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	(19*2^473242+1)/11	142461	Lelio R Paula	09/2015
2002	(61*10^142446-1)/3	142448	Robert Price	01/2020
2003	(14*10^142440+61)/3	142441	Robert Price	12/2018
2004	(10^142425+359)/9	142425	Serge Batalov	12/2014
2005	2^473101+773027	142418	Enzo Doria	05/2016
2006	(13*2^472838-1)/3	142340	Lelio R Paula	09/2015
2007	(17*2^472789-1)/187347	142320	Lelio R Paula	09/2015
2008	2^472634-109511	142278	Enzo Doria	04/2014
2009	(48^84589+1)/49	142213	Robert Price	01/2014
2010	7*10^142189+87	142190	Robert Price	07/2019
2011	2^472258+7	142164	Lelio R Paula	08/2015
2012	(23*10^142105+91)/3	142106	Robert Price	08/2019
2013	tau(317^10330)	142098	Nik Lygeros / Olivier Rozier / LR team	10/2013
2014	(11*2^471913-1)/21	142060	Lelio R Paula	09/2015
2015	(16*10^142058+197)/3	142059	Robert Price	04/2019
2016	2^471792+1880881	142024	Enzo Doria	11/2016
2017	(31*2^471580-1)/135	141960	Lelio R Paula	08/2015
2018	(4*10^141926-79)/3	141927	Robert Price	02/2018
2019	(904*19^110984-1)/3	141924	Curtis Bright	05/2015
2020	(14*10^141853+37)/3	141854	Robert Price	12/2018
2021	(41*10^141836-59)/9	141837	Robert Price	10/2018
2022	4*5^202913-9	141831	Lelio R Paula	04/2015
2023	2*7^167812-3	141818	Lelio R Paula	12/2014
2024	2^471043+35	141799	Robert Price	11/2015
2025	(11*2^470956-1)/7945	141770	Lelio R Paula	08/2015
2026	(11*10^141718-131)/3	141719	Robert Price	09/2018
2027	2^470692+76771	141693	Enzo Doria	05/2016
2028	(21*2^470391+1)/533	141601	Lelio R Paula	09/2015
2029	2^470305-459373	141576	Enzo Doria	05/2015
2030	2^470183+72623	141540	Enzo Doria	04/2016
2031	2^470173-16465	141537	Enzo Doria	04/2013
2032	2^469974-1841	141477	Enzo Doria	05/2014
2033	(23*2^469939+1)/25	141466	Lelio R Paula	08/2015
2034	2*10^141448+63	141449	Robert Price	05/2018
2035	2^469824+43	141432	Lelio R Paula	09/2017
2036	2*10^141407-27	141408	Robert Price	05/2018
2037	2^469630-59711	141373	Enzo Doria	10/2015
2038	(25*10^141366-331)/9	141367	Robert Price	08/2018
2039	(2^469564-3)/611	141351	Lelio R Paula	08/2015
2040	197^61601+2	141342	Lelio R Paula	08/2017
2041	2^469372-112949	141296	Enzo Doria	07/2014
2043	143^(2^16)+106^(2^16)	141253	Valeryi Kuryshev	02/2011
2042	143^65536+106^65536	141253	Serge Batalov	03/2018
2044	2^469198+782569	141243	Enzo Doria	10/2016
2045	2^469076-2786939	141206	Enzo Doria	11/2015
2046	2^468804+1874941	141125	Enzo Doria	06/2016
2047	2^468787+81353	141119	Enzo Doria	08/2016
2048	2^468595-350407	141062	Enzo Doria	06/2015
2049	2^468564+87855	141052	Lelio R Paula	01/2016
2050	2^468551-21987	141048	Enzo Doria	07/2013
2051	2^468523-7	141040	Lelio R Paula	08/2015
2052	(25*10^141019-13)/3	141020	Robert Price	09/2019
2053	2^468405+87855	141004	Lelio R Paula	01/2016
2054	2^467978-113051	140876	Enzo Doria	07/2014
2055	2^467780-344429	140816	Enzo Doria	07/2015
2056	9*10^140802-89	140803	Robert Price	04/2020
2057	2^467605-1855603	140764	Enzo Doria	09/2015
2058	5*10^140744-7	140745	Robert Price	09/2015
2059	(5^201359-1)/4	140744	Paul Bourdelais	12/2008
2060	2^467401-1850023	140702	Enzo Doria	08/2015
2061	(266*10^140681-17)/3	140683	Robert Price	07/2020
2062	(2^467270+78557)/23247	140658	Lelio R Paula	07/2015
2063	(29*2^467205+1)/2780517107	140635	Lelio R Paula	08/2015
2064	2^467166-1854941	140631	Enzo Doria	09/2015
2065	(85*10^140609+473)/9	140610	Robert Price	01/2020
2066	2^466866-1840571	140541	Enzo Doria	06/2015
