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	(11*2^456978+1)/15	137564	Lelio R Paula	07/2015
2002	(7*25^98399+10613)/12	137556	Curtis Bright	05/2015
2003	2^456796-113513	137510	Enzo Doria	08/2014
2004	(7*2^456655+1)/39	137467	Lelio R Paula	07/2015
2005	2^456503-114361	137422	Enzo Doria	01/2015
2006	(11*2^456387+1)/19	137386	Lelio R Paula	07/2015
2007	(71*10^137250+1)/9	137251	Serge Batalov	05/2010
2008	2^455922+76249	137247	Enzo Doria	05/2016
2009	14^119741-119741^14	137239	Serge Batalov	04/2016
2010	(19*2^455760+1)/3455	137196	Lelio R Paula	07/2015
2012	124^(2^16)+57^(2^16)	137195	Valeryi Kuryshev	02/2011
2011	124^65536+57^65536	137195	Serge Batalov	03/2018
2013	2^455689+72677	137177	Enzo Doria	04/2016
2014	(17948!)^2+Prime(17948)	137118	Robert Price	08/2014
2015	(37^87421-1)/36	137093	Robert Price	03/2012
2016	2^455323-57	137066	Lelio R Paula	09/2017
2017	(73*17^111333-9)/16	136991	Curtis Bright	05/2015
2018	2^455025-112723	136977	Enzo Doria	06/2014
2019	2^454675-1777	136871	Yves Minet	10/2011
2020	3*10^136829+29	136830	Robert Price	05/2018
2021	4*10^136813-57	136814	Robert Price	10/2018
2022	(6092*28^94536-143)/9	136812	Curtis Bright	05/2015
2023	2^454348-53	136773	Lelio R Paula	09/2017
2024	31^91680-2	136729	Lelio R Paula	05/2017
2025	2^454199-113697	136728	Enzo Doria	09/2014
2026	7*10^136716+69	136717	Robert Price	07/2019
2027	(13*10^136687+47)/3	136688	Robert Price	10/2018
2028	2^453935-2791357	136649	Enzo Doria	01/2016
2029	2^453906-69131	136640	Enzo Doria	11/2015
2030	2^453791+1873913	136605	Enzo Doria	06/2016
2031	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
2032	580^49413+49413^580	136550	Norbert Schneider	02/2019
2033	2^453503-2788297	136519	Enzo Doria	11/2015
2034	2^453267-113827	136447	Enzo Doria	09/2014
2035	2^453102+1877629	136398	Enzo Doria	08/2016
2036	(62*10^136384-791)/9	136385	Robert Price	06/2019
2037	(25*10^136303+161)/3	136304	Robert Price	09/2019
2038	(182*10^136291+1)/3	136293	Robert Price	02/2020
2039	23*10^136225-7	136227	Robert Price	02/2020
2040	L(651821)	136223	Henri Lifchitz	09/2008
2041	2^452460+77701	136205	Enzo Doria	05/2016
2042	2^452440-114755	136199	Enzo Doria	04/2015
2043	(47*10^136141+493)/9	136142	Robert Price	03/2019
2044	2*10^136057-43	136058	Robert Price	04/2018
2045	(2^451956-5)/181	136051	Lelio R Paula	07/2015
2046	2^451947-22165	136050	Enzo Doria	07/2013
2047	2^451787-21805	136002	Enzo Doria	07/2013
2048	2^451734-112817	135986	Enzo Doria	06/2014
2049	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
2050	2^451705-21879	135977	Enzo Doria	07/2013
2051	2^451560-112349	135934	Enzo Doria	06/2014
2052	2^451530+45	135925	Lelio R Paula	08/2017
2053	(25*10^135906-73)/3	135907	Robert Price	09/2019
2054	2^451450-21743	135900	Enzo Doria	07/2013
2055	2^450805+65	135706	Lelio R Paula	08/2017
2056	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
2057	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
2058	2^449944-113247	135447	Enzo Doria	07/2014
2059	2^449770-113247	135395	Enzo Doria	07/2014
2060	2^449637-21471	135355	Enzo Doria	07/2013
2061	2^449571-75	135335	Lelio R Paula	08/2017
2062	(14*10^135301-53)/3	135302	Robert Price	12/2018
2063	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
