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 (> 30000)	Who ?	When ?
2001	2^381806-4481	114936	Yves Minet	07/2011
2002	2^381774-112373	114926	Enzo Doria	06/2014
2003	2^381555-109051	114860	Enzo Doria	04/2014
2004	2^381546-113501	114857	Enzo Doria	08/2014
2005	2^381360-110429	114801	Enzo Doria	05/2014
2006	2^381252-115079	114769	Enzo Doria	06/2015
2007	2^381209-29323	114756	Enzo Doria	07/2015
2008	569^41651-568^41651	114754	Jean-Louis Charton	11/2009
2009	2^381201+1873205	114753	Enzo Doria	06/2016
2010	2^380974-112991	114685	Enzo Doria	07/2014
2011	88^58949-87	114626	Norbert Schneider	11/2015
2012	2^380700+91	114603	Lelio R Paula	03/2013
2014	10^114575+3^114576	114576	Mike Oakes	09/2010
2013	10^114575+66561	114576	Patrick De Geest	02/2017
2015	10^114575-581081	114575	Patrick De Geest	02/2017
2016	2^380587-115315	114569	Enzo Doria	06/2015
2017	2^380513-216925	114546	Enzo Doria	05/2014
2018	2^380451-1840087	114528	Enzo Doria	06/2015
2019	(15*2^380388-1)/539	114507	Lelio R Paula	04/2014
2020	2^380279-461347	114476	Enzo Doria	07/2015
2021	2^380021+1871147	114398	Enzo Doria	05/2016
2022	2^380005+1869707	114393	Enzo Doria	05/2016
2023	2^379958-113297	114379	Enzo Doria	07/2014
2024	2^379881-109105	114356	Enzo Doria	04/2014
2025	(21*2^379857-1)/13	114349	Lelio R Paula	03/2014
2026	88^58773-87	114284	Norbert Schneider	11/2015
2027	2^379529-2790283	114250	Enzo Doria	03/2016
2028	2^379522+1869115	114248	Enzo Doria	05/2016
2029	(145*10^114226-1)/9	114228	Serge Batalov	12/2014
2030	2^379317-115033	114186	Enzo Doria	06/2015
2031	(17*2^379246-1)/17407	114162	Lelio R Paula	03/2014
2032	2*10^113941+9	113942	Dmitry Domanov	11/2010
2033	2^378272-16565	113872	Enzo Doria	04/2013
2034	2^378217-109075	113855	Enzo Doria	04/2014
2035	2^378198+67	113849	Lelio R Paula	03/2013
2036	2^378173-3249	113842	Yves Minet	12/2014
2037	(2^378155-5)/6597	113833	Lelio R Paula	03/2014
2038	2^378128-262977	113828	Enzo Doria	05/2014
2039	2^378123-113215	113827	Enzo Doria	07/2014
2040	6^146274-18893	113824	Enzo Doria	03/2013
2041	2^378078+75	113813	Lelio R Paula	03/2013
2042	2^377940+63	113772	Lelio R Paula	03/2013
2043	2^377941-2785843	113772	Enzo Doria	04/2016
2044	2^377810+1875109	113733	Enzo Doria	09/2016
2045	2^377803-1838635	113731	Enzo Doria	05/2015
2046	2^377799+52223	113729	Yves Minet	08/2010
2047	11^109190-270	113710	Enzo Doria	12/2012
2048	7*10^113693+9	113694	Robert Price	09/2015
2049	2^377408-2798279	113612	Enzo Doria	04/2016
2050	2^377222+93679	113556	Yves Minet	02/2011
2051	262147#+316847	113552	Makoto Morimoto	02/2016
2052	2^377026-458903	113497	Enzo Doria	04/2015
2053	35^73477-34^73477	113454	Robert Price	05/2012
2054	2^376790+27	113426	Lelio R Paula	03/2013
2055	2^376786-112701	113424	Enzo Doria	06/2014
2056	2^376731+21	113408	Lelio R Paula	03/2013
2058	2^376634+1871245	113379	Enzo Doria	05/2016
2057	(4^188318+17)/3	113379	Robert Price	02/2017
2059	2^376576-344369	113361	Enzo Doria	07/2015
2060	(17*2^376526-1)/223	113345	Lelio R Paula	03/2014
2061	(27*2^376441-1)/811	113319	Lelio R Paula	03/2014
2062	2^376128-21237	113226	Enzo Doria	06/2013
