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	(2^441799+78557)/5	132995	Lelio R Paula	07/2015
2002	2^441781-2787883	132990	Enzo Doria	03/2016
2003	(3*2^441685+1)/749	132959	Lelio R Paula	07/2015
2004	2^441618+37	132941	Lelio R Paula	08/2017
2005	2^441521-113575	132912	Enzo Doria	08/2014
2006	7*10^132884-99	132885	Robert Price	06/2019
2007	2^441396-65	132874	Lelio R Paula	08/2017
2008	2^441330+1871959	132854	Enzo Doria	05/2016
2009	2^441063+383	132774	Lelio R Paula	06/2012
2010	(22*10^132746+53)/3	132747	Robert Price	07/2019
2011	2^440846+1870909	132708	Enzo Doria	05/2016
2012	2^440656-113489	132651	Enzo Doria	08/2014
2013	numbpart(14180123587)	132646	Serge Batalov	04/2017
2014	(19*10^132550+191)/3	132551	Robert Price	05/2019
2015	(2^440399-1)/(1621082028116197820931518475633880799)	132538	Dario Alpern	01/2015
2016	(38^83891+1)/39	132529	Robert Price	09/2013
2017	2*10^132493-43	132494	Robert Price	04/2018
2018	2^439931-21	132433	Lelio R Paula	08/2017
2019	47^79201-46^79201	132432	Robert Price	10/2012
2020	2^439897-113653	132423	Enzo Doria	08/2014
2021	(5*2^439822+1)/9	132400	Lelio R Paula	06/2015
2022	(112*10^132337-1)/3	132339	Serge Batalov	12/2014
2023	2^439576-113247	132326	Enzo Doria	07/2014
2024	2^439497-29143	132302	Enzo Doria	07/2015
2025	2^439409-114193	132276	Enzo Doria	12/2014
2026	(44*10^132233-233)/9	132234	Robert Price	01/2019
2027	9*10^132148-7	132149	Robert Price	09/2015
2028	(47*10^132125-119)/9	132126	Robert Price	05/2019
2029	2^438845+1870217	132106	Enzo Doria	05/2016
2030	2^438789+87855	132089	Lelio R Paula	01/2016
2031	2^438774-2786411	132085	Enzo Doria	03/2016
2032	2^438755-1848205	132079	Enzo Doria	07/2015
2033	2^438739-112087	132074	Enzo Doria	06/2014
2034	13907#+(318259#)/(13907#)	131923	Makoto Morimoto	10/2017
2035	L(631181)	131910	Henri Lifchitz	09/2008
2036	(47*10^131886-119)/9	131887	Robert Price	05/2019
2037	(3*2^438121+1)/4308193883	131879	Lelio R Paula	06/2015
2038	2^438079-1863877	131875	Enzo Doria	03/2016
2039	(2^438067+5)/329	131869	Lelio R Paula	06/2015
2040	2^437908-113855	131824	Enzo Doria	09/2014
2041	2^437884-286349	131817	Enzo Doria	07/2015
2042	(11*10^131784-17)/3	131785	Robert Price	06/2018
2043	3^276062-112292	131716	Enzo Doria	07/2014
2044	2^437343+75953	131654	Enzo Doria	04/2016
2045	35^85243-34^85243	131621	Robert Price	05/2012
2046	(68^71713+1)/69	131413	Paul Bourdelais	09/2017
2047	2^436451+1884713	131385	Enzo Doria	03/2017
2048	2^436365+35	131359	Robert Price	11/2015
2050	2^436300+1866871	131340	Enzo Doria	03/2016
2049	(7*10^131339+179)/3	131340	Robert Price	09/2018
2051	(37*10^131270+341)/9	131271	Robert Price	08/2018
2052	(5*10^131223-29)/3	131224	Robert Price	03/2018
2053	(23*2^435891-1)/699	131215	Lelio R Paula	07/2015
2054	(11*2^435879+1)/3337	131211	Lelio R Paula	06/2015
2055	(2^435808+1)/641/6700417	131182	Lelio R Paula	02/2012
2056	(2^435808+1)/4294967297	131182	Serge Batalov	12/2016
2057	2^435773+1875557	131181	Enzo Doria	06/2016
2058	(16*10^131180+167)/3	131181	Robert Price	06/2019
2059	(25*10^131144-7)/9	131145	Robert Price	05/2018
2060	2^435612-2789939	131133	Enzo Doria	12/2015
2061	66^72047-65^72047	131093	Robert Price	09/2013
2062	(5*10^131090+37)/3	131091	Robert Price	03/2018
