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	2^405514-115511	122072	Enzo Doria	07/2015
2002	2^405422-113261	122045	Enzo Doria	07/2014
2003	2^405173+71237	121970	Enzo Doria	04/2016
2004	(2^405016+1)/257	121920	Lelio R Paula	04/2014
2005	2^404858+71329	121875	Enzo Doria	04/2016
2006	2^404813-114703	121861	Enzo Doria	04/2015
2007	2^404764+77791	121847	Enzo Doria	05/2016
2008	317^48694+48694^317	121787	Norbert Schneider	08/2015
2009	2^404536-115259	121778	Enzo Doria	06/2015
2010	2^404501-631	121767	Yves Minet	07/2012
2011	63^67620+2	121672	Lelio R Paula	08/2015
2012	(17*10^121621+1)/9	121622	Serge Batalov	05/2010
2013	(15*2^403912+1)/271	121589	Lelio R Paula	05/2014
2014	(10^121543-79)/3	121543	Robert Price	01/2018
2015	2^403676+76831	121519	Enzo Doria	05/2016
2016	(7*10^121487+143)/3	121488	Robert Price	03/2018
2017	2^403363-113635	121425	Enzo Doria	08/2014
2018	2^403336-1861469	121417	Enzo Doria	03/2016
2019	p(24442)#/2-64	121381	Robert Price	04/2017
2020	11^116555-720	121380	Enzo Doria	11/2012
2021	2^403100-461267	121346	Enzo Doria	07/2015
2022	2^403093-112213	121344	Enzo Doria	06/2014
2023	(316^48539+1)/317	121330	Eric Chen	10/2017
2024	2^403004+1866361	121317	Enzo Doria	03/2016
2025	2^402953+89	121301	Lelio R Paula	10/2013
2026	2^402944-2788319	121299	Enzo Doria	03/2016
2027	(27*2^402865+1)/5	121276	Lelio R Paula	04/2014
2028	2^402828-113183	121264	Enzo Doria	07/2014
2029	(17*10^121242+1)/9	121243	Serge Batalov	05/2010
2030	(15*2^402757+1)/101	121242	Lelio R Paula	05/2014
2031	2^402715+1874223	121230	Enzo Doria	06/2016
2032	(91^61879+1)/92	121222	Paul Bourdelais	09/2017
2033	7*10^121144+9	121145	Robert Price	09/2015
2034	2^401725-113251	120932	Enzo Doria	07/2014
2035	(15*2^401677-1)/19	120917	Lelio R Paula	05/2014
2036	2^401652+73711	120910	Enzo Doria	04/2016
2037	(2^401632+3)/79	120902	Lelio R Paula	04/2014
2038	2^401406-2791331	120836	Enzo Doria	03/2016
2039	(28^83497+1)/29	120832	Robert Price	07/2013
2040	2^401369+1867367	120825	Enzo Doria	03/2016
2041	(10^120782+29)/3	120782	Serge Batalov	12/2014
2042	2^401215-1657	120778	Yves Minet	07/2014
2043	2^401159+53	120761	Lelio R Paula	10/2013
2044	2^401031-113047	120723	Enzo Doria	07/2014
2045	(29*2^400909-1)/303	120685	Lelio R Paula	04/2014
2046	2^400571-15	120584	Lelio R Paula	10/2013
2047	(10^120574+359)/9	120574	Serge Batalov	12/2014
2048	2^400424-216413	120540	Enzo Doria	04/2013
2049	(17*2^400200-1)/587	120471	Lelio R Paula	05/2014
2050	2^400166+1874899	120462	Enzo Doria	06/2016
2051	(3*2^400045-1)/865	120424	Lelio R Paula	04/2014
2052	2^399966+73759	120402	Enzo Doria	04/2016
2053	(112*10^120395-1)/3	120397	Serge Batalov	12/2014
2054	2^399918-95	120388	Lelio R Paula	04/2013
2055	2^399792-1849259	120350	Enzo Doria	08/2015
2056	9*10^120342-7	120343	Robert Price	09/2015
2057	2^399526-1861721	120270	Enzo Doria	11/2015
2058	(10^(260126+1)+3610^60126-1)/9	120253	Robert Price	10/2015
2059	2^399322-2798111	120208	Enzo Doria	04/2016
2060	72^64693-71^64693	120157	Robert Price	03/2014
2061	2^399111-28489	120145	Enzo Doria	08/2015
2063	2^398877+105	120074	Donovan Johnson	01/2006
2062	(101*10^120072-87)/7	120074	Hans Havermann	02/2015
