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	2^427824-1851507	128788	Enzo Doria	08/2015
2002	2^427807-21469	128783	Enzo Doria	07/2013
2003	11^123594-240	128710	Enzo Doria	09/2012
2004	2^427504-21503	128692	Enzo Doria	07/2013
2005	2^427420+91	128667	Lelio R Paula	05/2017
2006	2^427269-113635	128621	Enzo Doria	08/2014
2007	2^427130+1877569	128579	Enzo Doria	08/2016
2008	2^427016-115349	128545	Enzo Doria	07/2015
2009	(4*10^128510+137)/3	128511	Robert Price	03/2018
2010	2^426889-112879	128507	Enzo Doria	06/2014
2011	2^426804+1869931	128481	Enzo Doria	05/2016
2012	2^426750+77635	128465	Enzo Doria	05/2016
2013	2^426425-91	128367	Lelio R Paula	05/2017
2014	(15*2^426398-1)/11	128359	Lelio R Paula	05/2014
2015	2^426352+74971	128345	Enzo Doria	04/2016
2016	4*10^128343-21	128344	Robert Price	09/2018
2017	2^426300-1863689	128330	Enzo Doria	03/2016
2018	2^426293+1881017	128327	Enzo Doria	11/2016
2019	2^426043+35	128252	Robert Price	11/2015
2020	(4*10^128244-19)/3	128245	Robert Price	03/2018
2021	2^425808-459959	128181	Enzo Doria	06/2015
2022	2^425627-113605	128127	Enzo Doria	08/2014
2023	18565^30002-30002^18565	128070	Norbert Schneider	01/2015
2024	(2^425287-9)/2737	128021	Lelio R Paula	05/2015
2025	(3*2^425233-1)/25	128007	Lelio R Paula	05/2014
2026	2^425205+4911	128000	Marek Hubal	02/2017
2027	2^425118-113663	127974	Enzo Doria	08/2014
2028	2^425061+1869761	127957	Enzo Doria	05/2016
2029	2^424918-21141	127914	Enzo Doria	07/2013
2030	2^424864-29489	127897	Enzo Doria	08/2015
2031	(97*10^127858-1)/3	127860	Serge Batalov	12/2014
2032	2^424632-2786639	127827	Enzo Doria	03/2016
2033	2^424577-113755	127811	Enzo Doria	09/2014
2034	(7*2^424512-1)/3	127792	Lelio R Paula	05/2014
2035	11^122629-720	127705	Enzo Doria	11/2012
2036	2^423696-21429	127546	Enzo Doria	07/2013
2037	2^423664-1864559	127536	Enzo Doria	03/2016
2038	3^267267-4	127519	Henri Lifchitz	10/2014
2039	(19^99689+5^99689)/24	127477	Robert Price	09/2013
2040	(21*2^423372+1)/101	127447	Lelio R Paula	05/2014
2041	2^423328-21537	127435	Enzo Doria	07/2013
2042	(2^423165-7)/25	127384	Lelio R Paula	05/2015
2043	(F(5)^182099-F(4)^182099)/F(3)	127282	Wayne Halsdorf	08/2013
2044	(234483*27^88884-145)/26	127230	Curtis Bright	05/2015
2045	2^422515-114997	127190	Enzo Doria	06/2015
2046	5*10^127179-3	127180	Robert Price	07/2015
2047	(44*10^127169-233)/9	127170	Robert Price	01/2019
2048	5*10^127153+77	127154	Robert Price	12/2018
2049	-516776642557847117490*Bern(37960)/34256837217082767928421792453	127042	Thomas Ritschel	06/2017
2050	(78^67141-1)/77	127036	Paul Bourdelais	09/2017
2051	2^421860-113285	126993	Enzo Doria	07/2014
2052	(2^421827-7)/11	126982	Lelio R Paula	05/2015
2053	11^121910-840	126957	Enzo Doria	12/2012
2054	(71^68539+1)/72	126882	Paul Bourdelais	09/2017
2055	(5*10^126871-119)/3	126872	Robert Price	03/2018
2056	331^50339-10004	126846	Enzo Doria	07/2012
2057	2^421363-2790757	126843	Enzo Doria	03/2016
2058	(106*10^126839-1)/3	126841	Serge Batalov	12/2014
2059	(7*2^421243+1)/39	126807	Lelio R Paula	05/2014
2060	(14*10^126784-83)/3	126785	Robert Price	12/2018
2061	2^421161-286183	126783	Enzo Doria	06/2015
2062	2^420939-113935	126716	Enzo Doria	10/2014