2063	2^375638-1787171	113079	Enzo Doria	03/2016
2064	2^375537+4847	113048	Yves Minet	02/2011
2065	(17^91837+16^91837)/33	113000	Robert Price	08/2013
2066	5F(270343)(F(270343)+1)+1	112997	Serge Batalov	04/2015
2067	2^375350-3221	112992	Yves Minet	07/2011
2068	(13*2^375306+1)/7	112979	Lelio R Paula	03/2014
2069	2^375305+76757	112979	Enzo Doria	05/2016
2070	2^375258+1874989	112964	Enzo Doria	07/2016
2071	(29^77237-1)/28	112950	Robert Price	04/2012
2072	2^375154+74959	112933	Enzo Doria	04/2016
2073	2^374993-2787163	112885	Enzo Doria	11/2015
2074	123^53970+2	112793	Lelio R Paula	06/2013
2075	p(22852)#/2+512	112745	Robert Price	05/2017
2076	2^374441-21049	112718	Enzo Doria	06/2013
2077	(2^374321+1)/3	112682	H.&R. Lifchitz	12/2000
2078	(13^101089-1)/12	112607	Paul Bourdelais	03/2010
2079	3^236011-8828	112606	Enzo Doria	05/2014
2080	39^70666+2	112435	Lelio R Paula	11/2013
2081	(2^373350-7)/3	112390	Lelio R Paula	03/2014
2082	2^373306-1840931	112377	Enzo Doria	06/2015
2083	2^373117+1872107	112320	Enzo Doria	05/2016
2084	2^373040+2792761	112297	Enzo Doria	03/2016
2085	EPrime(112280)	112280	Eric W. Weisstein	10/2010
2086	2^372950+7	112270	Lelio R Paula	03/2013
2087	2^372945+1872167	112268	Enzo Doria	05/2016
2088	2^372695+72113	112193	Enzo Doria	04/2016
2089	2^372689-2563	112191	Yves Minet	07/2014
2090	2^372638-1859441	112176	Enzo Doria	03/2016
2091	3^235074-113056	112159	Enzo Doria	07/2014
2092	(91*10^112098-1)/9	112100	Robert Price	04/2015
2093	2^372310-85061	112077	Paul Bourdelais	02/2012
2094	(10^112067+53)/9	112067	Serge Batalov	07/2015
2095	75^59760+2	112054	Lelio R Paula	08/2013
2096	2^372108+74221	112016	Enzo Doria	04/2016
2097	2^371970-459491	111975	Enzo Doria	05/2015
2098	41^69427-40^69427	111971	Robert Price	07/2012
2099	(10^111902+71)/9	111902	Serge Batalov	07/2015
2100	2^371440-112865	111815	Enzo Doria	06/2014
2101	2^371426-459161	111811	Enzo Doria	05/2015
2102	2^371276-461267	111766	Enzo Doria	07/2015
2103	2^371098-113261	111712	Enzo Doria	07/2014
2104	(7*10^111706-61)/9	111706	Erik Branger	01/2011
2105	2^371044+1869391	111696	Enzo Doria	05/2016
2106	88^57416+87	111645	Norbert Schneider	11/2015
2107	2^370829-109693	111631	Enzo Doria	04/2014
2108	15^94906-2	111619	Lelio R Paula	11/2013
2110	2^370643-37	111575	Yves Minet	01/2012
2109	(2^370655-5)/2439	111575	Lelio R Paula	03/2014
2111	2^370610-3911	111565	Yves Minet	04/2017
2112	286^45405+45405^286	111532	Norbert Schneider	04/2015
2113	4*5^159563-9	111531	Lelio R Paula	11/2014
2114	2^370393-2797093	111500	Enzo Doria	03/2016
2115	(21*2^370382-1)/629	111495	Lelio R Paula	03/2014
2116	2^370292-2791979	111469	Enzo Doria	03/2016
2117	2^370177-461551	111435	Enzo Doria	07/2015
2118	109^54683-108	111413	Norbert Schneider	02/2017
2119	numbpart(10^10+76282)	111391	Serge Batalov	04/2015
2120	2^369974+733	111374	Lelio R Paula	05/2013
2121	2^369915-286267	111356	Enzo Doria	07/2015
2122	2^369855-1615	111338	Lelio R Paula	05/2017
2123	7*10^111325+3	111326	Robert Price	08/2015
2124	51^65176+2	111293	Lelio R Paula	08/2013
2125	2^369643-1865767	111274	Enzo Doria	03/2016
2126	2^369603+885	111262	Lelio R Paula	05/2017