2064	(88^61751+1)/89	120072	Paul Bourdelais	09/2017
2065	2^398710+57	120024	Lelio R Paula	04/2013
2066	2^398691-115057	120018	Enzo Doria	06/2015
2067	L(574219)	120005	Renaud Lifchitz	03/2004
2068	2^398571+60413	119982	Yves Minet	03/2011
2069	p(24179)#/2-64	119949	Robert Price	04/2017
2070	2^398448+1872001	119945	Enzo Doria	05/2016
2071	8*10^119930-3	119931	Ray Chandler	04/2011
2072	(10^119880+179)/9	119880	Serge Batalov	12/2014
2073	(9*2^398145+1)/73	119853	Lelio R Paula	04/2014
2074	(10^119836+77)/3	119836	Robert Price	01/2018
2075	2^398029+1872527	119819	Enzo Doria	05/2016
2076	2^397897-113541	119779	Enzo Doria	08/2014
2077	(21*2^397661-1)/27593	119705	Lelio R Paula	04/2014
2078	(58^67853-1)/57	119653	Paul Bourdelais	09/2017
2079	2^397426+73849	119638	Enzo Doria	04/2016
2080	2^396933-112723	119489	Enzo Doria	06/2014
2081	11^114738-150	119488	Enzo Doria	10/2012
2082	(4*10^119474+149)/9	119474	Robert Price	04/2018
2083	2^396790-21	119446	Lelio R Paula	04/2013
2084	(2^396633-7)/5	119398	Lelio R Paula	04/2014
2085	105^59050+104	119352	Norbert Schneider	11/2016
2086	2^396374+73729	119321	Enzo Doria	04/2016
2087	2^396258-459491	119286	Enzo Doria	05/2015
2088	(2^395986+5)/76881	119199	Lelio R Paula	04/2014
2089	(23*2^395942-1)/91	119190	Lelio R Paula	04/2014
2090	(11*2^395548+1)/3	119073	Lelio R Paula	04/2014
2091	(30^80599+1)/31	119054	Robert Price	07/2013
2092	2^395062-109121	118926	Enzo Doria	04/2014
2093	(2^394918+78557)/3	118882	Lelio R Paula	01/2015
2094	(2^394739+3)/1883	118826	Lelio R Paula	04/2014
2095	2^394266+71389	118686	Enzo Doria	04/2016
2096	5^169727+2	118635	Lelio R Paula	08/2013
2097	2^394034-3	118617	M. Frind & P. Underwood	09/2002
2098	3^248572-6242	118599	Enzo Doria	05/2014
2099	(3*2^393964-1)/181	118594	Lelio R Paula	04/2014
2100	7^140303-6	118570	Robert Price	11/2014
2101	2^393427+75683	118434	Enzo Doria	04/2016
2102	2^393376-114749	118418	Enzo Doria	04/2015
2103	2^393180+73	118359	Lelio R Paula	04/2013
2104	p(23881)#/2+256	118328	Robert Price	05/2017
2105	(10^118324+359)/9	118324	Serge Batalov	12/2014
2106	p(23879)#/2+64	118317	Robert Price	03/2017
2107	(53*10^118216+1)/9	118217	Serge Batalov	11/2010
2108	(7*2^392697+1)/15	118214	Renaud Lifchitz	03/2011
2109	(157^53819-1)/156	118179	Alexander Zhirkov	06/2016
2110	(19*2^392551+1)/3	118171	Lelio R Paula	04/2014
2111	2^392516-29219	118160	Enzo Doria	07/2015
2112	Phi(177231,10)	118152	Maksym Voznyy	09/2015
2113	2^392413-112123	118129	Enzo Doria	06/2014
2114	(2^392342+5)/27	118106	Lelio R Paula	04/2014
2115	2^392300-1841429	118095	Enzo Doria	06/2015
2116	2^392220+75241	118070	Enzo Doria	04/2016
2117	10^118009-20001	118009	Robert Price	01/2018
2118	2^391933+5897	117984	Yves Minet	02/2011
2119	2^391912-1849259	117978	Enzo Doria	08/2015
2120	(2^391812+5)/14181	117944	Lelio R Paula	04/2014
2121	(7*2^391521+1)/285	117858	Lelio R Paula	04/2014
2122	2^391324+90901	117801	Yves Minet	02/2011
2123	2^391301-1859923	117794	Enzo Doria	03/2016
2124	2^391261-4131	117782	Yves Minet	02/2018
2125	(2^391115-7)/11791	117734	Lelio R Paula	04/2014
2126	2^390960+1880881	117691	Enzo Doria	11/2016
