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	(29*2^433547-1)/27	130511	Lelio R Paula	06/2015
2002	4*10^130480+9	130481	Robert Price	05/2015
2003	(23*2^433449-1)/75	130481	Lelio R Paula	06/2015
2004	(23*2^433334-1)/3731	130445	Lelio R Paula	06/2015
2005	2^433023-113497	130353	Enzo Doria	08/2014
2006	2^433002+1179379	130347	Enzo Doria	06/2016
2007	2^432974+19	130339	Robert Price	08/2015
2008	(2^432457-1)/1672739247834685086279697	130159	Tony Prest / Never Odd Or Even	09/2013
2009	2^432217+41	130111	Lelio R Paula	06/2017
2010	(2^216089*(2^216091-1)-339)/25	130098	Makoto Morimoto	03/2017
2011	((2^216091+1066)^2+(2^216091+1066)+41)/47/2069	130095	Makoto Morimoto	05/2016
2012	97^65480-2	130094	Lelio R Paula	05/2017
2013	4*10^130088-89	130089	Robert Price	11/2018
2014	2^432117-113215	130081	Enzo Doria	07/2014
2015	2^431804+72511	129986	Enzo Doria	04/2016
2016	(3^272141-3^136071+1)/7	129844	Serge Batalov	03/2014
2017	(9*2^431141+1)/17	129787	Lelio R Paula	06/2015
2018	(29*2^430881-1)/21	129709	Lelio R Paula	06/2015
2019	2^430807+1869563	129686	Enzo Doria	05/2016
2020	2^430721-21429	129660	Enzo Doria	07/2013
2021	2^430415-276271	129568	Enzo Doria	07/2015
2022	2^430142-2791721	129486	Enzo Doria	03/2016
2023	(7*10^129472-13)/3	129473	Robert Price	07/2018
2024	2^429568-21017	129313	Enzo Doria	07/2013
2025	(11*10^129239-179)/3	129240	Robert Price	09/2018
2026	2^429194-112685	129201	Enzo Doria	06/2014
2027	2^429145-2780449	129186	Enzo Doria	04/2016
2028	2^428892-113453	129110	Enzo Doria	07/2014
2029	(11*2^428881-7)/15	129106	Renaud Lifchitz	03/2011
2030	2^428727-113959	129060	Enzo Doria	10/2014
2031	(7*2^428725-1)/13	129059	Lelio R Paula	05/2014
2032	(10^129051-31)/3	129051	Serge Batalov	12/2014
2033	2^428564+71161	129011	Enzo Doria	04/2016
2034	2^428502-113285	128992	Enzo Doria	07/2014
2035	2^428421-21373	128968	Enzo Doria	06/2013
2036	L(616787)	128901	Henri Lifchitz	09/2008
2037	91^65772-2	128851	Lelio R Paula	05/2017
2038	2^428022+43	128848	Lelio R Paula	05/2017
2039	2^427999-459397	128841	Enzo Doria	05/2015
2040	2^427993+76847	128839	Enzo Doria	05/2016
2041	2^427824-1851507	128788	Enzo Doria	08/2015
2042	2^427807-21469	128783	Enzo Doria	07/2013
2043	11^123594-240	128710	Enzo Doria	09/2012
2044	2^427504-21503	128692	Enzo Doria	07/2013
2045	2^427420+91	128667	Lelio R Paula	05/2017
2046	2^427269-113635	128621	Enzo Doria	08/2014
2047	2^427130+1877569	128579	Enzo Doria	08/2016
2048	2^427016-115349	128545	Enzo Doria	07/2015
2049	(4*10^128510+137)/3	128511	Robert Price	03/2018
2050	2^426889-112879	128507	Enzo Doria	06/2014
2051	2^426804+1869931	128481	Enzo Doria	05/2016
2052	2^426750+77635	128465	Enzo Doria	05/2016
2053	2^426425-91	128367	Lelio R Paula	05/2017
2054	(15*2^426398-1)/11	128359	Lelio R Paula	05/2014
2055	2^426352+74971	128345	Enzo Doria	04/2016
2056	4*10^128343-21	128344	Robert Price	09/2018
2057	2^426300-1863689	128330	Enzo Doria	03/2016
2058	2^426293+1881017	128327	Enzo Doria	11/2016
2059	2^426043+35	128252	Robert Price	11/2015
2060	(4*10^128244-19)/3	128245	Robert Price	03/2018
2061	2^425808-459959	128181	Enzo Doria	06/2015
2062	2^425627-113605	128127	Enzo Doria	08/2014