2063	2^435468+75631	131089	Enzo Doria	04/2016
2064	37^83588-2	131083	Lelio R Paula	08/2015
2065	(4^217720+11)/3	131081	Robert Price	02/2017
2066	2^435202-113193	131009	Enzo Doria	07/2014
2067	9*10^130998-19	130999	Robert Price	07/2019
2068	floor((sqrt(5)-1)/2*10^130911)	130911	Serge Batalov	06/2017
2069	2^434835-111937	130899	Enzo Doria	05/2014
2070	2^434685+72257	130854	Enzo Doria	04/2016
2071	(7*10^130825+113)/3	130826	Robert Price	02/2018
2072	2^434539-29317	130810	Enzo Doria	07/2015
2073	2^434469-114259	130789	Enzo Doria	01/2015
2074	2^434246+33	130722	Robert Price	11/2015
2075	2^433911-91	130621	Lelio R Paula	06/2017
2076	2^433744-114419	130570	Enzo Doria	02/2015
2078	2^433708+1869451	130560	Enzo Doria	05/2016
2077	2^433710+93	130560	Lelio R Paula	06/2017
2079	(29*2^433547-1)/27	130511	Lelio R Paula	06/2015
2080	4*10^130480+9	130481	Robert Price	05/2015
2081	(23*2^433449-1)/75	130481	Lelio R Paula	06/2015
2082	(23*2^433334-1)/3731	130445	Lelio R Paula	06/2015
2083	2^433023-113497	130353	Enzo Doria	08/2014
2084	2^433002+1179379	130347	Enzo Doria	06/2016
2085	2^432974+19	130339	Robert Price	08/2015
2086	(2^432457-1)/1672739247834685086279697	130159	Tony Prest / Never Odd Or Even	09/2013
2087	2^432217+41	130111	Lelio R Paula	06/2017
2088	(2^216089*(2^216091-1)-339)/25	130098	Makoto Morimoto	03/2017
2089	((2^216091+1066)^2+(2^216091+1066)+41)/47/2069	130095	Makoto Morimoto	05/2016
2090	97^65480-2	130094	Lelio R Paula	05/2017
2091	4*10^130088-89	130089	Robert Price	11/2018
2092	2^432117-113215	130081	Enzo Doria	07/2014
2093	2^431804+72511	129986	Enzo Doria	04/2016
2094	(3^272141-3^136071+1)/7	129844	Serge Batalov	03/2014
2095	(47*10^129789-119)/9	129790	Robert Price	05/2019
2096	(9*2^431141+1)/17	129787	Lelio R Paula	06/2015
2097	(29*2^430881-1)/21	129709	Lelio R Paula	06/2015
2098	2^430807+1869563	129686	Enzo Doria	05/2016
2099	2^430721-21429	129660	Enzo Doria	07/2013
2100	2^430415-276271	129568	Enzo Doria	07/2015
2101	2^430142-2791721	129486	Enzo Doria	03/2016
2102	(7*10^129472-13)/3	129473	Robert Price	07/2018
2103	2^429568-21017	129313	Enzo Doria	07/2013
2104	(11*10^129239-179)/3	129240	Robert Price	09/2018
2105	2^429194-112685	129201	Enzo Doria	06/2014
2106	2^429145-2780449	129186	Enzo Doria	04/2016
2107	2^428892-113453	129110	Enzo Doria	07/2014
2108	(11*2^428881-7)/15	129106	Renaud Lifchitz	03/2011
2109	2^428727-113959	129060	Enzo Doria	10/2014
2110	(7*2^428725-1)/13	129059	Lelio R Paula	05/2014
2111	(10^129051-31)/3	129051	Serge Batalov	12/2014
2112	2^428564+71161	129011	Enzo Doria	04/2016
2113	2^428502-113285	128992	Enzo Doria	07/2014
2114	2^428421-21373	128968	Enzo Doria	06/2013
2115	L(616787)	128901	Henri Lifchitz	09/2008
2116	91^65772-2	128851	Lelio R Paula	05/2017
2117	2^428022+43	128848	Lelio R Paula	05/2017
2118	2^427999-459397	128841	Enzo Doria	05/2015
2119	2^427993+76847	128839	Enzo Doria	05/2016
2120	2^427824-1851507	128788	Enzo Doria	08/2015
2121	2^427807-21469	128783	Enzo Doria	07/2013
2122	11^123594-240	128710	Enzo Doria	09/2012
2123	2^427504-21503	128692	Enzo Doria	07/2013
2124	2^427420+91	128667	Lelio R Paula	05/2017
2125	(68*10^128645-257)/9	128646	Robert Price	07/2019