2127	L(532277)	111240	Renaud Lifchitz	03/2004
2128	2^369392+29835	111199	Lelio R Paula	05/2017
2129	2^369354-3413	111187	Yves Minet	12/2016
2130	2^369296-27	111170	Lelio R Paula	02/2013
2131	2^369239-109837	111153	Enzo Doria	05/2014
2132	2^369224-291839	111148	Enzo Doria	07/2015
2133	2^369216+2798881	111146	Enzo Doria	04/2016
2134	10^111111+163849	111112	Patrick De Geest	03/2017
2135	10^111111-312911	111111	Patrick De Geest	03/2017
2136	2^369092-216923	111108	Enzo Doria	05/2014
2137	2^369081-55	111105	Lelio R Paula	02/2013
2138	88^57124-87	111077	Norbert Schneider	11/2015
2139	2^368980+753	111075	Lelio R Paula	05/2013
2140	2^368946-3623	111064	Yves Minet	03/2017
2141	2^368929+29835	111059	Lelio R Paula	05/2017
2142	4^184463-3^184463	111058	Jean-Louis Charton	12/2004
2143	111^54298+110	111057	Norbert Schneider	04/2017
2144	(4*10^111032-7)/3	111033	Ray Chandler	04/2011
2145	2^368641-460303	110972	Enzo Doria	06/2015
2146	2^368619-109087	110966	Enzo Doria	04/2014
2147	3*2^368489+7	110927	Lelio R Paula	09/2014
2148	97411!4-2	110913	Robert Price	07/2017
2149	(9179*2^368330-1)/35	110881	Lelio R Paula	05/2015
2150	(34*10^110882-7)/9/13/29/1019374319	110871	Makoto Morimoto	05/2016
2151	2^368050-64875	110795	Lelio R Paula	05/2017
2152	2^368048+25	110794	Lelio R Paula	02/2013
2153	69^60239-2	110771	Lelio R Paula	10/2013
2154	(23*2^367952+1)/15717	110762	Lelio R Paula	03/2014
2155	2^367924-69	110757	Lelio R Paula	02/2013
2156	2^367709-109723	110692	Enzo Doria	04/2014
2157	(3*2^367644-1)/107	110671	Lelio R Paula	03/2014
2158	(23*2^367398+1)/57963	110595	Lelio R Paula	03/2014
2159	2^367215+1879223	110543	Enzo Doria	09/2016
2160	2^367141+41	110521	Lelio R Paula	02/2013
2161	2^367126+29835	110516	Lelio R Paula	05/2017
2162	(31*2^366976+1)/7	110472	Lelio R Paula	03/2014
2163	2^366853+5711	110434	Lelio R Paula	05/2017
2164	(21181*2^366833+1)/3	110432	Lelio R Paula	07/2014
2165	2^366816+315	110423	Lelio R Paula	05/2017
2166	2^366775-2787037	110411	Enzo Doria	03/2016
2167	(112*10^110405-1)/3	110407	Serge Batalov	12/2014
2168	2^366751+2797553	110404	Enzo Doria	03/2016
2169	2^366748+255	110403	Lelio R Paula	05/2017
2170	2^366738-2985	110400	Yves Minet	09/2014
2171	(23*2^366739+1)/74575	110396	Lelio R Paula	03/2014
2172	2^366716+1871791	110393	Enzo Doria	05/2016
2173	2^366649+1871687	110373	Enzo Doria	05/2016
2174	2^366629-351205	110367	Enzo Doria	06/2015
2175	2^366558+1874479	110345	Enzo Doria	06/2016
2176	18^87853-4409	110280	Enzo Doria	03/2013
2177	2^366218-23	110243	Lelio R Paula	02/2013
2178	(21*2^366193-1)/197	110235	Lelio R Paula	03/2014
2179	2^366178-343991	110231	Enzo Doria	07/2015
2180	2^365944+1871341	110161	Enzo Doria	05/2016
2181	2^365838-461267	110129	Enzo Doria	07/2015
2182	2^365763-6555	110106	Lelio R Paula	04/2017
2183	(2^365689+2^182845+1)/5	110083		11/2006
2184	2^365666-459161	110077	Enzo Doria	05/2015
2185	3*10^110076-7	110077	Robert Price	08/2015
2186	13^98785-72	110041	Lelio R Paula	03/2017
2187	(25^78707+1)/26	110027	Robert Price	06/2013
2188	6^141361-7	110001	Lelio R Paula	11/2014
2189	20^84536+81	109984	Lelio R Paula	03/2017
2190	5*2^365347-9	109982	Lelio R Paula	09/2014