2127	2^390897-1860553	117672	Enzo Doria	11/2015
2128	2^390889-115003	117670	Enzo Doria	06/2015
2129	2^390779-30337	117637	Paul Bourdelais	02/2012
2130	11^112916-780	117590	Enzo Doria	12/2012
2131	(16^97613-5^97613)/11	117537	Robert Price	07/2013
2132	(17*2^390272+1)/1983	117482	Lelio R Paula	04/2014
2133	31^78759-30	117459	Theodore Burton	02/2007
2134	2^389998+37	117402	Lelio R Paula	03/2013
2135	2^389478+43	117245	Lelio R Paula	03/2013
2136	(29*2^389351-1)/9	117207	Lelio R Paula	04/2014
2137	(2^389341-7)/3865	117200	Lelio R Paula	03/2014
2138	10^117142+209223	117143	Patrick De Geest	04/2018
2140	10^117142-1000000001	117142	Robert Price	03/2018
2139	10^117142-966057	117142	Patrick De Geest	04/2018
2141	10^117135-401	117135	Robert Price	01/2018
2142	2^389033-12797413	117111	Enzo Doria	04/2016
2143	2^388960-109505	117089	Enzo Doria	04/2014
2144	(2^388928-5)/569	117077	Lelio R Paula	03/2014
2145	2^388888-1529	117067	Yves Minet	01/2013
2146	10^117059+28879	117060	Patrick De Geest	05/2016
2147	(10^117059-71)/1	117059	Serge Batalov	12/2014
2148	3^245154-6256	116969	Enzo Doria	05/2014
2149	2^388536-113495	116961	Enzo Doria	08/2014
2150	2^388469-43	116941	Lelio R Paula	03/2013
2151	(7*2^388372-1)/111	116911	Lelio R Paula	04/2014
2152	(7*2^388335-1)/25	116900	Lelio R Paula	04/2014
2153	2^388180+93	116854	Donovan Johnson	07/2008
2154	(2^388081+7)/1179	116821	Lelio R Paula	03/2014
2155	2^387946-113261	116784	Enzo Doria	07/2014
2156	2^387745+75557	116723	Enzo Doria	04/2016
2157	2^387554+71455	116666	Enzo Doria	04/2016
2158	(2^387447+78557)/365	116631	Lelio R Paula	12/2014
2159	(145*10^116610-1)/9	116612	Serge Batalov	12/2014
2160	(17*2^387284-1)/59	116584	Lelio R Paula	04/2014
2161	(31*2^386968+1)/7	116490	Lelio R Paula	03/2014
2162	2^386947+1869143	116483	Enzo Doria	05/2016
2163	(30^78857-1)/29	116480	Robert Price	12/2011
2164	(2^386903-3)/5	116469	Lelio R Paula	03/2014
2165	2^386389-1864783	116315	Enzo Doria	03/2016
2166	(31*2^386231-1)/1711	116266	Lelio R Paula	03/2014
2167	(2^386087-5)/40959	116220	Lelio R Paula	03/2014
2168	2^385969-823	116189	Yves Minet	05/2012
2169	57^66162+2	116173	Lelio R Paula	08/2013
2170	2^385854+75049	116154	Enzo Doria	04/2016
2171	2^385775-109587	116130	Enzo Doria	04/2014
2172	2^385622+71839	116084	Enzo Doria	04/2016
2173	2^385564+781	116067	Lelio R Paula	01/2012
2174	2^385410+71893	116020	Enzo Doria	04/2016
2175	(25*2^385091+1)/27	115924	Lelio R Paula	04/2014
2176	2^384953-111943	115883	Paul Bourdelais	02/2012
2177	43^70942-2	115882	Lelio R Paula	04/2014
2178	7*10^115863+3	115864	Robert Price	08/2015
2179	2^384834+93	115847	Donovan Johnson	07/2008
2180	2^384809+71297	115840	Enzo Doria	04/2016
2181	(7*2^384759-1)/5	115825	Lelio R Paula	04/2014
2182	(71*10^115810-17)/9	115811	Ray Chandler	08/2011
2183	(97*10^115794-1)/3	115796	Serge Batalov	12/2014
2184	10^115773+126739	115774	Patrick De Geest	04/2018
2186	10^115773-1000000001	115773	Robert Price	03/2018
2185	10^115773-396221	115773	Patrick De Geest	04/2018
2187	2^384530+1874305	115756	Enzo Doria	06/2016
2188	(3*2^384524-1)/7631	115750	Lelio R Paula	03/2014
2189	2^384312+81091	115690	Yves Minet	02/2010