2064	(13*10^135279+437)/9	135280	Robert Price	04/2018
2065	2^449330-35	135262	Lelio R Paula	08/2017
2066	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
2067	(13*10^135184-43)/3	135185	Robert Price	11/2018
2068	2^449049-115309	135178	Enzo Doria	07/2015
2069	(10^135174+191)/3	135174	Robert Price	02/2018
2070	2^449030-15	135172	Lelio R Paula	08/2017
2071	(27*2^448936-1)/11	135144	Lelio R Paula	07/2015
2072	2^448762-351401	135091	Enzo Doria	07/2015
2073	2*10^135083-43	135084	Robert Price	04/2018
2074	5*10^135019+77	135020	Robert Price	12/2018
2075	(10^135011+719)/9	135011	Serge Batalov	12/2014
2076	2^448386-2786261	134978	Enzo Doria	03/2016
2077	(73*10^134939+143)/9	134940	Robert Price	07/2019
2078	2^448113-113949	134896	Enzo Doria	11/2014
2079	2^447888-2786639	134828	Enzo Doria	03/2016
2080	2^447870-396765	134823	Enzo Doria	07/2013
2081	2^447766-21791	134791	Enzo Doria	07/2013
2082	(19*10^134786-49)/3	134787	Robert Price	05/2019
2083	Phi(202173,10)/10064306514895399941409	134758	Makoto Kamada	05/2019
2084	(23*2^447647+1)/155	134755	Lelio R Paula	07/2015
2085	2^447552-1019	134727	Yves Minet	02/2014
2086	(2*10^134720-41)/3	134720	Robert Price	02/2018
2087	2^447437-113569	134692	Enzo Doria	08/2014
2088	2^447426-65	134689	Lelio R Paula	08/2017
2089	2^447357-2797573	134668	Enzo Doria	04/2016
2090	2^447278+93	134645	Lelio R Paula	08/2017
2091	2^447094-113193	134589	Enzo Doria	07/2014
2092	3^282041-9934	134568	Enzo Doria	05/2014
2093	2^447019-109039	134567	Enzo Doria	04/2014
2094	2^446990-22041	134558	Enzo Doria	07/2013
2095	123^64370+122	134528	Karsten Bonath	04/2018
2096	2^446782-39701	134495	Enzo Doria	09/2015
2097	2^446494-16485	134409	Enzo Doria	04/2013
2098	29504^30069-30069^29504	134405	Norbert Schneider	12/2014
2099	2^446441+65	134393	Lelio R Paula	08/2017
2100	(10^134385+719)/9	134385	Serge Batalov	12/2014
2101	(2*10^134364+529)/9	134364	Robert Price	01/2018
2102	(13*2^446187-1)/661	134314	Lelio R Paula	07/2015
2103	5^192103+3^192103+2^192103+1	134275	Matthias Baur	12/2019
2104	(2^446022-7)/339	134264	Lelio R Paula	07/2015
2105	63^74568+2	134174	Lelio R Paula	06/2017
2106	2^445671-22071	134161	Enzo Doria	07/2013
2107	532^49205+49205^532	134129	Norbert Schneider	02/2019
2108	(28*10^134122-1)/9	134123	Serge Batalov	10/2014
2109	2^445515-113859	134114	Enzo Doria	10/2014
2110	(22*10^134111-37)/3	134112	Robert Price	04/2019
2111	2^445328-216917	134058	Enzo Doria	05/2014
2112	2^445202+1874899	134020	Enzo Doria	06/2016
2113	(13*2^445102+1)/17	133989	Lelio R Paula	07/2015
2114	(35*10^133979-593)/9	133980	Robert Price	07/2018
2115	2*10^133955+51	133956	Robert Price	05/2018
2116	2^444964-113639	133948	Enzo Doria	08/2014
2117	28118^30097-30097^28118	133902	Norbert Schneider	01/2015
2118	2^444784-113859	133894	Enzo Doria	10/2014
2119	(89*10^133580+1)/9	133581	Serge Batalov	05/2010
2120	62^74521-61^74521	133571	Robert Price	05/2013
2121	(182*10^133543+1)/3	133545	Robert Price	02/2020
2122	2^443198-1867301	133416	Enzo Doria	03/2016
2123	(19*10^133390+101)/3	133391	Robert Price	09/2019
2124	(71^72043-1)/70	133369	Paul Bourdelais	09/2017
2125	2^442799+1874633	133296	Enzo Doria	06/2016
2126	L(637751)	133283	Henri Lifchitz	09/2008