2126	2^427269-113635	128621	Enzo Doria	08/2014
2127	2^427130+1877569	128579	Enzo Doria	08/2016
2128	2^427016-115349	128545	Enzo Doria	07/2015
2129	(4*10^128510+137)/3	128511	Robert Price	03/2018
2130	2^426889-112879	128507	Enzo Doria	06/2014
2131	2^426804+1869931	128481	Enzo Doria	05/2016
2132	2^426750+77635	128465	Enzo Doria	05/2016
2133	2^426425-91	128367	Lelio R Paula	05/2017
2134	(15*2^426398-1)/11	128359	Lelio R Paula	05/2014
2135	2^426352+74971	128345	Enzo Doria	04/2016
2136	4*10^128343-21	128344	Robert Price	09/2018
2137	2^426300-1863689	128330	Enzo Doria	03/2016
2138	2^426293+1881017	128327	Enzo Doria	11/2016
2139	2^426043+35	128252	Robert Price	11/2015
2140	(4*10^128244-19)/3	128245	Robert Price	03/2018
2141	2^425808-459959	128181	Enzo Doria	06/2015
2142	2^425627-113605	128127	Enzo Doria	08/2014
2143	(22*10^128094+53)/3	128095	Robert Price	07/2019
2144	18565^30002-30002^18565	128070	Norbert Schneider	01/2015
2145	(2^425287-9)/2737	128021	Lelio R Paula	05/2015
2146	(3*2^425233-1)/25	128007	Lelio R Paula	05/2014
2147	2^425205+4911	128000	Marek Hubal	02/2017
2148	2^425118-113663	127974	Enzo Doria	08/2014
2149	2^425061+1869761	127957	Enzo Doria	05/2016
2150	746^44541+44541^746	127955	Norbert Schneider	07/2019
2151	2^424918-21141	127914	Enzo Doria	07/2013
2152	2^424864-29489	127897	Enzo Doria	08/2015
2153	(97*10^127858-1)/3	127860	Serge Batalov	12/2014
2154	2^424632-2786639	127827	Enzo Doria	03/2016
2155	2^424577-113755	127811	Enzo Doria	09/2014
2156	(7*2^424512-1)/3	127792	Lelio R Paula	05/2014
2157	(56*10^127752+691)/9	127753	Robert Price	05/2019
2158	11^122629-720	127705	Enzo Doria	11/2012
2159	2^423696-21429	127546	Enzo Doria	07/2013
2160	2^423664-1864559	127536	Enzo Doria	03/2016
2161	3^267267-4	127519	Henri Lifchitz	10/2014
2162	(19^99689+5^99689)/24	127477	Robert Price	09/2013
2163	(21*2^423372+1)/101	127447	Lelio R Paula	05/2014
2164	2^423328-21537	127435	Enzo Doria	07/2013
2165	(2^423165-7)/25	127384	Lelio R Paula	05/2015
2166	(F(5)^182099-F(4)^182099)/F(3)	127282	Wayne Halsdorf	08/2013
2167	(16*10^127259+197)/3	127260	Robert Price	04/2019
2168	(234483*27^88884-145)/26	127230	Curtis Bright	05/2015
2169	2^422515-114997	127190	Enzo Doria	06/2015
2170	5*10^127179-3	127180	Robert Price	07/2015
2171	(44*10^127169-233)/9	127170	Robert Price	01/2019
2172	5*10^127153+77	127154	Robert Price	12/2018
2173	736^44335+44335^736	127104	Norbert Schneider	07/2019
2174	-516776642557847117490*Bern(37960)/34256837217082767928421792453	127042	Thomas Ritschel	06/2017
2175	(78^67141-1)/77	127036	Paul Bourdelais	09/2017
2176	2^421860-113285	126993	Enzo Doria	07/2014
2177	(2^421827-7)/11	126982	Lelio R Paula	05/2015
2178	11^121910-840	126957	Enzo Doria	12/2012
2179	(71^68539+1)/72	126882	Paul Bourdelais	09/2017
2180	(5*10^126871-119)/3	126872	Robert Price	03/2018
2181	331^50339-10004	126846	Enzo Doria	07/2012
2182	2^421363-2790757	126843	Enzo Doria	03/2016
2183	(106*10^126839-1)/3	126841	Serge Batalov	12/2014
2184	(7*2^421243+1)/39	126807	Lelio R Paula	05/2014
2185	(14*10^126784-83)/3	126785	Robert Price	12/2018
2186	2^421161-286183	126783	Enzo Doria	06/2015
2187	2^420939-113935	126716	Enzo Doria	10/2014
2188	177^56363-2	126703	Lelio R Paula	10/2017