2063	177^56363-2	126703	Lelio R Paula	10/2017
2064	2^420741-113659	126656	Enzo Doria	08/2014
2065	2^420694-21	126642	Lelio R Paula	05/2017
2066	(13*10^126638+437)/9	126639	Robert Price	04/2018
2067	4*10^126625+87	126626	Robert Price	08/2018
2068	(31*2^420556+1)/7	126601	Lelio R Paula	05/2014
2069	2^420424-59189	126561	Enzo Doria	10/2015
2070	2^420126+71893	126471	Enzo Doria	04/2016
2071	(43*10^126441+47)/9	126442	Robert Price	12/2018
2072	2^419866+1877059	126393	Enzo Doria	07/2016
2073	F(604711)	126377	Henri Lifchitz	02/2005
2074	2^419757+72707	126360	Enzo Doria	04/2016
2075	2^419720-21569	126349	Enzo Doria	07/2013
2076	2^419637+29	126324	Henri Lifchitz	02/2006
2077	2^419612+1876741	126316	Enzo Doria	07/2016
2078	2^419520+2793271	126289	Enzo Doria	03/2016
2079	(2^419447-5)/369	126264	Lelio R Paula	05/2014
2080	2^419328-1859939	126231	Enzo Doria	03/2016
2081	2^419282-1851507	126217	Enzo Doria	08/2015
2082	2^419251+1866143	126208	Enzo Doria	03/2016
2083	11^121185+2	126202	Robert Price	05/2014
2084	(23*2^419036-1)/1393	126141	Lelio R Paula	05/2014
2085	2^418851+23	126087	Robert Price	09/2015
2086	(2^418849-9)/2681	126083	Lelio R Paula	05/2014
2087	2^418829+167	126081	Lelio R Paula	01/2012
2088	(31*2^418782-1)/75891	126063	Lelio R Paula	05/2014
2089	(19*2^418754-1)/15	126058	Lelio R Paula	05/2014
2090	2^418319-109501	125927	Enzo Doria	04/2014
2091	2^418316-112373	125926	Enzo Doria	06/2014
2092	(8*10^125894-29)/3	125895	Robert Price	07/2018
2093	(26*10^125886-413)/9	125887	Robert Price	05/2018
2094	2^417968+1869811	125821	Enzo Doria	06/2016
2095	2^417902+63	125802	Lelio R Paula	09/2015
2096	(10^125792-91)/9	125792	Serge Batalov	12/2014
2097	(35*10^125754-593)/9	125755	Robert Price	07/2018
2098	(32*10^125751-77)/9	125752	Robert Price	06/2018
2099	2^417704+77011	125742	Enzo Doria	05/2016
2100	(10^125706+149)/3	125706	Serge Batalov	12/2014
2101	2^417419-115309	125656	Enzo Doria	07/2015
2102	2^417300+77281	125620	Enzo Doria	05/2016
2103	2^417095-1657	125559	Yves Minet	07/2014
2104	2^416773-25	125462	Lelio R Paula	09/2015
2105	(289511#+292834)/(2^3*146417)	125444	Makoto Morimoto	10/2017
2106	(11*2^416691+1)/43	125436	Lelio R Paula	05/2014
2107	2^416641-2*416641+1	125422	Robert Price	05/2018
2108	(21*2^416566-1)/17	125399	Lelio R Paula	05/2014
2109	2^416530+1870429	125389	Enzo Doria	05/2016
2110	2^416490+1875109	125376	Enzo Doria	09/2016
2111	2^416416-114929	125354	Enzo Doria	05/2015
2112	(172*10^125292-1)/9	125294	Serge Batalov	12/2014
2113	2^416134+1865899	125269	Enzo Doria	03/2016
2114	153^57337-152	125264	Norbert Schneider	12/2018
2115	(9*2^415992+1)/13560845	125220	Lelio R Paula	05/2014
2116	(23^91943-1)/22	125201	Robert Price	01/2012
2117	43125^27010-106	125185	Enzo Doria	08/2012
2118	(38*10^125166+349)/9	125167	Robert Price	10/2018
2119	2^415765-112603	125158	Enzo Doria	06/2014
2120	2^415290-113591	125015	Enzo Doria	08/2014
2121	2^415276-460919	125011	Enzo Doria	06/2015
2122	2^415259+77243	125006	Enzo Doria	05/2016
2123	2^415144-3683	124971	Yves Minet	10/2011
2124	2^414874+79	124890	Lelio R Paula	01/2015
2125	(2^414765+7)/1389	124854	Lelio R Paula	05/2014
2126	2^414618+79459	124813	Enzo Doria	06/2016