2067	2^466829-459523	140530	Enzo Doria	05/2015
2068	2^466692-113213	140489	Enzo Doria	07/2014
2069	(44*10^140410-503)/9	140411	Robert Price	12/2018
2070	153^64265-2	140400	Lelio R Paula	11/2017
2071	(112*10^140357-1)/3	140359	Serge Batalov	12/2014
2072	(29*10^140337-17)/3	140338	Robert Price	09/2019
2073	2^466181-112735	140335	Enzo Doria	07/2014
2074	(5*10^140281-119)/3	140282	Robert Price	03/2018
2075	(27*2^465872+1)/691	140241	Lelio R Paula	08/2015
2076	2^465803-114817	140221	Enzo Doria	05/2015
2077	floor(Pi*10^140344)%10^140165	140165	Serge Batalov	08/2012
2078	2^465503-112735	140131	Enzo Doria	07/2014
2079	(16*10^140091+167)/3	140092	Robert Price	06/2019
2080	6^179964+179964^6-1	140040	Robert Price	04/2014
2081	(89*10^140008-179)/9	140009	Robert Price	12/2019
2082	(29*2^465077-1)/9	140003	Lelio R Paula	08/2015
2083	2^465072-344789	140001	Enzo Doria	07/2015
2084	5*10^139945+81	139946	Robert Price	03/2019
2085	2^464864-17	139939	Lelio R Paula	09/2017
2086	8*10^139920+51	139921	Robert Price	08/2019
2087	(85*10^139913-1)/3	139915	Robert Price	02/2020
2088	(17^113621+1)/18	139804	Paul Bourdelais	09/2011
2089	2*10^139800-21	139801	Robert Price	09/2020
2090	(13*10^139782+191)/3	139783	Robert Price	11/2018
2091	(19*2^464312-1)/3	139773	Lelio R Paula	08/2015
2092	(74*10^139723+133)/9	139724	Robert Price	06/2019
2093	3*10^139722+13	139723	Robert Price	07/2018
2094	77*10^139692+3	139694	Robert Price	06/2020
2095	(31*2^463970+1)/5	139670	Lelio R Paula	08/2015
2096	(18203^(2^15)+(18201)^(2^15))/2	139597	Robert Price	05/2018
2097	2^463633-2788423	139568	Enzo Doria	11/2015
2098	2^463271-109501	139459	Enzo Doria	04/2014
2099	(5*10^139457+79)/3	139458	Robert Price	03/2018
2100	2^463237-99	139449	Lelio R Paula	09/2017
2101	(49*10^139442+383)/9	139443	Robert Price	04/2019
2102	(7*10^139417-547)/9	139417	Robert Price	01/2018
2103	(10^139398+191)/3	139398	Robert Price	02/2018
2104	2^463019+79463	139383	Enzo Doria	06/2016
2105	3^292129-112756	139381	Enzo Doria	07/2014
2106	(15*2^462951+1)/527	139361	Lelio R Paula	08/2015
2107	2^462855-1865707	139334	Enzo Doria	02/2016
2108	(86*10^139315+121)/9	139316	Robert Price	08/2019
2109	2^462786-292043	139313	Enzo Doria	08/2015
2110	(26*10^139289+1)/9	139290	Serge Batalov	05/2010
2111	(17*10^139239+67)/3	139240	Robert Price	01/2019
2112	2^462238-935	139148	Yves Minet	02/2014
2113	2^461228+1870441	138844	Enzo Doria	05/2016
2114	2^461204-113675	138837	Enzo Doria	08/2014
2115	(2^461139-7)/47	138815	Lelio R Paula	08/2015
2116	(17*10^138812-521)/9	138813	Robert Price	04/2018
2117	3*10^138811-11	138812	Robert Price	07/2018
2118	(28*10^138768+173)/3	138769	Robert Price	12/2019
2119	(17*2^460963+1)/124051613	138757	Lelio R Paula	08/2015
2120	(379*10^138737-1)/9	138739	Robert Price	02/2020
2121	(43*10^138648+101)/9	138649	Robert Price	11/2018
2122	2^460567-113541	138645	Enzo Doria	08/2014
2123	7*10^138604+3	138605	Robert Price	08/2015
2124	2^460330+69	138574	Lelio R Paula	09/2017
2125	(17*10^138569-77)/3	138570	Robert Price	08/2019
2126	2^460078-69581	138498	Enzo Doria	12/2015
2127	2^459768+1531	138404	Lelio R Paula	06/2012
2128	(266*10^138328-17)/3	138330	Robert Price	07/2020
2129	2^459343-113611	138277	Enzo Doria	08/2014
2130	(28*10^138240+113)/3	138241	Robert Price	03/2020
2131	2^459199+1874393	138233	Enzo Doria	06/2016
2132	2^459063-345307	138192	Enzo Doria	06/2015
2133	2*10^138162-43	138163	Robert Price	04/2018