2127	109^65410-2	133269	Lelio R Paula	10/2017
2128	2^442688-113489	133263	Enzo Doria	08/2014
2129	(7*2^442640-1)/783	133246	Lelio R Paula	07/2015
2130	(9*2^442463+1)/17441	133192	Lelio R Paula	07/2015
2131	2^442437-1849993	133187	Enzo Doria	08/2015
2132	2^442430-2791721	133185	Enzo Doria	03/2016
2133	(13*2^442428-1)/309	133183	Lelio R Paula	07/2015
2134	(25*2^442379-1)/71	133169	Lelio R Paula	07/2015
2135	(2^441799+78557)/5	132995	Lelio R Paula	07/2015
2136	2^441781-2787883	132990	Enzo Doria	03/2016
2137	(3*2^441685+1)/749	132959	Lelio R Paula	07/2015
2138	2^441618+37	132941	Lelio R Paula	08/2017
2139	2^441521-113575	132912	Enzo Doria	08/2014
2140	7*10^132884-99	132885	Robert Price	06/2019
2141	2^441396-65	132874	Lelio R Paula	08/2017
2142	2^441330+1871959	132854	Enzo Doria	05/2016
2143	2^441063+383	132774	Lelio R Paula	06/2012
2144	(22*10^132746+53)/3	132747	Robert Price	07/2019
2145	2^440846+1870909	132708	Enzo Doria	05/2016
2146	2^440656-113489	132651	Enzo Doria	08/2014
2147	numbpart(14180123587)	132646	Serge Batalov	04/2017
2148	(19*10^132550+191)/3	132551	Robert Price	05/2019
2149	(2^440399-1)/(1621082028116197820931518475633880799)	132538	Dario Alpern	01/2015
2150	(38^83891+1)/39	132529	Robert Price	09/2013
2151	2*10^132493-43	132494	Robert Price	04/2018
2152	(418*10^132441+23)/9	132443	Robert Price	02/2020
2153	2^439931-21	132433	Lelio R Paula	08/2017
2154	47^79201-46^79201	132432	Robert Price	10/2012
2155	2^439897-113653	132423	Enzo Doria	08/2014
2156	(5*2^439822+1)/9	132400	Lelio R Paula	06/2015
2157	(112*10^132337-1)/3	132339	Serge Batalov	12/2014
2158	2^439576-113247	132326	Enzo Doria	07/2014
2159	2^439497-29143	132302	Enzo Doria	07/2015
2160	2^439409-114193	132276	Enzo Doria	12/2014
2161	(44*10^132233-233)/9	132234	Robert Price	01/2019
2162	9*10^132148-7	132149	Robert Price	09/2015
2163	(47*10^132125-119)/9	132126	Robert Price	05/2019
2164	2^438845+1870217	132106	Enzo Doria	05/2016
2165	2^438789+87855	132089	Lelio R Paula	01/2016
2166	2^438774-2786411	132085	Enzo Doria	03/2016
2167	2^438755-1848205	132079	Enzo Doria	07/2015
2168	2^438739-112087	132074	Enzo Doria	06/2014
2169	13907#+(318259#)/(13907#)	131923	Makoto Morimoto	10/2017
2170	L(631181)	131910	Henri Lifchitz	09/2008
2171	(47*10^131886-119)/9	131887	Robert Price	05/2019
2172	(3*2^438121+1)/4308193883	131879	Lelio R Paula	06/2015
2173	2^438079-1863877	131875	Enzo Doria	03/2016
2174	(2^438067+5)/329	131869	Lelio R Paula	06/2015
2175	2^437908-113855	131824	Enzo Doria	09/2014
2176	2^437884-286349	131817	Enzo Doria	07/2015
2177	(11*10^131784-17)/3	131785	Robert Price	06/2018
2178	3^276062-112292	131716	Enzo Doria	07/2014
2179	2^437343+75953	131654	Enzo Doria	04/2016
2180	35^85243-34^85243	131621	Robert Price	05/2012
2181	(203*10^131457+1)/3	131459	Robert Price	03/2020
2182	(68^71713+1)/69	131413	Paul Bourdelais	09/2017
2183	2^436451+1884713	131385	Enzo Doria	03/2017
2184	2^436365+35	131359	Robert Price	11/2015
2185	2^436300+1866871	131340	Enzo Doria	03/2016
2186	(7*10^131339+179)/3	131340	Robert Price	09/2018
2187	(37*10^131270+341)/9	131271	Robert Price	08/2018
2188	(5*10^131223-29)/3	131224	Robert Price	03/2018
2189	(23*2^435891-1)/699	131215	Lelio R Paula	07/2015
