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	(25*2^410192+1)/10397	123478	Lelio R Paula	04/2014
2002	2^409909-189	123395	Enzo Doria	05/2014
2003	2^409896-109043	123391	Enzo Doria	04/2014
2004	2^409890+75409	123390	Enzo Doria	04/2016
2005	133^58076-2	123345	Lelio R Paula	10/2017
2006	F(590041)	123311	Henri Lifchitz	01/2005
2007	2^409566-113501	123292	Enzo Doria	08/2014
2008	2^409533+77747	123282	Enzo Doria	05/2016
2009	2^409436-112799	123253	Enzo Doria	06/2014
2010	2^409225+1873787	123189	Enzo Doria	06/2016
2011	2^409174+73009	123174	Enzo Doria	04/2016
2012	2^409058-112685	123139	Enzo Doria	06/2014
2013	2^408778+77689	123055	Enzo Doria	05/2016
2014	2^408690-75	123028	Lelio R Paula	11/2013
2015	2^408574-2787341	122994	Enzo Doria	03/2016
2016	Phi(157825,10)	122961	Maksym Voznyy	06/2015
2017	(13*2^408283+1)/1665	122904	Lelio R Paula	05/2014
2018	(11*2^408100-1)/35	122850	Lelio R Paula	04/2014
2019	(2^407821-lucasV(1,2,407821)+1)/2	122767	Mike Oakes	11/2016
2020	(32*10^122733-77)/9	122734	Robert Price	06/2018
2021	(21*2^407604-1)/215	122701	Lelio R Paula	04/2014
2022	(21*2^407433-1)/13	122650	Lelio R Paula	04/2014
2023	(73*10^122592-1)/9	122593	Robert Price	01/2015
2024	(5*10^122592+91)/3	122593	Robert Price	04/2018
2025	2^407179-112075	122574	Enzo Doria	06/2014
2026	(21*2^407131+1)/207517523	122552	Lelio R Paula	04/2014
2027	(66^67349+1)/67	122543	Paul Bourdelais	09/2017
2028	2^407008-1867919	122522	Enzo Doria	04/2016
2029	11^117642-300	122512	Enzo Doria	10/2012
2030	(F(397700+1)^2+L(397700+1)^2)/2	122509	Henri Lifchitz	10/2017
2031	2^406949+72197	122504	Enzo Doria	04/2016
2032	2^406826-65	122467	Lelio R Paula	11/2013
2033	2^406821-2797363	122466	Enzo Doria	04/2016
2034	2^406758-17	122447	Lelio R Paula	11/2013
2035	(30^82883-1)/29	122427	Robert Price	12/2011
2036	(2^406583-1)/813167	122388	Jens K. Andersen	02/2009
2037	97^61575-2	122336	Lelio R Paula	12/2014
2038	2^406298+2799109	122308	Enzo Doria	04/2016
2039	(27*2^406241-1)/10277	122289	Lelio R Paula	04/2014
2040	2^406229-1849993	122288	Enzo Doria	08/2015
2041	3*10^122274+7	122275	Robert Price	07/2015
2042	2^406117+1876577	122254	Enzo Doria	07/2016
2043	3^256199-2^256199	122238	Mike Oakes	06/2005
2044	2^405992-78557	122216	Jorge Menendez	03/2018
2045	(8*10^122203+43)/3	122204	Robert Price	06/2018
2046	2^405774+179149	122151	Enzo Doria	06/2016
2047	2^405514-3311	122072	Yves Minet	12/2014
2048	2^405514-115511	122072	Enzo Doria	07/2015
2049	2^405422-113261	122045	Enzo Doria	07/2014
2050	2^405173+71237	121970	Enzo Doria	04/2016
2051	(2^405016+1)/257	121920	Lelio R Paula	04/2014
2052	2^404858+71329	121875	Enzo Doria	04/2016
2053	2^404813-114703	121861	Enzo Doria	04/2015
2054	2^404764+77791	121847	Enzo Doria	05/2016
2055	317^48694+48694^317	121787	Norbert Schneider	08/2015
2056	2^404536-115259	121778	Enzo Doria	06/2015
2057	2^404501-631	121767	Yves Minet	07/2012
2058	63^67620+2	121672	Lelio R Paula	08/2015
2059	(17*10^121621+1)/9	121622	Serge Batalov	05/2010
2060	(15*2^403912+1)/271	121589	Lelio R Paula	05/2014
2061	(10^121543-79)/3	121543	Robert Price	01/2018
2062	2^403676+76831	121519	Enzo Doria	05/2016
2063	(7*10^121487+143)/3	121488	Robert Price	03/2018
