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	43125^27010-106	125185	Enzo Doria	08/2012
2002	2^415765-112603	125158	Enzo Doria	06/2014
2003	2^415290-113591	125015	Enzo Doria	08/2014
2004	2^415276-460919	125011	Enzo Doria	06/2015
2005	2^415259+77243	125006	Enzo Doria	05/2016
2006	2^415144-3683	124971	Yves Minet	10/2011
2007	2^414874+79	124890	Lelio R Paula	01/2015
2008	(2^414765+7)/1389	124854	Lelio R Paula	05/2014
2009	2^414618+79459	124813	Enzo Doria	06/2016
2010	2^414432-1846709	124757	Enzo Doria	07/2015
2011	2*10^124751-51	124752	Robert Price	04/2018
2012	(13*2^414274-1)/153	124708	Lelio R Paula	05/2014
2013	(7*10^124648+197)/3	124649	Robert Price	07/2018
2015	2^414032-5	124637	Henri Lifchitz	07/2006
2014	2^414032+1872331	124637	Enzo Doria	05/2016
2016	14120^30009-30009^14120	124533	Norbert Schneider	02/2015
2017	64^68909-63^68909	124463	Robert Price	07/2013
2018	2^413387+76253	124442	Enzo Doria	04/2016
2019	287117#+391613	124424	Nicolas PALAU	01/2017
2020	(4*10^124420+83)/3	124421	Robert Price	02/2018
2021	(27*2^413207-1)/108335	124385	Lelio R Paula	05/2014
2022	2^412868-120599	124286	Paul Bourdelais	02/2012
2023	45^75145-2	124231	Lelio R Paula	08/2015
2024	2^412645-112213	124219	Enzo Doria	06/2014
2025	2^412248+74611	124100	Enzo Doria	04/2016
2026	(22*10^124096-13)/9	124097	Robert Price	06/2018
2027	2^412192-3329	124083	Yves Minet	12/2014
2028	(25*2^412191-1)/23	124082	Lelio R Paula	05/2014
2029	F(593689)	124074	Henri Lifchitz	01/2005
2030	(11*2^412161+1)/19	124073	Lelio R Paula	05/2014
2031	2^411884-113279	123990	Enzo Doria	07/2014
2032	(2^411832+1)/257	123972	Lelio R Paula	05/2014
2033	(26*10^123970-89)/9	123971	Robert Price	06/2018
2034	2^411790-1853531	123962	Enzo Doria	08/2015
2035	(5^177337+1)/6	123953	Paul Bourdelais	11/2008
2036	2^411711-113257	123938	Enzo Doria	07/2014
2037	(23*2^411675-1)/3	123928	Lelio R Paula	05/2014
2038	2^411325-351103	123822	Enzo Doria	06/2015
2039	2^411052+1872481	123739	Enzo Doria	05/2016
2040	2^410997+39	123723	Lelio R Paula	05/2014
2041	2^410596-39	123602	Lelio R Paula	05/2014
2042	2^410540-115079	123585	Enzo Doria	06/2015
2043	(7*10^123563+107)/3	123564	Robert Price	02/2018
2044	(3*2^410392-1)/9229	123537	Lelio R Paula	05/2014
2045	2^410206-113081	123485	Enzo Doria	07/2014
2046	(25*2^410192+1)/10397	123478	Lelio R Paula	04/2014
2047	2^409909-189	123395	Enzo Doria	05/2014
2048	2^409896-109043	123391	Enzo Doria	04/2014
2049	2^409890+75409	123390	Enzo Doria	04/2016
2050	133^58076-2	123345	Lelio R Paula	10/2017
2051	F(590041)	123311	Henri Lifchitz	01/2005
2052	2^409566-113501	123292	Enzo Doria	08/2014
2053	2^409533+77747	123282	Enzo Doria	05/2016
2054	2^409436-112799	123253	Enzo Doria	06/2014
2055	2^409225+1873787	123189	Enzo Doria	06/2016
2056	2^409174+73009	123174	Enzo Doria	04/2016
2057	2^409058-112685	123139	Enzo Doria	06/2014
2058	2^408778+77689	123055	Enzo Doria	05/2016
2059	2^408690-75	123028	Lelio R Paula	11/2013
2060	2^408574-2787341	122994	Enzo Doria	03/2016
2061	Phi(157825,10)	122961	Maksym Voznyy	06/2015
2062	(13*2^408283+1)/1665	122904	Lelio R Paula	05/2014
2063	(11*2^408100-1)/35	122850	Lelio R Paula	04/2014
2064	(2^407821-lucasV(1,2,407821)+1)/2	122767	Mike Oakes	11/2016
