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	3^267267-4	127519	Henri Lifchitz	10/2014
2002	(19^99689+5^99689)/24	127477	Robert Price	09/2013
2003	(21*2^423372+1)/101	127447	Lelio R Paula	05/2014
2004	2^423328-21537	127435	Enzo Doria	07/2013
2005	(2^423165-7)/25	127384	Lelio R Paula	05/2015
2006	(F(5)^182099-F(4)^182099)/F(3)	127282	Wayne Halsdorf	08/2013
2007	(234483*27^88884-145)/26	127230	Curtis Bright	05/2015
2008	2^422515-114997	127190	Enzo Doria	06/2015
2009	5*10^127179-3	127180	Robert Price	07/2015
2010	-516776642557847117490*Bern(37960)/34256837217082767928421792453	127042	Thomas Ritschel	06/2017
2011	(78^67141-1)/77	127036	Paul Bourdelais	09/2017
2012	2^421860-113285	126993	Enzo Doria	07/2014
2013	(2^421827-7)/11	126982	Lelio R Paula	05/2015
2014	11^121910-840	126957	Enzo Doria	12/2012
2015	(71^68539+1)/72	126882	Paul Bourdelais	09/2017
2016	(5*10^126871-119)/3	126872	Robert Price	03/2018
2017	331^50339-10004	126846	Enzo Doria	07/2012
2018	2^421363-2790757	126843	Enzo Doria	03/2016
2019	(106*10^126839-1)/3	126841	Serge Batalov	12/2014
2020	(7*2^421243+1)/39	126807	Lelio R Paula	05/2014
2021	2^421161-286183	126783	Enzo Doria	06/2015
2022	2^420939-113935	126716	Enzo Doria	10/2014
2023	177^56363-2	126703	Lelio R Paula	10/2017
2024	2^420741-113659	126656	Enzo Doria	08/2014
2025	2^420694-21	126642	Lelio R Paula	05/2017
2026	(13*10^126638+437)/9	126639	Robert Price	04/2018
2027	4*10^126625+87	126626	Robert Price	08/2018
2028	(31*2^420556+1)/7	126601	Lelio R Paula	05/2014
2029	2^420424-59189	126561	Enzo Doria	10/2015
2030	2^420126+71893	126471	Enzo Doria	04/2016
2031	(43*10^126441+47)/9	126442	Robert Price	12/2018
2032	2^419866+1877059	126393	Enzo Doria	07/2016
2033	F(604711)	126377	Henri Lifchitz	02/2005
2034	2^419757+72707	126360	Enzo Doria	04/2016
2035	2^419720-21569	126349	Enzo Doria	07/2013
2036	2^419637+29	126324	Henri Lifchitz	02/2006
2037	2^419612+1876741	126316	Enzo Doria	07/2016
2038	2^419520+2793271	126289	Enzo Doria	03/2016
2039	(2^419447-5)/369	126264	Lelio R Paula	05/2014
2040	2^419328-1859939	126231	Enzo Doria	03/2016
2041	2^419282-1851507	126217	Enzo Doria	08/2015
2042	2^419251+1866143	126208	Enzo Doria	03/2016
2043	11^121185+2	126202	Robert Price	05/2014
2044	(23*2^419036-1)/1393	126141	Lelio R Paula	05/2014
2045	2^418851+23	126087	Robert Price	09/2015
2046	(2^418849-9)/2681	126083	Lelio R Paula	05/2014
2047	2^418829+167	126081	Lelio R Paula	01/2012
2048	(31*2^418782-1)/75891	126063	Lelio R Paula	05/2014
2049	(19*2^418754-1)/15	126058	Lelio R Paula	05/2014
2050	2^418319-109501	125927	Enzo Doria	04/2014
2051	2^418316-112373	125926	Enzo Doria	06/2014
2052	(8*10^125894-29)/3	125895	Robert Price	07/2018
2053	(26*10^125886-413)/9	125887	Robert Price	05/2018
2054	2^417968+1869811	125821	Enzo Doria	06/2016
2055	2^417902+63	125802	Lelio R Paula	09/2015
2056	(10^125792-91)/9	125792	Serge Batalov	12/2014
2057	(35*10^125754-593)/9	125755	Robert Price	07/2018
2058	(32*10^125751-77)/9	125752	Robert Price	06/2018
2059	2^417704+77011	125742	Enzo Doria	05/2016
2060	(10^125706+149)/3	125706	Serge Batalov	12/2014
2061	2^417419-115309	125656	Enzo Doria	07/2015
2062	2^417300+77281	125620	Enzo Doria	05/2016