2127	2^414432-1846709	124757	Enzo Doria	07/2015
2128	2*10^124751-51	124752	Robert Price	04/2018
2129	(13*2^414274-1)/153	124708	Lelio R Paula	05/2014
2130	(7*10^124648+197)/3	124649	Robert Price	07/2018
2131	2^414032-5	124637	Henri Lifchitz	07/2006
2132	2^414032+1872331	124637	Enzo Doria	05/2016
2133	14120^30009-30009^14120	124533	Norbert Schneider	02/2015
2134	64^68909-63^68909	124463	Robert Price	07/2013
2135	2^413387+76253	124442	Enzo Doria	04/2016
2136	2^413352+524287	124432	Paul Underwood	09/2018
2137	287117#+391613	124424	Nicolas PALAU	01/2017
2138	(4*10^124420+83)/3	124421	Robert Price	02/2018
2139	(27*2^413207-1)/108335	124385	Lelio R Paula	05/2014
2140	(41*10^124335-383)/9	124336	Robert Price	11/2018
2141	2^412868-120599	124286	Paul Bourdelais	02/2012
2142	45^75145-2	124231	Lelio R Paula	08/2015
2143	2^412645-112213	124219	Enzo Doria	06/2014
2144	2^412248+74611	124100	Enzo Doria	04/2016
2145	(22*10^124096-13)/9	124097	Robert Price	06/2018
2146	2^412192-3329	124083	Yves Minet	12/2014
2147	(25*2^412191-1)/23	124082	Lelio R Paula	05/2014
2148	F(593689)	124074	Henri Lifchitz	01/2005
2149	(11*2^412161+1)/19	124073	Lelio R Paula	05/2014
2150	2^411884-113279	123990	Enzo Doria	07/2014
2151	(2^411832+1)/257	123972	Lelio R Paula	05/2014
2152	(26*10^123970-89)/9	123971	Robert Price	06/2018
2153	2^411790-1853531	123962	Enzo Doria	08/2015
2154	(5^177337+1)/6	123953	Paul Bourdelais	11/2008
2155	2^411711-113257	123938	Enzo Doria	07/2014
2156	(23*2^411675-1)/3	123928	Lelio R Paula	05/2014
2157	(11*10^123899-179)/3	123900	Robert Price	09/2018
2158	2^411325-351103	123822	Enzo Doria	06/2015
2159	2^411052+1872481	123739	Enzo Doria	05/2016
2160	2^410997+39	123723	Lelio R Paula	05/2014
2161	155^56438+154	123618	Norbert Schneider	01/2019
2162	2^410596-39	123602	Lelio R Paula	05/2014
2163	2^410540-115079	123585	Enzo Doria	06/2015
2164	(7*10^123563+107)/3	123564	Robert Price	02/2018
2165	(3*2^410392-1)/9229	123537	Lelio R Paula	05/2014
2166	2^410206-113081	123485	Enzo Doria	07/2014
2167	(25*2^410192+1)/10397	123478	Lelio R Paula	04/2014
2168	2^409909-189	123395	Enzo Doria	05/2014
2169	2^409896-109043	123391	Enzo Doria	04/2014
2170	2^409890+75409	123390	Enzo Doria	04/2016
2171	133^58076-2	123345	Lelio R Paula	10/2017
2172	F(590041)	123311	Henri Lifchitz	01/2005
2173	2^409566-113501	123292	Enzo Doria	08/2014
2174	2^409533+77747	123282	Enzo Doria	05/2016
2175	2^409436-112799	123253	Enzo Doria	06/2014
2176	2^409225+1873787	123189	Enzo Doria	06/2016
2177	2^409174+73009	123174	Enzo Doria	04/2016
2178	2^409058-112685	123139	Enzo Doria	06/2014
2179	(13*10^123137-61)/3	123138	Robert Price	11/2018
2180	4*10^123113+21	123114	Robert Price	12/2018
2181	2^408778+77689	123055	Enzo Doria	05/2016
2182	2^408690-75	123028	Lelio R Paula	11/2013
2183	(29*10^122996+673)/9	122997	Robert Price	12/2018
2184	2^408574-2787341	122994	Enzo Doria	03/2016
2185	3*10^122977+37	122978	Robert Price	08/2018
2186	Phi(157825,10)	122961	Maksym Voznyy	06/2015
2187	(13*2^408283+1)/1665	122904	Lelio R Paula	05/2014
2188	(11*2^408100-1)/35	122850	Lelio R Paula	04/2014
2189	(2^407821-lucasV(1,2,407821)+1)/2	122767	Mike Oakes	11/2016