2190	(11*2^435879+1)/3337	131211	Lelio R Paula	06/2015
2192	(2^435808+1)/641/6700417	131182	Lelio R Paula	02/2012
2191	(2^435808+1)/4294967297	131182	Serge Batalov	12/2016
2195	2^435773+1875557	131181	Enzo Doria	06/2016
2194	(16*10^131180+167)/3	131181	Robert Price	06/2019
2193	(26*10^131180-77)/3	131181	Robert Price	11/2019
2196	(25*10^131144-7)/9	131145	Robert Price	05/2018
2197	2^435612-2789939	131133	Enzo Doria	12/2015
2198	66^72047-65^72047	131093	Robert Price	09/2013
2199	(5*10^131090+37)/3	131091	Robert Price	03/2018
2200	2^435468+75631	131089	Enzo Doria	04/2016
2201	37^83588-2	131083	Lelio R Paula	08/2015
2202	(4^217720+11)/3	131081	Robert Price	02/2017
2203	2^435202-113193	131009	Enzo Doria	07/2014
2204	9*10^130998-19	130999	Robert Price	07/2019
2205	floor((sqrt(5)-1)/2*10^130911)	130911	Serge Batalov	06/2017
2206	2^434835-111937	130899	Enzo Doria	05/2014
2207	2^434685+72257	130854	Enzo Doria	04/2016
2208	(7*10^130825+113)/3	130826	Robert Price	02/2018
2209	2^434539-29317	130810	Enzo Doria	07/2015
2210	2^434469-114259	130789	Enzo Doria	01/2015
2211	2^434246+33	130722	Robert Price	11/2015
2212	2^433911-91	130621	Lelio R Paula	06/2017
2213	2^433744-114419	130570	Enzo Doria	02/2015
2215	2^433708+1869451	130560	Enzo Doria	05/2016
2214	2^433710+93	130560	Lelio R Paula	06/2017
2216	(29*2^433547-1)/27	130511	Lelio R Paula	06/2015
2217	4*10^130480+9	130481	Robert Price	05/2015
2218	(23*2^433449-1)/75	130481	Lelio R Paula	06/2015
2219	(23*2^433334-1)/3731	130445	Lelio R Paula	06/2015
2220	2^433023-113497	130353	Enzo Doria	08/2014
2221	2^433002+1179379	130347	Enzo Doria	06/2016
2222	2^432974+19	130339	Robert Price	08/2015
2223	(2^432457-1)/1672739247834685086279697	130159	Tony Prest / Never Odd Or Even	09/2013
2224	2^432217+41	130111	Lelio R Paula	06/2017
2225	(2^216089*(2^216091-1)-339)/25	130098	Makoto Morimoto	03/2017
2226	((2^216091+1066)^2+(2^216091+1066)+41)/47/2069	130095	Makoto Morimoto	05/2016
2227	97^65480-2	130094	Lelio R Paula	05/2017
2228	4*10^130088-89	130089	Robert Price	11/2018
2229	2^432117-113215	130081	Enzo Doria	07/2014
2230	2^431804+72511	129986	Enzo Doria	04/2016
2231	(3^272141-3^136071+1)/7	129844	Serge Batalov	03/2014
2232	(47*10^129789-119)/9	129790	Robert Price	05/2019
2233	(9*2^431141+1)/17	129787	Lelio R Paula	06/2015
2234	(29*2^430881-1)/21	129709	Lelio R Paula	06/2015
2235	2^430807+1869563	129686	Enzo Doria	05/2016
2236	2^430721-21429	129660	Enzo Doria	07/2013
2237	2^430415-276271	129568	Enzo Doria	07/2015
2238	2^430142-2791721	129486	Enzo Doria	03/2016
2239	(7*10^129472-13)/3	129473	Robert Price	07/2018
2240	2^429568-21017	129313	Enzo Doria	07/2013
2241	(11*10^129239-179)/3	129240	Robert Price	09/2018
2242	2^429194-112685	129201	Enzo Doria	06/2014
2243	2^429145-2780449	129186	Enzo Doria	04/2016
2244	2^428892-113453	129110	Enzo Doria	07/2014
2245	(11*2^428881-7)/15	129106	Renaud Lifchitz	03/2011
2246	2^428727-113959	129060	Enzo Doria	10/2014
2247	(7*2^428725-1)/13	129059	Lelio R Paula	05/2014
2248	(10^129051-31)/3	129051	Serge Batalov	12/2014
2249	(134*10^129038+7)/3	129040	Robert Price	02/2020
2250	2^428564+71161	129011	Enzo Doria	04/2016

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