2063	2^417095-1657	125559	Yves Minet	07/2014
2064	2^416773-25	125462	Lelio R Paula	09/2015
2065	(289511#+292834)/(2^3*146417)	125444	Makoto Morimoto	10/2017
2066	(11*2^416691+1)/43	125436	Lelio R Paula	05/2014
2067	2^416641-2*416641+1	125422	Robert Price	05/2018
2068	(21*2^416566-1)/17	125399	Lelio R Paula	05/2014
2069	2^416530+1870429	125389	Enzo Doria	05/2016
2070	2^416490+1875109	125376	Enzo Doria	09/2016
2071	2^416416-114929	125354	Enzo Doria	05/2015
2072	(172*10^125292-1)/9	125294	Serge Batalov	12/2014
2073	2^416134+1865899	125269	Enzo Doria	03/2016
2074	(9*2^415992+1)/13560845	125220	Lelio R Paula	05/2014
2075	(23^91943-1)/22	125201	Robert Price	01/2012
2076	43125^27010-106	125185	Enzo Doria	08/2012
2077	(38*10^125166+349)/9	125167	Robert Price	10/2018
2078	2^415765-112603	125158	Enzo Doria	06/2014
2079	2^415290-113591	125015	Enzo Doria	08/2014
2080	2^415276-460919	125011	Enzo Doria	06/2015
2081	2^415259+77243	125006	Enzo Doria	05/2016
2082	2^415144-3683	124971	Yves Minet	10/2011
2083	2^414874+79	124890	Lelio R Paula	01/2015
2084	(2^414765+7)/1389	124854	Lelio R Paula	05/2014
2085	2^414618+79459	124813	Enzo Doria	06/2016
2086	2^414432-1846709	124757	Enzo Doria	07/2015
2087	2*10^124751-51	124752	Robert Price	04/2018
2088	(13*2^414274-1)/153	124708	Lelio R Paula	05/2014
2089	(7*10^124648+197)/3	124649	Robert Price	07/2018
2090	2^414032-5	124637	Henri Lifchitz	07/2006
2091	2^414032+1872331	124637	Enzo Doria	05/2016
2092	14120^30009-30009^14120	124533	Norbert Schneider	02/2015
2093	64^68909-63^68909	124463	Robert Price	07/2013
2094	2^413387+76253	124442	Enzo Doria	04/2016
2095	2^413352+524287	124432	Paul Underwood	09/2018
2096	287117#+391613	124424	Nicolas PALAU	01/2017
2097	(4*10^124420+83)/3	124421	Robert Price	02/2018
2098	(27*2^413207-1)/108335	124385	Lelio R Paula	05/2014
2099	(41*10^124335-383)/9	124336	Robert Price	11/2018
2100	2^412868-120599	124286	Paul Bourdelais	02/2012
2101	45^75145-2	124231	Lelio R Paula	08/2015
2102	2^412645-112213	124219	Enzo Doria	06/2014
2103	2^412248+74611	124100	Enzo Doria	04/2016
2104	(22*10^124096-13)/9	124097	Robert Price	06/2018
2105	2^412192-3329	124083	Yves Minet	12/2014
2106	(25*2^412191-1)/23	124082	Lelio R Paula	05/2014
2107	F(593689)	124074	Henri Lifchitz	01/2005
2108	(11*2^412161+1)/19	124073	Lelio R Paula	05/2014
2109	2^411884-113279	123990	Enzo Doria	07/2014
2110	(2^411832+1)/257	123972	Lelio R Paula	05/2014
2111	(26*10^123970-89)/9	123971	Robert Price	06/2018
2112	2^411790-1853531	123962	Enzo Doria	08/2015
2113	(5^177337+1)/6	123953	Paul Bourdelais	11/2008
2114	2^411711-113257	123938	Enzo Doria	07/2014
2115	(23*2^411675-1)/3	123928	Lelio R Paula	05/2014
2116	(11*10^123899-179)/3	123900	Robert Price	09/2018
2117	2^411325-351103	123822	Enzo Doria	06/2015
2118	2^411052+1872481	123739	Enzo Doria	05/2016
2119	2^410997+39	123723	Lelio R Paula	05/2014
2120	2^410596-39	123602	Lelio R Paula	05/2014
2121	2^410540-115079	123585	Enzo Doria	06/2015
2122	(7*10^123563+107)/3	123564	Robert Price	02/2018
2123	(3*2^410392-1)/9229	123537	Lelio R Paula	05/2014
2124	2^410206-113081	123485	Enzo Doria	07/2014
2125	(25*2^410192+1)/10397	123478	Lelio R Paula	04/2014