2191	9*6^141303+7	109957	Lelio R Paula	11/2014
2192	78^58099+77	109929	Norbert Schneider	02/2015
2193	2*10^109928-7	109929	Robert Price	10/2015
2194	(27*2^365137-1)/2021	109916	Lelio R Paula	03/2014
2195	(4441*29^75152-24)/7	109905	Curtis Bright	05/2015
2196	(2^365087+7)/6015	109899	Lelio R Paula	01/2014
2197	18^87533-11	109878	Lelio R Paula	04/2017
2198	2^364982-5	109871	Henri Lifchitz	04/2006
2199	2^364936-1867979	109857	Enzo Doria	04/2016
2200	2^364867-112087	109836	Enzo Doria	06/2014
2201	4^182415-85061	109825	Mike Oakes	06/2011
2202	(17^89227+16^89227)/33	109788	Robert Price	08/2013
2203	2^364687-187	109782	Lelio R Paula	01/2012
2204	2^364644+67	109769	Lelio R Paula	01/2012
2205	(9787*2^364625-1)/24947	109763	Lelio R Paula	05/2015
2206	(2^364616+5)/9	109760	Lelio R Paula	01/2014
2207	12^101694+73	109747	Lelio R Paula	03/2017
2208	13^98518-66	109744	Lelio R Paula	03/2017
2209	2^364478-113261	109719	Enzo Doria	07/2014
2210	(24737*2^364454+1)/3	109716	Lelio R Paula	07/2014
2211	(62*10^109673+1)/9	109674	Serge Batalov	11/2010
2212	3^229824+340	109654	Lelio R Paula	03/2017
2213	2^364169-112813	109626	Enzo Doria	06/2014
2214	10^109615+21	109616	Lelio R Paula	03/2017
2215	10^109615-456267	109615	Patrick De Geest	03/2017
2216	2^364094-113	109604	Lelio R Paula	01/2012
2217	(4^182026+11)/3	109591	Robert Price	02/2017
2218	2^364041-6883	109588	Lelio R Paula	09/2011
2219	12^101545+11	109586	Lelio R Paula	03/2017
2220	2^363842-2787101	109528	Enzo Doria	03/2016
2221	(22699*2^363782+1)/763	109511	Lelio R Paula	07/2014
2222	2^363769+5711	109506	Lelio R Paula	04/2017
2223	(31*2^363748+1)/49	109499	Lelio R Paula	03/2014
2224	p(22245)#/2-8	109462	Robert Price	01/2017
2225	2^363556+55	109442	Lelio R Paula	01/2012
2226	(55459*2^363411+1)/81	109401	Lelio R Paula	07/2014
2227	2^363406+1871569	109397	Enzo Doria	05/2016
2228	(2^363349+7)/9	109378	Lelio R Paula	01/2014
2229	3^229236+100	109374	Lelio R Paula	03/2017
2230	2^363268-58695	109355	Lelio R Paula	04/2017
2231	2^363191-112321	109332	Enzo Doria	06/2014
2232	2^363120+3	109311	Donovan Johnson	04/2006
2233	(10^109297-1)/9	109297	Paul Bourdelais, Harvey Dubner	04/2007
2234	2^363042-114641	109287	Enzo Doria	04/2015
2235	2^363020-112793	109280	Enzo Doria	06/2014
2236	(67607*2^362695+1)/70499	109183	Lelio R Paula	07/2014
2237	(9*2^362644+1)/5	109167	Lelio R Paula	03/2014
2238	5^156181+38	109166	Lelio R Paula	02/2017
2239	3^228750+68	109142	Lelio R Paula	03/2017
2240	(10223*2^362376+1)/9	109090	Lelio R Paula	07/2014
2241	65^60167-64^60167	109078	Robert Price	08/2013
2242	7*3^228589-2	109066	Lelio R Paula	09/2014
2243	(78557*2^362188+1)/189	109033	Lelio R Paula	07/2014
2244	2*7^129008+9	109025	Lelio R Paula	11/2014
2245	2^361957+76367	108960	Enzo Doria	05/2016
2246	2^361873-1411	108935	Yves Minet	01/2013
2247	(24737*2^361857+1)/35	108933	Lelio R Paula	07/2014
2248	13^97745-24	108883	Lelio R Paula	03/2017
2249	17^88475+8	108864	Lelio R Paula	04/2017
2250	2^361567+51	108843	Lelio R Paula	01/2012

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Probable Primes Top 10000

(180278 PRPs in the top)