2064	2^403363-113635	121425	Enzo Doria	08/2014
2065	2^403336-1861469	121417	Enzo Doria	03/2016
2066	p(24442)#/2-64	121381	Robert Price	04/2017
2067	11^116555-720	121380	Enzo Doria	11/2012
2068	2^403100-461267	121346	Enzo Doria	07/2015
2069	2^403093-112213	121344	Enzo Doria	06/2014
2070	(316^48539+1)/317	121330	Eric Chen	10/2017
2071	2^403004+1866361	121317	Enzo Doria	03/2016
2072	2^402953+89	121301	Lelio R Paula	10/2013
2073	2^402944-2788319	121299	Enzo Doria	03/2016
2074	(27*2^402865+1)/5	121276	Lelio R Paula	04/2014
2075	2^402828-113183	121264	Enzo Doria	07/2014
2076	(17*10^121242+1)/9	121243	Serge Batalov	05/2010
2077	(15*2^402757+1)/101	121242	Lelio R Paula	05/2014
2078	2^402715+1874223	121230	Enzo Doria	06/2016
2079	(91^61879+1)/92	121222	Paul Bourdelais	09/2017
2080	7*10^121144+9	121145	Robert Price	09/2015
2081	2^401725-113251	120932	Enzo Doria	07/2014
2082	(15*2^401677-1)/19	120917	Lelio R Paula	05/2014
2083	2^401652+73711	120910	Enzo Doria	04/2016
2084	(2^401632+3)/79	120902	Lelio R Paula	04/2014
2085	2^401406-2791331	120836	Enzo Doria	03/2016
2086	(28^83497+1)/29	120832	Robert Price	07/2013
2087	2^401369+1867367	120825	Enzo Doria	03/2016
2088	(10^120782+29)/3	120782	Serge Batalov	12/2014
2089	2^401215-1657	120778	Yves Minet	07/2014
2090	2^401159+53	120761	Lelio R Paula	10/2013
2091	2^401031-113047	120723	Enzo Doria	07/2014
2092	(29*2^400909-1)/303	120685	Lelio R Paula	04/2014
2093	2^400571-15	120584	Lelio R Paula	10/2013
2094	(10^120574+359)/9	120574	Serge Batalov	12/2014
2095	2^400424-216413	120540	Enzo Doria	04/2013
2096	(17*2^400200-1)/587	120471	Lelio R Paula	05/2014
2097	2^400166+1874899	120462	Enzo Doria	06/2016
2098	(3*2^400045-1)/865	120424	Lelio R Paula	04/2014
2099	2^399966+73759	120402	Enzo Doria	04/2016
2100	(112*10^120395-1)/3	120397	Serge Batalov	12/2014
2101	2^399918-95	120388	Lelio R Paula	04/2013
2102	2^399792-1849259	120350	Enzo Doria	08/2015
2103	9*10^120342-7	120343	Robert Price	09/2015
2104	2^399526-1861721	120270	Enzo Doria	11/2015
2105	(10^(260126+1)+3610^60126-1)/9	120253	Robert Price	10/2015
2106	2^399322-2798111	120208	Enzo Doria	04/2016
2107	72^64693-71^64693	120157	Robert Price	03/2014
2108	2^399111-28489	120145	Enzo Doria	08/2015
2110	2^398877+105	120074	Donovan Johnson	01/2006
2109	(101*10^120072-87)/7	120074	Hans Havermann	02/2015
2111	(88^61751+1)/89	120072	Paul Bourdelais	09/2017
2112	2^398710+57	120024	Lelio R Paula	04/2013
2113	2^398691-115057	120018	Enzo Doria	06/2015
2114	L(574219)	120005	Renaud Lifchitz	03/2004
2115	2^398571+60413	119982	Yves Minet	03/2011
2116	p(24179)#/2-64	119949	Robert Price	04/2017
2117	2^398448+1872001	119945	Enzo Doria	05/2016
2118	8*10^119930-3	119931	Ray Chandler	04/2011
2119	(10^119880+179)/9	119880	Serge Batalov	12/2014
2120	(9*2^398145+1)/73	119853	Lelio R Paula	04/2014
2121	(10^119836+77)/3	119836	Robert Price	01/2018
2122	2^398029+1872527	119819	Enzo Doria	05/2016
2123	2^397897-113541	119779	Enzo Doria	08/2014
2124	(21*2^397661-1)/27593	119705	Lelio R Paula	04/2014
2125	(58^67853-1)/57	119653	Paul Bourdelais	09/2017
2126	2^397426+73849	119638	Enzo Doria	04/2016
2127	2^396933-112723	119489	Enzo Doria	06/2014
2128	11^114738-150	119488	Enzo Doria	10/2012