2190	(4*10^115668-79)/3	115669	Robert Price	02/2018
2191	(266947#+273808)/(2109157)	115646	Makoto Morimoto	10/2017
2192	3^242337-4042	115625	Enzo Doria	05/2014
2193	(11*2^383859-13)/15	115553	Renaud Lifchitz	03/2011
2194	2^383780-3149	115530	Yves Minet	10/2014
2195	2^383560-455	115464	Yves Minet	03/2012
2196	(2^383544+5)/3	115458	Lelio R Paula	03/2014
2197	89^59221-88^59221	115445	Robert Price	06/2015
2198	2^383347+1869413	115399	Enzo Doria	05/2016
2199	(2^383130-7)/131793	115329	Lelio R Paula	03/2014
2200	(12^106859+1)/13	115320	Paul Bourdelais	02/2010
2201	2^383039+1869509	115307	Enzo Doria	05/2016
2202	(13*2^382968+1)/7	115286	Lelio R Paula	04/2014
2203	2^382633+73697	115185	Enzo Doria	04/2016
2204	2^382509-113593	115147	Enzo Doria	08/2014
2205	2^382502-2791721	115145	Enzo Doria	03/2016
2206	9^120590-120590	115073	Robert Price	03/2014
2207	2^382198+9	115054	Lelio R Paula	03/2013
2208	2^381883-59197	114959	Enzo Doria	10/2015
2210	2^381806-4481	114936	Yves Minet	07/2011
2209	2^381808-1851507	114936	Enzo Doria	08/2015
2211	2^381774-112373	114926	Enzo Doria	06/2014
2212	2^381555-109051	114860	Enzo Doria	04/2014
2213	2^381546-113501	114857	Enzo Doria	08/2014
2214	2^381360-110429	114801	Enzo Doria	05/2014
2215	(66^63079+1)/67	114774	Paul Bourdelais	09/2017
2216	2^381252-115079	114769	Enzo Doria	06/2015
2217	2^381209-29323	114756	Enzo Doria	07/2015
2218	569^41651-568^41651	114754	Jean-Louis Charton	11/2009
2219	2^381201+1873205	114753	Enzo Doria	06/2016
2220	2^380974-112991	114685	Enzo Doria	07/2014
2221	88^58949-87	114626	Norbert Schneider	11/2015
2222	2^380700+91	114603	Lelio R Paula	03/2013
2223	10^114575+3^114576	114576	Mike Oakes	09/2010
2224	10^114575+66561	114576	Patrick De Geest	02/2017
2225	10^114575-581081	114575	Patrick De Geest	02/2017
2226	2^380587-115315	114569	Enzo Doria	06/2015
2227	2^380513-216925	114546	Enzo Doria	05/2014
2228	2^380451-1840087	114528	Enzo Doria	06/2015
2229	(15*2^380388-1)/539	114507	Lelio R Paula	04/2014
2230	2^380279-461347	114476	Enzo Doria	07/2015
2231	2^380021+1871147	114398	Enzo Doria	05/2016
2232	2^380005+1869707	114393	Enzo Doria	05/2016
2233	2^379958-113297	114379	Enzo Doria	07/2014
2234	2^379881-109105	114356	Enzo Doria	04/2014
2235	(21*2^379857-1)/13	114349	Lelio R Paula	03/2014
2236	(4*10^114340+83)/3	114341	Robert Price	02/2018
2237	(4*10^114296+149)/9	114296	Robert Price	04/2018
2238	88^58773-87	114284	Norbert Schneider	11/2015
2239	2^379529-2790283	114250	Enzo Doria	03/2016
2240	2^379522+1869115	114248	Enzo Doria	05/2016
2241	(145*10^114226-1)/9	114228	Serge Batalov	12/2014
2242	2^379317-115033	114186	Enzo Doria	06/2015
2243	(17*2^379246-1)/17407	114162	Lelio R Paula	03/2014
2244	(4*10^114076+143)/3	114077	Robert Price	03/2018
2245	2*10^113941+9	113942	Dmitry Domanov	11/2010
2246	2^378272-16565	113872	Enzo Doria	04/2013
2247	2^378217-109075	113855	Enzo Doria	04/2014
2248	2^378198+67	113849	Lelio R Paula	03/2013
2249	2^378173-3249	113842	Yves Minet	12/2014
2250	(2^378155-5)/6597	113833	Lelio R Paula	03/2014

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Probable Primes Top 10000

(205873 PRPs in the top)