2189	2^420741-113659	126656	Enzo Doria	08/2014
2190	2^420694-21	126642	Lelio R Paula	05/2017
2191	(13*10^126638+437)/9	126639	Robert Price	04/2018
2192	4*10^126625+87	126626	Robert Price	08/2018
2193	(31*2^420556+1)/7	126601	Lelio R Paula	05/2014
2194	7*10^126600-99	126601	Robert Price	06/2019
2195	2^420424-59189	126561	Enzo Doria	10/2015
2196	2^420126+71893	126471	Enzo Doria	04/2016
2197	(43*10^126441+47)/9	126442	Robert Price	12/2018
2198	2^419866+1877059	126393	Enzo Doria	07/2016
2199	F(604711)	126377	Henri Lifchitz	02/2005
2200	2^419757+72707	126360	Enzo Doria	04/2016
2201	2^419720-21569	126349	Enzo Doria	07/2013
2202	2^419637+29	126324	Henri Lifchitz	02/2006
2203	2^419612+1876741	126316	Enzo Doria	07/2016
2204	2^419520+2793271	126289	Enzo Doria	03/2016
2205	(2^419447-5)/369	126264	Lelio R Paula	05/2014
2206	2^419328-1859939	126231	Enzo Doria	03/2016
2207	2^419282-1851507	126217	Enzo Doria	08/2015
2208	2^419251+1866143	126208	Enzo Doria	03/2016
2209	11^121185+2	126202	Robert Price	05/2014
2210	(23*2^419036-1)/1393	126141	Lelio R Paula	05/2014
2211	2^418851+23	126087	Robert Price	09/2015
2212	(2^418849-9)/2681	126083	Lelio R Paula	05/2014
2213	2^418829+167	126081	Lelio R Paula	01/2012
2214	(31*2^418782-1)/75891	126063	Lelio R Paula	05/2014
2215	(19*2^418754-1)/15	126058	Lelio R Paula	05/2014
2216	2^418319-109501	125927	Enzo Doria	04/2014
2217	2^418316-112373	125926	Enzo Doria	06/2014
2218	(8*10^125894-29)/3	125895	Robert Price	07/2018
2219	(26*10^125886-413)/9	125887	Robert Price	05/2018
2220	2^417968+1869811	125821	Enzo Doria	06/2016
2221	2^417902+63	125802	Lelio R Paula	09/2015
2222	(10^125792-91)/9	125792	Serge Batalov	12/2014
2223	(35*10^125754-593)/9	125755	Robert Price	07/2018
2224	(32*10^125751-77)/9	125752	Robert Price	06/2018
2225	2^417704+77011	125742	Enzo Doria	05/2016
2226	(10^125706+149)/3	125706	Serge Batalov	12/2014
2227	2^417419-115309	125656	Enzo Doria	07/2015
2228	2^417300+77281	125620	Enzo Doria	05/2016
2229	2^417095-1657	125559	Yves Minet	07/2014
2230	2^416773-25	125462	Lelio R Paula	09/2015
2231	(289511#+292834)/(2^3*146417)	125444	Makoto Morimoto	10/2017
2232	(11*2^416691+1)/43	125436	Lelio R Paula	05/2014
2233	(289511#+1896)/(23^3797801939911849)	125434	Makoto Morimoto	06/2019
2234	2^416641-2*416641+1	125422	Robert Price	05/2018
2235	(21*2^416566-1)/17	125399	Lelio R Paula	05/2014
2236	2^416530+1870429	125389	Enzo Doria	05/2016
2237	(56*10^125385+691)/9	125386	Robert Price	05/2019
2238	2^416490+1875109	125376	Enzo Doria	09/2016
2239	2^416416-114929	125354	Enzo Doria	05/2015
2240	(172*10^125292-1)/9	125294	Serge Batalov	12/2014
2241	2^416134+1865899	125269	Enzo Doria	03/2016
2242	153^57337-152	125264	Norbert Schneider	12/2018
2243	(9*2^415992+1)/13560845	125220	Lelio R Paula	05/2014
2244	(23^91943-1)/22	125201	Robert Price	01/2012
2245	43125^27010-106	125185	Enzo Doria	08/2012
2246	(38*10^125166+349)/9	125167	Robert Price	10/2018
2247	2^415765-112603	125158	Enzo Doria	06/2014
2248	8*10^125088-13	125089	Robert Price	08/2019
2249	2^415290-113591	125015	Enzo Doria	08/2014
2250	2^415276-460919	125011	Enzo Doria	06/2015

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Probable Primes Top 10000

(253466 PRPs in the top)