2129	(4*10^119474+149)/9	119474	Robert Price	04/2018
2130	2^396790-21	119446	Lelio R Paula	04/2013
2131	(2^396633-7)/5	119398	Lelio R Paula	04/2014
2132	105^59050+104	119352	Norbert Schneider	11/2016
2133	2^396374+73729	119321	Enzo Doria	04/2016
2134	2^396258-459491	119286	Enzo Doria	05/2015
2135	2^396128-396128-1	119247	Karsten Bonath	06/2018
2136	(2^395986+5)/76881	119199	Lelio R Paula	04/2014
2137	(23*2^395942-1)/91	119190	Lelio R Paula	04/2014
2138	(11*2^395548+1)/3	119073	Lelio R Paula	04/2014
2139	(30^80599+1)/31	119054	Robert Price	07/2013
2140	2^395062-109121	118926	Enzo Doria	04/2014
2141	(2^394918+78557)/3	118882	Lelio R Paula	01/2015
2142	(2^394739+3)/1883	118826	Lelio R Paula	04/2014
2143	2^394266+71389	118686	Enzo Doria	04/2016
2144	2^394215-51261	118671	Tony Prest / Never Odd Or Even	04/2018
2145	(2^394215-48793)/5/5	118670	Tony Prest / Never Odd Or Even	04/2018
2146	(2^394215-17063)/3/3/5	118669	Tony Prest / Never Odd Or Even	04/2018
2147	(2^394215-24393)/5/5/5/5/5	118668	Tony Prest / Never Odd Or Even	04/2018
2148	(2^394215-35885)/3/71/173	118666	Tony Prest / Never Odd Or Even	04/2018
2149	(2^394215-47925)/353/2269	118665	Tony Prest / Never Odd Or Even	04/2018
2150	(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673	118650	Tony Prest / Never Odd Or Even	04/2018
2151	5^169727+2	118635	Lelio R Paula	08/2013
2152	2^394034-3	118617	M. Frind & P. Underwood	09/2002
2153	3^248572-6242	118599	Enzo Doria	05/2014
2154	(3*2^393964-1)/181	118594	Lelio R Paula	04/2014
2155	7^140303-6	118570	Robert Price	11/2014
2156	2^393427+75683	118434	Enzo Doria	04/2016
2157	2^393376-114749	118418	Enzo Doria	04/2015
2158	2^393180+73	118359	Lelio R Paula	04/2013
2159	p(23881)#/2+256	118328	Robert Price	05/2017
2160	(10^118324+359)/9	118324	Serge Batalov	12/2014
2161	p(23879)#/2+64	118317	Robert Price	03/2017
2162	(53*10^118216+1)/9	118217	Serge Batalov	11/2010
2163	(7*2^392697+1)/15	118214	Renaud Lifchitz	03/2011
2164	(157^53819-1)/156	118179	Alexander Zhirkov	06/2016
2165	(19*2^392551+1)/3	118171	Lelio R Paula	04/2014
2166	2^392516-29219	118160	Enzo Doria	07/2015
2167	Phi(177231,10)	118152	Maksym Voznyy	09/2015
2168	2^392413-112123	118129	Enzo Doria	06/2014
2169	(2^392342+5)/27	118106	Lelio R Paula	04/2014
2170	2^392300-1841429	118095	Enzo Doria	06/2015
2171	2^392220+75241	118070	Enzo Doria	04/2016
2172	10^118009-20001	118009	Robert Price	01/2018
2173	2^391933+5897	117984	Yves Minet	02/2011
2174	2^391912-1849259	117978	Enzo Doria	08/2015
2175	(2^391812+5)/14181	117944	Lelio R Paula	04/2014
2176	(7*2^391521+1)/285	117858	Lelio R Paula	04/2014
2177	2^391324+90901	117801	Yves Minet	02/2011
2178	2^391301-1859923	117794	Enzo Doria	03/2016
2179	2^391261-4131	117782	Yves Minet	02/2018
2180	(2^391115-7)/11791	117734	Lelio R Paula	04/2014
2181	2^390960+1880881	117691	Enzo Doria	11/2016
2182	2^390897-1860553	117672	Enzo Doria	11/2015
2183	2^390889-115003	117670	Enzo Doria	06/2015
2184	2^390779-30337	117637	Paul Bourdelais	02/2012
2185	11^112916-780	117590	Enzo Doria	12/2012
2186	(16^97613-5^97613)/11	117537	Robert Price	07/2013
2187	(17*2^390272+1)/1983	117482	Lelio R Paula	04/2014
2188	31^78759-30	117459	Theodore Burton	02/2007
2189	2^389998+37	117402	Lelio R Paula	03/2013