2065	(32*10^122733-77)/9	122734	Robert Price	06/2018
2066	(21*2^407604-1)/215	122701	Lelio R Paula	04/2014
2067	(21*2^407433-1)/13	122650	Lelio R Paula	04/2014
2068	(73*10^122592-1)/9	122593	Robert Price	01/2015
2069	(5*10^122592+91)/3	122593	Robert Price	04/2018
2070	2^407179-112075	122574	Enzo Doria	06/2014
2071	(21*2^407131+1)/207517523	122552	Lelio R Paula	04/2014
2072	(66^67349+1)/67	122543	Paul Bourdelais	09/2017
2073	2^407008-1867919	122522	Enzo Doria	04/2016
2074	11^117642-300	122512	Enzo Doria	10/2012
2075	(F(397700+1)^2+L(397700+1)^2)/2	122509	Henri Lifchitz	10/2017
2076	2^406949+72197	122504	Enzo Doria	04/2016
2077	2^406826-65	122467	Lelio R Paula	11/2013
2078	2^406821-2797363	122466	Enzo Doria	04/2016
2079	2^406758-17	122447	Lelio R Paula	11/2013
2080	(30^82883-1)/29	122427	Robert Price	12/2011
2081	(2^406583-1)/813167	122388	Jens K. Andersen	02/2009
2082	3*10^122345-97	122346	Robert Price	07/2018
2083	97^61575-2	122336	Lelio R Paula	12/2014
2084	2^406298+2799109	122308	Enzo Doria	04/2016
2085	(27*2^406241-1)/10277	122289	Lelio R Paula	04/2014
2086	2^406229-1849993	122288	Enzo Doria	08/2015
2087	3*10^122274+7	122275	Robert Price	07/2015
2088	2^406117+1876577	122254	Enzo Doria	07/2016
2089	3^256199-2^256199	122238	Mike Oakes	06/2005
2090	2^405992-78557	122216	Jorge Menendez	03/2018
2091	(8*10^122203+43)/3	122204	Robert Price	06/2018
2092	2^405774+179149	122151	Enzo Doria	06/2016
2093	2^405514-3311	122072	Yves Minet	12/2014
2094	2^405514-115511	122072	Enzo Doria	07/2015
2095	2^405422-113261	122045	Enzo Doria	07/2014
2096	2^405173+71237	121970	Enzo Doria	04/2016
2097	(2^405016+1)/257	121920	Lelio R Paula	04/2014
2098	2^404858+71329	121875	Enzo Doria	04/2016
2099	2^404813-114703	121861	Enzo Doria	04/2015
2100	2^404764+77791	121847	Enzo Doria	05/2016
2101	317^48694+48694^317	121787	Norbert Schneider	08/2015
2102	2^404536-115259	121778	Enzo Doria	06/2015
2103	2^404501-631	121767	Yves Minet	07/2012
2104	63^67620+2	121672	Lelio R Paula	08/2015
2105	(17*10^121621+1)/9	121622	Serge Batalov	05/2010
2106	(15*2^403912+1)/271	121589	Lelio R Paula	05/2014
2107	(10^121543-79)/3	121543	Robert Price	01/2018
2108	2^403676+76831	121519	Enzo Doria	05/2016
2109	(7*10^121487+143)/3	121488	Robert Price	03/2018
2110	2^403363-113635	121425	Enzo Doria	08/2014
2111	2^403336-1861469	121417	Enzo Doria	03/2016
2112	p(24442)#/2-64	121381	Robert Price	04/2017
2113	11^116555-720	121380	Enzo Doria	11/2012
2114	2^403100-461267	121346	Enzo Doria	07/2015
2115	2^403093-112213	121344	Enzo Doria	06/2014
2116	(316^48539+1)/317	121330	Eric Chen	10/2017
2117	2^403004+1866361	121317	Enzo Doria	03/2016
2118	2^402953+89	121301	Lelio R Paula	10/2013
2119	2^402944-2788319	121299	Enzo Doria	03/2016
2120	(27*2^402865+1)/5	121276	Lelio R Paula	04/2014
2121	2^402828-113183	121264	Enzo Doria	07/2014
2122	(17*10^121242+1)/9	121243	Serge Batalov	05/2010
2123	(15*2^402757+1)/101	121242	Lelio R Paula	05/2014
2125	2^402715+1874223	121230	Enzo Doria	06/2016
2124	(35*10^121229-593)/9	121230	Robert Price	07/2018
2126	(91^61879+1)/92	121222	Paul Bourdelais	09/2017
2127	7*10^121144+9	121145	Robert Price	09/2015
2128	2^401725-113251	120932	Enzo Doria	07/2014