2063	18565^30002-30002^18565	128070	Norbert Schneider	01/2015
2064	(2^425287-9)/2737	128021	Lelio R Paula	05/2015
2065	(3*2^425233-1)/25	128007	Lelio R Paula	05/2014
2066	2^425205+4911	128000	Marek Hubal	02/2017
2067	2^425118-113663	127974	Enzo Doria	08/2014
2068	2^425061+1869761	127957	Enzo Doria	05/2016
2069	2^424918-21141	127914	Enzo Doria	07/2013
2070	2^424864-29489	127897	Enzo Doria	08/2015
2071	(97*10^127858-1)/3	127860	Serge Batalov	12/2014
2072	2^424632-2786639	127827	Enzo Doria	03/2016
2073	2^424577-113755	127811	Enzo Doria	09/2014
2074	(7*2^424512-1)/3	127792	Lelio R Paula	05/2014
2075	11^122629-720	127705	Enzo Doria	11/2012
2076	2^423696-21429	127546	Enzo Doria	07/2013
2077	2^423664-1864559	127536	Enzo Doria	03/2016
2078	3^267267-4	127519	Henri Lifchitz	10/2014
2079	(19^99689+5^99689)/24	127477	Robert Price	09/2013
2080	(21*2^423372+1)/101	127447	Lelio R Paula	05/2014
2081	2^423328-21537	127435	Enzo Doria	07/2013
2082	(2^423165-7)/25	127384	Lelio R Paula	05/2015
2083	(F(5)^182099-F(4)^182099)/F(3)	127282	Wayne Halsdorf	08/2013
2084	(16*10^127259+197)/3	127260	Robert Price	04/2019
2085	(234483*27^88884-145)/26	127230	Curtis Bright	05/2015
2086	2^422515-114997	127190	Enzo Doria	06/2015
2087	5*10^127179-3	127180	Robert Price	07/2015
2088	(44*10^127169-233)/9	127170	Robert Price	01/2019
2089	5*10^127153+77	127154	Robert Price	12/2018
2090	-516776642557847117490*Bern(37960)/34256837217082767928421792453	127042	Thomas Ritschel	06/2017
2091	(78^67141-1)/77	127036	Paul Bourdelais	09/2017
2092	2^421860-113285	126993	Enzo Doria	07/2014
2093	(2^421827-7)/11	126982	Lelio R Paula	05/2015
2094	11^121910-840	126957	Enzo Doria	12/2012
2095	(71^68539+1)/72	126882	Paul Bourdelais	09/2017
2096	(5*10^126871-119)/3	126872	Robert Price	03/2018
2097	331^50339-10004	126846	Enzo Doria	07/2012
2098	2^421363-2790757	126843	Enzo Doria	03/2016
2099	(106*10^126839-1)/3	126841	Serge Batalov	12/2014
2100	(7*2^421243+1)/39	126807	Lelio R Paula	05/2014
2101	(14*10^126784-83)/3	126785	Robert Price	12/2018
2102	2^421161-286183	126783	Enzo Doria	06/2015
2103	2^420939-113935	126716	Enzo Doria	10/2014
2104	177^56363-2	126703	Lelio R Paula	10/2017
2105	2^420741-113659	126656	Enzo Doria	08/2014
2106	2^420694-21	126642	Lelio R Paula	05/2017
2107	(13*10^126638+437)/9	126639	Robert Price	04/2018
2108	4*10^126625+87	126626	Robert Price	08/2018
2109	(31*2^420556+1)/7	126601	Lelio R Paula	05/2014
2110	2^420424-59189	126561	Enzo Doria	10/2015
2111	2^420126+71893	126471	Enzo Doria	04/2016
2112	(43*10^126441+47)/9	126442	Robert Price	12/2018
2113	2^419866+1877059	126393	Enzo Doria	07/2016
2114	F(604711)	126377	Henri Lifchitz	02/2005
2115	2^419757+72707	126360	Enzo Doria	04/2016
2116	2^419720-21569	126349	Enzo Doria	07/2013
2117	2^419637+29	126324	Henri Lifchitz	02/2006
2118	2^419612+1876741	126316	Enzo Doria	07/2016
2119	2^419520+2793271	126289	Enzo Doria	03/2016
2120	(2^419447-5)/369	126264	Lelio R Paula	05/2014
2121	2^419328-1859939	126231	Enzo Doria	03/2016
2122	2^419282-1851507	126217	Enzo Doria	08/2015
2123	2^419251+1866143	126208	Enzo Doria	03/2016
2124	11^121185+2	126202	Robert Price	05/2014
2125	(23*2^419036-1)/1393	126141	Lelio R Paula	05/2014
2126	2^418851+23	126087	Robert Price	09/2015