2190	2^389478+43	117245	Lelio R Paula	03/2013
2191	(29*2^389351-1)/9	117207	Lelio R Paula	04/2014
2192	(2^389341-7)/3865	117200	Lelio R Paula	03/2014
2193	10^117142+209223	117143	Patrick De Geest	04/2018
2195	10^117142-1000000001	117142	Robert Price	03/2018
2194	10^117142-966057	117142	Patrick De Geest	04/2018
2196	10^117135-401	117135	Robert Price	01/2018
2197	2^389033-12797413	117111	Enzo Doria	04/2016
2198	2^388960-109505	117089	Enzo Doria	04/2014
2199	(2^388928-5)/569	117077	Lelio R Paula	03/2014
2200	2^388888-1529	117067	Yves Minet	01/2013
2201	10^117059+28879	117060	Patrick De Geest	05/2016
2202	(10^117059-71)/1	117059	Serge Batalov	12/2014
2203	3^245154-6256	116969	Enzo Doria	05/2014
2204	2^388536-113495	116961	Enzo Doria	08/2014
2205	2^388469-43	116941	Lelio R Paula	03/2013
2206	(7*2^388372-1)/111	116911	Lelio R Paula	04/2014
2207	(7*2^388335-1)/25	116900	Lelio R Paula	04/2014
2208	2^388180+93	116854	Donovan Johnson	07/2008
2209	(2^388081+7)/1179	116821	Lelio R Paula	03/2014
2210	2^387946-113261	116784	Enzo Doria	07/2014
2211	2^387745+75557	116723	Enzo Doria	04/2016
2212	2^387554+71455	116666	Enzo Doria	04/2016
2213	(2^387447+78557)/365	116631	Lelio R Paula	12/2014
2214	(145*10^116610-1)/9	116612	Serge Batalov	12/2014
2215	(17*2^387284-1)/59	116584	Lelio R Paula	04/2014
2216	(31*2^386968+1)/7	116490	Lelio R Paula	03/2014
2217	2^386947+1869143	116483	Enzo Doria	05/2016
2218	(30^78857-1)/29	116480	Robert Price	12/2011
2219	(2^386903-3)/5	116469	Lelio R Paula	03/2014
2220	2^386389-1864783	116315	Enzo Doria	03/2016
2221	(31*2^386231-1)/1711	116266	Lelio R Paula	03/2014
2222	(2^386087-5)/40959	116220	Lelio R Paula	03/2014
2223	2^385969-823	116189	Yves Minet	05/2012
2224	57^66162+2	116173	Lelio R Paula	08/2013
2225	2^385854+75049	116154	Enzo Doria	04/2016
2226	2^385775-109587	116130	Enzo Doria	04/2014
2227	2^385622+71839	116084	Enzo Doria	04/2016
2228	2^385564+781	116067	Lelio R Paula	01/2012
2229	2^385410+71893	116020	Enzo Doria	04/2016
2230	(25*2^385091+1)/27	115924	Lelio R Paula	04/2014
2231	2^384953-111943	115883	Paul Bourdelais	02/2012
2232	43^70942-2	115882	Lelio R Paula	04/2014
2233	7*10^115863+3	115864	Robert Price	08/2015
2234	2^384834+93	115847	Donovan Johnson	07/2008
2235	2^384809+71297	115840	Enzo Doria	04/2016
2236	(7*2^384759-1)/5	115825	Lelio R Paula	04/2014
2237	(71*10^115810-17)/9	115811	Ray Chandler	08/2011
2238	(97*10^115794-1)/3	115796	Serge Batalov	12/2014
2239	2*10^115784-27	115785	Robert Price	05/2018
2240	10^115773+126739	115774	Patrick De Geest	04/2018
2242	10^115773-1000000001	115773	Robert Price	03/2018
2241	10^115773-396221	115773	Patrick De Geest	04/2018
2243	2^384530+1874305	115756	Enzo Doria	06/2016
2244	(3*2^384524-1)/7631	115750	Lelio R Paula	03/2014
2245	2^384312+81091	115690	Yves Minet	02/2010
2246	(4*10^115668-79)/3	115669	Robert Price	02/2018
2247	(266947#+273808)/(2109157)	115646	Makoto Morimoto	10/2017
2248	3^242337-4042	115625	Enzo Doria	05/2014
2249	(11*2^383859-13)/15	115553	Renaud Lifchitz	03/2011
2250	2^383780-3149	115530	Yves Minet	10/2014

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Probable Primes Top 10000

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