2129	(15*2^401677-1)/19	120917	Lelio R Paula	05/2014
2130	2^401652+73711	120910	Enzo Doria	04/2016
2131	(2^401632+3)/79	120902	Lelio R Paula	04/2014
2132	2^401406-2791331	120836	Enzo Doria	03/2016
2133	(28^83497+1)/29	120832	Robert Price	07/2013
2134	2^401369+1867367	120825	Enzo Doria	03/2016
2135	(10^120782+29)/3	120782	Serge Batalov	12/2014
2136	2^401215-1657	120778	Yves Minet	07/2014
2137	2^401159+53	120761	Lelio R Paula	10/2013
2138	2^401031-113047	120723	Enzo Doria	07/2014
2139	(29*2^400909-1)/303	120685	Lelio R Paula	04/2014
2140	2^400571-15	120584	Lelio R Paula	10/2013
2141	(10^120574+359)/9	120574	Serge Batalov	12/2014
2142	2^400424-216413	120540	Enzo Doria	04/2013
2143	(17*2^400200-1)/587	120471	Lelio R Paula	05/2014
2144	2^400166+1874899	120462	Enzo Doria	06/2016
2145	(3*2^400045-1)/865	120424	Lelio R Paula	04/2014
2146	2^399966+73759	120402	Enzo Doria	04/2016
2147	(112*10^120395-1)/3	120397	Serge Batalov	12/2014
2148	2^399918-95	120388	Lelio R Paula	04/2013
2149	2^399792-1849259	120350	Enzo Doria	08/2015
2150	9*10^120342-7	120343	Robert Price	09/2015
2151	2^399526-1861721	120270	Enzo Doria	11/2015
2152	(10^(260126+1)+3610^60126-1)/9	120253	Robert Price	10/2015
2153	2^399322-2798111	120208	Enzo Doria	04/2016
2154	72^64693-71^64693	120157	Robert Price	03/2014
2155	2^399111-28489	120145	Enzo Doria	08/2015
2157	2^398877+105	120074	Donovan Johnson	01/2006
2156	(101*10^120072-87)/7	120074	Hans Havermann	02/2015
2158	(88^61751+1)/89	120072	Paul Bourdelais	09/2017
2159	2^398710+57	120024	Lelio R Paula	04/2013
2160	2^398691-115057	120018	Enzo Doria	06/2015
2161	L(574219)	120005	Renaud Lifchitz	03/2004
2162	2^398571+60413	119982	Yves Minet	03/2011
2163	p(24179)#/2-64	119949	Robert Price	04/2017
2164	2^398448+1872001	119945	Enzo Doria	05/2016
2165	8*10^119930-3	119931	Ray Chandler	04/2011
2166	(10^119880+179)/9	119880	Serge Batalov	12/2014
2167	(9*2^398145+1)/73	119853	Lelio R Paula	04/2014
2168	(10^119836+77)/3	119836	Robert Price	01/2018
2169	2^398029+1872527	119819	Enzo Doria	05/2016
2170	2^397897-113541	119779	Enzo Doria	08/2014
2171	(21*2^397661-1)/27593	119705	Lelio R Paula	04/2014
2172	(58^67853-1)/57	119653	Paul Bourdelais	09/2017
2173	2^397426+73849	119638	Enzo Doria	04/2016
2174	2^396933-112723	119489	Enzo Doria	06/2014
2175	11^114738-150	119488	Enzo Doria	10/2012
2176	(4*10^119474+149)/9	119474	Robert Price	04/2018
2177	2^396790-21	119446	Lelio R Paula	04/2013
2178	(2^396633-7)/5	119398	Lelio R Paula	04/2014
2179	105^59050+104	119352	Norbert Schneider	11/2016
2180	2^396374+73729	119321	Enzo Doria	04/2016
2181	2^396258-459491	119286	Enzo Doria	05/2015
2182	2^396128-396128-1	119247	Karsten Bonath	06/2018
2183	(2^395986+5)/76881	119199	Lelio R Paula	04/2014
2184	(23*2^395942-1)/91	119190	Lelio R Paula	04/2014
2185	(11*2^395548+1)/3	119073	Lelio R Paula	04/2014
2186	(30^80599+1)/31	119054	Robert Price	07/2013
2187	2^395062-109121	118926	Enzo Doria	04/2014
2188	(2^394918+78557)/3	118882	Lelio R Paula	01/2015
2189	(2^394739+3)/1883	118826	Lelio R Paula	04/2014
2190	2^394266+71389	118686	Enzo Doria	04/2016
2191	2^394215-51261	118671	Tony Prest / Never Odd Or Even	04/2018
2192	(2^394215-48793)/5/5	118670	Tony Prest / Never Odd Or Even	04/2018