2190	(32*10^122733-77)/9	122734	Robert Price	06/2018
2191	(21*2^407604-1)/215	122701	Lelio R Paula	04/2014
2192	(21*2^407433-1)/13	122650	Lelio R Paula	04/2014
2193	(73*10^122592-1)/9	122593	Robert Price	01/2015
2194	(5*10^122592+91)/3	122593	Robert Price	04/2018
2195	2^407179-112075	122574	Enzo Doria	06/2014
2196	(21*2^407131+1)/207517523	122552	Lelio R Paula	04/2014
2197	(66^67349+1)/67	122543	Paul Bourdelais	09/2017
2198	2^407008-1867919	122522	Enzo Doria	04/2016
2199	11^117642-300	122512	Enzo Doria	10/2012
2200	(F(397700+1)^2+L(397700+1)^2)/2	122509	Henri Lifchitz	10/2017
2201	2^406949+72197	122504	Enzo Doria	04/2016
2202	2^406826-65	122467	Lelio R Paula	11/2013
2203	2^406821-2797363	122466	Enzo Doria	04/2016
2204	2^406758-17	122447	Lelio R Paula	11/2013
2205	(30^82883-1)/29	122427	Robert Price	12/2011
2206	(2^406583-1)/813167	122388	Jens K. Andersen	02/2009
2207	4*10^122377+19	122378	Robert Price	10/2018
2208	3*10^122345-97	122346	Robert Price	07/2018
2209	97^61575-2	122336	Lelio R Paula	12/2014
2210	2^406298+2799109	122308	Enzo Doria	04/2016
2211	(27*2^406241-1)/10277	122289	Lelio R Paula	04/2014
2212	2^406229-1849993	122288	Enzo Doria	08/2015
2213	3*10^122274+7	122275	Robert Price	07/2015
2214	2^406117+1876577	122254	Enzo Doria	07/2016
2215	3^256199-2^256199	122238	Mike Oakes	06/2005
2216	2^405992-78557	122216	Jorge Menendez	03/2018
2217	(8*10^122203+43)/3	122204	Robert Price	06/2018
2218	2^405774+179149	122151	Enzo Doria	06/2016
2219	2^405514-3311	122072	Yves Minet	12/2014
2220	2^405514-115511	122072	Enzo Doria	07/2015
2221	2^405422-113261	122045	Enzo Doria	07/2014
2222	2^405173+71237	121970	Enzo Doria	04/2016
2223	(2^405016+1)/257	121920	Lelio R Paula	04/2014
2224	2^404858+71329	121875	Enzo Doria	04/2016
2225	2^404813-114703	121861	Enzo Doria	04/2015
2226	2^404764+77791	121847	Enzo Doria	05/2016
2227	317^48694+48694^317	121787	Norbert Schneider	08/2015
2228	2^404536-115259	121778	Enzo Doria	06/2015
2229	2^404501-631	121767	Yves Minet	07/2012
2230	63^67620+2	121672	Lelio R Paula	08/2015
2231	(17*10^121621+1)/9	121622	Serge Batalov	05/2010
2232	(15*2^403912+1)/271	121589	Lelio R Paula	05/2014
2233	(10^121543-79)/3	121543	Robert Price	01/2018
2234	2^403676+76831	121519	Enzo Doria	05/2016
2235	(7*10^121487+143)/3	121488	Robert Price	03/2018
2236	2^403363-113635	121425	Enzo Doria	08/2014
2237	2^403336-1861469	121417	Enzo Doria	03/2016
2238	p(24442)#/2-64	121381	Robert Price	04/2017
2239	11^116555-720	121380	Enzo Doria	11/2012
2240	2^403100-461267	121346	Enzo Doria	07/2015
2241	2^403093-112213	121344	Enzo Doria	06/2014
2242	(316^48539+1)/317	121330	Eric Chen	10/2017
2243	2^403004+1866361	121317	Enzo Doria	03/2016
2244	2^402953+89	121301	Lelio R Paula	10/2013
2245	2^402944-2788319	121299	Enzo Doria	03/2016
2246	(44*10^121297-719)/9	121298	Robert Price	12/2018
2247	(27*2^402865+1)/5	121276	Lelio R Paula	04/2014
2248	2^402828-113183	121264	Enzo Doria	07/2014
2249	(17*10^121242+1)/9	121243	Serge Batalov	05/2010
2250	(15*2^402757+1)/101	121242	Lelio R Paula	05/2014

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Probable Primes Top 10000

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