2127	(2^418849-9)/2681	126083	Lelio R Paula	05/2014
2128	2^418829+167	126081	Lelio R Paula	01/2012
2129	(31*2^418782-1)/75891	126063	Lelio R Paula	05/2014
2130	(19*2^418754-1)/15	126058	Lelio R Paula	05/2014
2131	2^418319-109501	125927	Enzo Doria	04/2014
2132	2^418316-112373	125926	Enzo Doria	06/2014
2133	(8*10^125894-29)/3	125895	Robert Price	07/2018
2134	(26*10^125886-413)/9	125887	Robert Price	05/2018
2135	2^417968+1869811	125821	Enzo Doria	06/2016
2136	2^417902+63	125802	Lelio R Paula	09/2015
2137	(10^125792-91)/9	125792	Serge Batalov	12/2014
2138	(35*10^125754-593)/9	125755	Robert Price	07/2018
2139	(32*10^125751-77)/9	125752	Robert Price	06/2018
2140	2^417704+77011	125742	Enzo Doria	05/2016
2141	(10^125706+149)/3	125706	Serge Batalov	12/2014
2142	2^417419-115309	125656	Enzo Doria	07/2015
2143	2^417300+77281	125620	Enzo Doria	05/2016
2144	2^417095-1657	125559	Yves Minet	07/2014
2145	2^416773-25	125462	Lelio R Paula	09/2015
2146	(289511#+292834)/(2^3*146417)	125444	Makoto Morimoto	10/2017
2147	(11*2^416691+1)/43	125436	Lelio R Paula	05/2014
2148	2^416641-2*416641+1	125422	Robert Price	05/2018
2149	(21*2^416566-1)/17	125399	Lelio R Paula	05/2014
2150	2^416530+1870429	125389	Enzo Doria	05/2016
2151	2^416490+1875109	125376	Enzo Doria	09/2016
2152	2^416416-114929	125354	Enzo Doria	05/2015
2153	(172*10^125292-1)/9	125294	Serge Batalov	12/2014
2154	2^416134+1865899	125269	Enzo Doria	03/2016
2155	153^57337-152	125264	Norbert Schneider	12/2018
2156	(9*2^415992+1)/13560845	125220	Lelio R Paula	05/2014
2157	(23^91943-1)/22	125201	Robert Price	01/2012
2158	43125^27010-106	125185	Enzo Doria	08/2012
2159	(38*10^125166+349)/9	125167	Robert Price	10/2018
2160	2^415765-112603	125158	Enzo Doria	06/2014
2161	2^415290-113591	125015	Enzo Doria	08/2014
2162	2^415276-460919	125011	Enzo Doria	06/2015
2163	2^415259+77243	125006	Enzo Doria	05/2016
2164	2^415144-3683	124971	Yves Minet	10/2011
2165	2^414874+79	124890	Lelio R Paula	01/2015
2166	(2^414765+7)/1389	124854	Lelio R Paula	05/2014
2167	2^414618+79459	124813	Enzo Doria	06/2016
2168	2^414432-1846709	124757	Enzo Doria	07/2015
2169	2*10^124751-51	124752	Robert Price	04/2018
2170	(13*2^414274-1)/153	124708	Lelio R Paula	05/2014
2171	(7*10^124648+197)/3	124649	Robert Price	07/2018
2172	2^414032-5	124637	Henri Lifchitz	07/2006
2173	2^414032+1872331	124637	Enzo Doria	05/2016
2174	14120^30009-30009^14120	124533	Norbert Schneider	02/2015
2175	64^68909-63^68909	124463	Robert Price	07/2013
2176	2^413387+76253	124442	Enzo Doria	04/2016
2177	2^413352+524287	124432	Paul Underwood	09/2018
2178	287117#+391613	124424	Nicolas PALAU	01/2017
2179	(4*10^124420+83)/3	124421	Robert Price	02/2018
2180	(27*2^413207-1)/108335	124385	Lelio R Paula	05/2014
2181	(41*10^124335-383)/9	124336	Robert Price	11/2018
2182	2^412868-120599	124286	Paul Bourdelais	02/2012
2183	45^75145-2	124231	Lelio R Paula	08/2015
2184	2^412645-112213	124219	Enzo Doria	06/2014
2185	2^412248+74611	124100	Enzo Doria	04/2016
2186	(22*10^124096-13)/9	124097	Robert Price	06/2018
2187	2^412192-3329	124083	Yves Minet	12/2014
2188	(25*2^412191-1)/23	124082	Lelio R Paula	05/2014
2189	F(593689)	124074	Henri Lifchitz	01/2005