2193	(2^394215-17063)/3/3/5	118669	Tony Prest / Never Odd Or Even	04/2018
2194	(2^394215-24393)/5/5/5/5/5	118668	Tony Prest / Never Odd Or Even	04/2018
2195	(2^394215-35885)/3/71/173	118666	Tony Prest / Never Odd Or Even	04/2018
2196	(2^394215-47925)/353/2269	118665	Tony Prest / Never Odd Or Even	04/2018
2197	(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673	118650	Tony Prest / Never Odd Or Even	04/2018
2198	5^169727+2	118635	Lelio R Paula	08/2013
2199	2^394034-3	118617	M. Frind & P. Underwood	09/2002
2200	3^248572-6242	118599	Enzo Doria	05/2014
2201	(3*2^393964-1)/181	118594	Lelio R Paula	04/2014
2202	7^140303-6	118570	Robert Price	11/2014
2203	2^393427+75683	118434	Enzo Doria	04/2016
2204	2^393376-114749	118418	Enzo Doria	04/2015
2205	2^393180+73	118359	Lelio R Paula	04/2013
2206	p(23881)#/2+256	118328	Robert Price	05/2017
2207	(10^118324+359)/9	118324	Serge Batalov	12/2014
2208	p(23879)#/2+64	118317	Robert Price	03/2017
2209	(53*10^118216+1)/9	118217	Serge Batalov	11/2010
2210	(7*2^392697+1)/15	118214	Renaud Lifchitz	03/2011
2211	(157^53819-1)/156	118179	Alexander Zhirkov	06/2016
2212	(19*2^392551+1)/3	118171	Lelio R Paula	04/2014
2213	2^392516-29219	118160	Enzo Doria	07/2015
2214	Phi(177231,10)	118152	Maksym Voznyy	09/2015
2215	2^392413-112123	118129	Enzo Doria	06/2014
2216	(2^392342+5)/27	118106	Lelio R Paula	04/2014
2217	2^392300-1841429	118095	Enzo Doria	06/2015
2218	2^392220+75241	118070	Enzo Doria	04/2016
2219	10^118009+664447	118010	Patrick De Geest	07/2018
2220	10^118009-20001	118009	Robert Price	01/2018
2221	2^391933+5897	117984	Yves Minet	02/2011
2222	2^391912-1849259	117978	Enzo Doria	08/2015
2223	(2^391812+5)/14181	117944	Lelio R Paula	04/2014
2224	(7*2^391521+1)/285	117858	Lelio R Paula	04/2014
2225	2^391324+90901	117801	Yves Minet	02/2011
2226	2^391301-1859923	117794	Enzo Doria	03/2016
2227	2^391261-4131	117782	Yves Minet	02/2018
2228	(2^391115-7)/11791	117734	Lelio R Paula	04/2014
2229	2^390960+1880881	117691	Enzo Doria	11/2016
2230	2^390897-1860553	117672	Enzo Doria	11/2015
2231	2^390889-115003	117670	Enzo Doria	06/2015
2232	2^390779-30337	117637	Paul Bourdelais	02/2012
2233	11^112916-780	117590	Enzo Doria	12/2012
2234	(16^97613-5^97613)/11	117537	Robert Price	07/2013
2235	(17*2^390272+1)/1983	117482	Lelio R Paula	04/2014
2236	31^78759-30	117459	Theodore Burton	02/2007
2237	2^389998+37	117402	Lelio R Paula	03/2013
2238	2^389478+43	117245	Lelio R Paula	03/2013
2239	(29*2^389351-1)/9	117207	Lelio R Paula	04/2014
2240	(2^389341-7)/3865	117200	Lelio R Paula	03/2014
2241	10^117142+209223	117143	Patrick De Geest	04/2018
2243	10^117142-1000000001	117142	Robert Price	03/2018
2242	10^117142-966057	117142	Patrick De Geest	04/2018
2244	10^117135+360577	117136	Patrick De Geest	07/2018
2245	10^117135-401	117135	Robert Price	01/2018
2246	4*10^117123+79	117124	Robert Price	08/2018
2247	2^389033-12797413	117111	Enzo Doria	04/2016
2248	2^388960-109505	117089	Enzo Doria	04/2014
2249	(2^388928-5)/569	117077	Lelio R Paula	03/2014
2250	2^388888-1529	117067	Yves Minet	01/2013

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Probable Primes Top 10000

(218736 PRPs in the top)