2126	2^409909-189	123395	Enzo Doria	05/2014
2127	2^409896-109043	123391	Enzo Doria	04/2014
2128	2^409890+75409	123390	Enzo Doria	04/2016
2129	133^58076-2	123345	Lelio R Paula	10/2017
2130	F(590041)	123311	Henri Lifchitz	01/2005
2131	2^409566-113501	123292	Enzo Doria	08/2014
2132	2^409533+77747	123282	Enzo Doria	05/2016
2133	2^409436-112799	123253	Enzo Doria	06/2014
2134	2^409225+1873787	123189	Enzo Doria	06/2016
2135	2^409174+73009	123174	Enzo Doria	04/2016
2136	2^409058-112685	123139	Enzo Doria	06/2014
2137	(13*10^123137-61)/3	123138	Robert Price	11/2018
2138	4*10^123113+21	123114	Robert Price	12/2018
2139	2^408778+77689	123055	Enzo Doria	05/2016
2140	2^408690-75	123028	Lelio R Paula	11/2013
2141	(29*10^122996+673)/9	122997	Robert Price	12/2018
2142	2^408574-2787341	122994	Enzo Doria	03/2016
2143	3*10^122977+37	122978	Robert Price	08/2018
2144	Phi(157825,10)	122961	Maksym Voznyy	06/2015
2145	(13*2^408283+1)/1665	122904	Lelio R Paula	05/2014
2146	(11*2^408100-1)/35	122850	Lelio R Paula	04/2014
2147	(2^407821-lucasV(1,2,407821)+1)/2	122767	Mike Oakes	11/2016
2148	(32*10^122733-77)/9	122734	Robert Price	06/2018
2149	(21*2^407604-1)/215	122701	Lelio R Paula	04/2014
2150	(21*2^407433-1)/13	122650	Lelio R Paula	04/2014
2151	(73*10^122592-1)/9	122593	Robert Price	01/2015
2152	(5*10^122592+91)/3	122593	Robert Price	04/2018
2153	2^407179-112075	122574	Enzo Doria	06/2014
2154	(21*2^407131+1)/207517523	122552	Lelio R Paula	04/2014
2155	(66^67349+1)/67	122543	Paul Bourdelais	09/2017
2156	2^407008-1867919	122522	Enzo Doria	04/2016
2157	11^117642-300	122512	Enzo Doria	10/2012
2158	(F(397700+1)^2+L(397700+1)^2)/2	122509	Henri Lifchitz	10/2017
2159	2^406949+72197	122504	Enzo Doria	04/2016
2160	2^406826-65	122467	Lelio R Paula	11/2013
2161	2^406821-2797363	122466	Enzo Doria	04/2016
2162	2^406758-17	122447	Lelio R Paula	11/2013
2163	(30^82883-1)/29	122427	Robert Price	12/2011
2164	(2^406583-1)/813167	122388	Jens K. Andersen	02/2009
2165	4*10^122377+19	122378	Robert Price	10/2018
2166	3*10^122345-97	122346	Robert Price	07/2018
2167	97^61575-2	122336	Lelio R Paula	12/2014
2168	2^406298+2799109	122308	Enzo Doria	04/2016
2169	(27*2^406241-1)/10277	122289	Lelio R Paula	04/2014
2170	2^406229-1849993	122288	Enzo Doria	08/2015
2171	3*10^122274+7	122275	Robert Price	07/2015
2172	2^406117+1876577	122254	Enzo Doria	07/2016
2173	3^256199-2^256199	122238	Mike Oakes	06/2005
2174	2^405992-78557	122216	Jorge Menendez	03/2018
2175	(8*10^122203+43)/3	122204	Robert Price	06/2018
2176	2^405774+179149	122151	Enzo Doria	06/2016
2177	2^405514-3311	122072	Yves Minet	12/2014
2178	2^405514-115511	122072	Enzo Doria	07/2015
2179	2^405422-113261	122045	Enzo Doria	07/2014
2180	2^405173+71237	121970	Enzo Doria	04/2016
2181	(2^405016+1)/257	121920	Lelio R Paula	04/2014
2182	2^404858+71329	121875	Enzo Doria	04/2016
2183	2^404813-114703	121861	Enzo Doria	04/2015
2184	2^404764+77791	121847	Enzo Doria	05/2016
2185	317^48694+48694^317	121787	Norbert Schneider	08/2015
2186	2^404536-115259	121778	Enzo Doria	06/2015
2187	2^404501-631	121767	Yves Minet	07/2012
2188	63^67620+2	121672	Lelio R Paula	08/2015
2189	(17*10^121621+1)/9	121622	Serge Batalov	05/2010