2190	(11*2^412161+1)/19	124073	Lelio R Paula	05/2014
2191	2^411884-113279	123990	Enzo Doria	07/2014
2192	(2^411832+1)/257	123972	Lelio R Paula	05/2014
2193	(26*10^123970-89)/9	123971	Robert Price	06/2018
2194	2^411790-1853531	123962	Enzo Doria	08/2015
2195	(5^177337+1)/6	123953	Paul Bourdelais	11/2008
2196	2^411711-113257	123938	Enzo Doria	07/2014
2197	(23*2^411675-1)/3	123928	Lelio R Paula	05/2014
2198	(11*10^123899-179)/3	123900	Robert Price	09/2018
2199	2^411325-351103	123822	Enzo Doria	06/2015
2200	2^411052+1872481	123739	Enzo Doria	05/2016
2201	2^410997+39	123723	Lelio R Paula	05/2014
2202	155^56438+154	123618	Norbert Schneider	01/2019
2203	2^410596-39	123602	Lelio R Paula	05/2014
2204	2^410540-115079	123585	Enzo Doria	06/2015
2205	(7*10^123563+107)/3	123564	Robert Price	02/2018
2206	(3*2^410392-1)/9229	123537	Lelio R Paula	05/2014
2207	2^410206-113081	123485	Enzo Doria	07/2014
2208	(25*2^410192+1)/10397	123478	Lelio R Paula	04/2014
2209	2^409909-189	123395	Enzo Doria	05/2014
2210	2^409896-109043	123391	Enzo Doria	04/2014
2211	2^409890+75409	123390	Enzo Doria	04/2016
2212	133^58076-2	123345	Lelio R Paula	10/2017
2213	F(590041)	123311	Henri Lifchitz	01/2005
2214	2^409566-113501	123292	Enzo Doria	08/2014
2215	2^409533+77747	123282	Enzo Doria	05/2016
2216	2^409436-112799	123253	Enzo Doria	06/2014
2217	2^409225+1873787	123189	Enzo Doria	06/2016
2218	2^409174+73009	123174	Enzo Doria	04/2016
2219	2^409058-112685	123139	Enzo Doria	06/2014
2220	(13*10^123137-61)/3	123138	Robert Price	11/2018
2221	4*10^123113+21	123114	Robert Price	12/2018
2222	2^408778+77689	123055	Enzo Doria	05/2016
2223	2^408690-75	123028	Lelio R Paula	11/2013
2224	(29*10^122996+673)/9	122997	Robert Price	12/2018
2225	2^408574-2787341	122994	Enzo Doria	03/2016
2226	3*10^122977+37	122978	Robert Price	08/2018
2227	Phi(157825,10)	122961	Maksym Voznyy	06/2015
2228	(13*2^408283+1)/1665	122904	Lelio R Paula	05/2014
2229	(16*10^122871+77)/3	122872	Robert Price	03/2019
2230	(11*2^408100-1)/35	122850	Lelio R Paula	04/2014
2231	(2^407821-lucasV(1,2,407821)+1)/2	122767	Mike Oakes	11/2016
2232	(32*10^122733-77)/9	122734	Robert Price	06/2018
2233	(21*2^407604-1)/215	122701	Lelio R Paula	04/2014
2234	(21*2^407433-1)/13	122650	Lelio R Paula	04/2014
2235	(73*10^122592-1)/9	122593	Robert Price	01/2015
2236	(5*10^122592+91)/3	122593	Robert Price	04/2018
2237	2^407179-112075	122574	Enzo Doria	06/2014
2238	(21*2^407131+1)/207517523	122552	Lelio R Paula	04/2014
2239	(66^67349+1)/67	122543	Paul Bourdelais	09/2017
2240	2^407008-1867919	122522	Enzo Doria	04/2016
2241	11^117642-300	122512	Enzo Doria	10/2012
2242	(F(397700+1)^2+L(397700+1)^2)/2	122509	Henri Lifchitz	10/2017
2243	2^406949+72197	122504	Enzo Doria	04/2016
2244	2^406826-65	122467	Lelio R Paula	11/2013
2245	2^406821-2797363	122466	Enzo Doria	04/2016
2246	2^406758-17	122447	Lelio R Paula	11/2013
2247	(30^82883-1)/29	122427	Robert Price	12/2011
2248	(2^406583-1)/813167	122388	Jens K. Andersen	02/2009
2249	4*10^122377+19	122378	Robert Price	10/2018
2250	3*10^122345-97	122346	Robert Price	07/2018

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Probable Primes Top 10000

(252675 PRPs in the top)