Doria	06/2015
2191	2^468564+87855	141052	Lelio R Paula	01/2016
2192	2^468551-21987	141048	Enzo Doria	07/2013
2193	2^468523-7	141040	Lelio R Paula	08/2015
2194	(25*10^141019-13)/3	141020	Robert Price	09/2019
2195	2^468405+87855	141004	Lelio R Paula	01/2016
2196	2^467978-113051	140876	Enzo Doria	07/2014
2197	2^467780-344429	140816	Enzo Doria	07/2015
2198	9*10^140802-89	140803	Robert Price	04/2020
2199	2^467605-1855603	140764	Enzo Doria	09/2015
2200	5*10^140744-7	140745	Robert Price	09/2015
2201	(5^201359-1)/4	140744	Paul Bourdelais	12/2008
2202	2^467401-1850023	140702	Enzo Doria	08/2015
2203	(266*10^140681-17)/3	140683	Robert Price	07/2020
2204	(2^467270+78557)/23247	140658	Lelio R Paula	07/2015
2205	(29*2^467205+1)/2780517107	140635	Lelio R Paula	08/2015
2206	2^467166-1854941	140631	Enzo Doria	09/2015
2207	(203*10^140615-11)/3	140617	Robert Price	12/2020
2208	(85*10^140609+473)/9	140610	Robert Price	01/2020
2209	2^466866-1840571	140541	Enzo Doria	06/2015
2210	2^466829-459523	140530	Enzo Doria	05/2015
2211	2^466692-113213	140489	Enzo Doria	07/2014
2212	(44*10^140410-503)/9	140411	Robert Price	12/2018
2213	153^64265-2	140400	Lelio R Paula	11/2017
2214	(112*10^140357-1)/3	140359	Serge Batalov	12/2014
2215	(29*10^140337-17)/3	140338	Robert Price	09/2019
2216	2^466181-112735	140335	Enzo Doria	07/2014
2217	(5*10^140281-119)/3	140282	Robert Price	03/2018
2218	(27*2^465872+1)/691	140241	Lelio R Paula	08/2015
2219	2^465803-114817	140221	Enzo Doria	05/2015
2220	floor(Pi*10^140344)%10^140165	140165	Serge Batalov	08/2012
2221	2^465503-112735	140131	Enzo Doria	07/2014
2222	(16*10^140091+167)/3	140092	Robert Price	06/2019
2223	6^179964+179964^6-1	140040	Robert Price	04/2014
2224	(89*10^140008-179)/9	140009	Robert Price	12/2019
2225	(29*2^465077-1)/9	140003	Lelio R Paula	08/2015
2226	2^465072-344789	140001	Enzo Doria	07/2015
2227	5*10^139945+81	139946	Robert Price	03/2019
2228	2^464864-17	139939	Lelio R Paula	09/2017
2229	8*10^139920+51	139921	Robert Price	08/2019
2230	(85*10^139913-1)/3	139915	Robert Price	02/2020
2231	(17^113621+1)/18	139804	Paul Bourdelais	09/2011
2232	2*10^139800-21	139801	Robert Price	09/2020
2233	(13*10^139782+191)/3	139783	Robert Price	11/2018
2234	(19*2^464312-1)/3	139773	Lelio R Paula	08/2015
2235	(74*10^139723+133)/9	139724	Robert Price	06/2019
2236	3*10^139722+13	139723	Robert Price	07/2018
2237	77*10^139692+3	139694	Robert Price	06/2020
2238	(31*2^463970+1)/5	139670	Lelio R Paula	08/2015
2239	(18203^(2^15)+(18201)^(2^15))/2	139597	Robert Price	05/2018
2240	2^463633-2788423	139568	Enzo Doria	11/2015
2241	2^463271-109501	139459	Enzo Doria	04/2014
2242	(5*10^139457+79)/3	139458	Robert Price	03/2018
2243	2^463237-99	139449	Lelio R Paula	09/2017
2244	(49*10^139442+383)/9	139443	Robert Price	04/2019
2245	(7*10^139417-547)/9	139417	Robert Price	01/2018
2246	(10^139398+191)/3	139398	Robert Price	02/2018
2247	2^463019+79463	139383	Enzo Doria	06/2016
2248	3^292129-112756	139381	Enzo Doria	07/2014
2249	(15*2^462951+1)/527	139361	Lelio R Paula	08/2015
2250	2^462855-1865707	139334	Enzo Doria	02/2016

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Probable Primes Top 10000

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