2190	(15*2^403912+1)/271	121589	Lelio R Paula	05/2014
2191	(10^121543-79)/3	121543	Robert Price	01/2018
2192	2^403676+76831	121519	Enzo Doria	05/2016
2193	(7*10^121487+143)/3	121488	Robert Price	03/2018
2194	2^403363-113635	121425	Enzo Doria	08/2014
2195	2^403336-1861469	121417	Enzo Doria	03/2016
2196	p(24442)#/2-64	121381	Robert Price	04/2017
2197	11^116555-720	121380	Enzo Doria	11/2012
2198	2^403100-461267	121346	Enzo Doria	07/2015
2199	2^403093-112213	121344	Enzo Doria	06/2014
2200	(316^48539+1)/317	121330	Eric Chen	10/2017
2201	2^403004+1866361	121317	Enzo Doria	03/2016
2202	2^402953+89	121301	Lelio R Paula	10/2013
2203	2^402944-2788319	121299	Enzo Doria	03/2016
2204	(27*2^402865+1)/5	121276	Lelio R Paula	04/2014
2205	2^402828-113183	121264	Enzo Doria	07/2014
2206	(17*10^121242+1)/9	121243	Serge Batalov	05/2010
2207	(15*2^402757+1)/101	121242	Lelio R Paula	05/2014
2209	2^402715+1874223	121230	Enzo Doria	06/2016
2208	(35*10^121229-593)/9	121230	Robert Price	07/2018
2210	(91^61879+1)/92	121222	Paul Bourdelais	09/2017
2211	7*10^121144+9	121145	Robert Price	09/2015
2212	2^401725-113251	120932	Enzo Doria	07/2014
2213	(15*2^401677-1)/19	120917	Lelio R Paula	05/2014
2214	2^401652+73711	120910	Enzo Doria	04/2016
2215	(2^401632+3)/79	120902	Lelio R Paula	04/2014
2216	2^401406-2791331	120836	Enzo Doria	03/2016
2217	(28^83497+1)/29	120832	Robert Price	07/2013
2218	2^401369+1867367	120825	Enzo Doria	03/2016
2219	(10^120782+29)/3	120782	Serge Batalov	12/2014
2220	2^401215-1657	120778	Yves Minet	07/2014
2221	2^401159+53	120761	Lelio R Paula	10/2013
2222	2^401031-113047	120723	Enzo Doria	07/2014
2223	(29*2^400909-1)/303	120685	Lelio R Paula	04/2014
2224	2^400571-15	120584	Lelio R Paula	10/2013
2225	(10^120574+359)/9	120574	Serge Batalov	12/2014
2226	2^400424-216413	120540	Enzo Doria	04/2013
2227	(17*2^400200-1)/587	120471	Lelio R Paula	05/2014
2228	2^400166+1874899	120462	Enzo Doria	06/2016
2229	(3*2^400045-1)/865	120424	Lelio R Paula	04/2014
2230	2^399966+73759	120402	Enzo Doria	04/2016
2231	(112*10^120395-1)/3	120397	Serge Batalov	12/2014
2232	2^399918-95	120388	Lelio R Paula	04/2013
2233	2^399792-1849259	120350	Enzo Doria	08/2015
2234	9*10^120342-7	120343	Robert Price	09/2015
2235	2^399526-1861721	120270	Enzo Doria	11/2015
2236	(10^(260126+1)+3610^60126-1)/9	120253	Robert Price	10/2015
2237	2^399322-2798111	120208	Enzo Doria	04/2016
2238	72^64693-71^64693	120157	Robert Price	03/2014
2239	2^399111-28489	120145	Enzo Doria	08/2015
2241	2^398877+105	120074	Donovan Johnson	01/2006
2240	(101*10^120072-87)/7	120074	Hans Havermann	02/2015
2242	(88^61751+1)/89	120072	Paul Bourdelais	09/2017
2243	2^398710+57	120024	Lelio R Paula	04/2013
2244	2^398691-115057	120018	Enzo Doria	06/2015
2245	L(574219)	120005	Renaud Lifchitz	03/2004
2246	2^398571+60413	119982	Yves Minet	03/2011
2247	p(24179)#/2-64	119949	Robert Price	04/2017
2248	2^398448+1872001	119945	Enzo Doria	05/2016
2249	8*10^119930-3	119931	Ray Chandler	04/2011
2250	(10^119880+179)/9	119880	Serge Batalov	12/2014

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Probable Primes Top 10000

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