2134	2^458927-112747	138151	Enzo Doria	06/2014
2135	2^458927-69217	138151	Enzo Doria	11/2015
2136	555555*2^458524+1513	138036	Darren Bedwell	08/2009
2137	2^458465+2^32+1	138012	T. D. Noe	06/2007
2138	2^458321-113053	137969	Enzo Doria	07/2014
2139	2^458298+79459	137962	Enzo Doria	06/2016
2140	2^458248-21815	137947	Enzo Doria	07/2013
2141	2^458194+1876549	137931	Enzo Doria	07/2016
2142	(318259#+325270)/(2^2511*2957)	137907	Makoto Morimoto	10/2017
2143	(318259#+2625)/(3^257^5*22965193)	137899	Makoto Morimoto	06/2019
2144	2^457937+57	137853	Lelio R Paula	09/2017
2145	(8*10^137845+13)/3	137846	Robert Price	06/2018
2146	2^457822+105	137819	Donovan Johnson	06/2006
2147	2^457754-113711	137798	Enzo Doria	09/2014
2148	11^132315-360	137792	Enzo Doria	09/2012
2149	2^457347-37	137676	Lelio R Paula	09/2017
2150	2^457322-2786393	137668	Enzo Doria	10/2015
2151	gcd(Phi(699340,10),(10^34967+1)^3(10^34967+1+10^17484)-(10^69934+10^34967)(10^17484-1)+10^104901)	137664	Serge Batalov	04/2015
2152	2^457240-59939	137643	Enzo Doria	10/2015
2153	(856*10^137633-1)/9	137635	Robert Price	03/2020
2154	2^457120-21575	137607	Enzo Doria	07/2013
2155	(11*2^456978+1)/15	137564	Lelio R Paula	07/2015
2156	(7*25^98399+10613)/12	137556	Curtis Bright	05/2015
2157	2^456796-113513	137510	Enzo Doria	08/2014
2158	(7*2^456655+1)/39	137467	Lelio R Paula	07/2015
2159	2^456503-114361	137422	Enzo Doria	01/2015
2160	(11*2^456387+1)/19	137386	Lelio R Paula	07/2015
2161	(71*10^137250+1)/9	137251	Serge Batalov	05/2010
2162	2^455922+76249	137247	Enzo Doria	05/2016
2163	14^119741-119741^14	137239	Serge Batalov	04/2016
2164	(19*2^455760+1)/3455	137196	Lelio R Paula	07/2015
2166	124^(2^16)+57^(2^16)	137195	Valeryi Kuryshev	02/2011
2165	124^65536+57^65536	137195	Serge Batalov	03/2018
2167	2^455689+72677	137177	Enzo Doria	04/2016
2168	(17948!)^2+Prime(17948)	137118	Robert Price	08/2014
2169	(37^87421-1)/36	137093	Robert Price	03/2012
2170	2^455323-57	137066	Lelio R Paula	09/2017
2171	(73*17^111333-9)/16	136991	Curtis Bright	05/2015
2172	2^455025-112723	136977	Enzo Doria	06/2014
2173	66*10^136894+7	136896	Robert Price	07/2020
2174	2^454675-1777	136871	Yves Minet	10/2011
2175	3*10^136829+29	136830	Robert Price	05/2018
2176	4*10^136813-57	136814	Robert Price	10/2018
2177	(6092*28^94536-143)/9	136812	Curtis Bright	05/2015
2178	2^454348-53	136773	Lelio R Paula	09/2017
2179	31^91680-2	136729	Lelio R Paula	05/2017
2180	2^454199-113697	136728	Enzo Doria	09/2014
2181	7*10^136716+69	136717	Robert Price	07/2019
2182	6*10^136692+53	136693	Robert Price	05/2020
2183	(13*10^136687+47)/3	136688	Robert Price	10/2018
2184	2^453935-2791357	136649	Enzo Doria	01/2016
2185	2^453906-69131	136640	Enzo Doria	11/2015
2186	2^453791+1873913	136605	Enzo Doria	06/2016
2187	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
2188	580^49413+49413^580	136550	Norbert Schneider	02/2019
2189	2^453503-2788297	136519	Enzo Doria	11/2015
2190	2^453267-113827	136447	Enzo Doria	09/2014
2191	2^453102+1877629	136398	Enzo Doria	08/2016
2192	(62*10^136384-791)/9	136385	Robert Price	06/2019
2193	(25*10^136303+161)/3	136304	Robert Price	09/2019
2194	(182*10^136291+1)/3	136293	Robert Price	02/2020
2195	23*10^136225-7	136227	Robert Price	02/2020
2196	L(651821)	136223	Henri Lifchitz	09/2008
2197	2^452460+77701	136205	Enzo Doria	05/2016
2198	2^452440-114755	136199	Enzo Doria	04/2015
2199	(47*10^136141+493)/9	136142	Robert Price	03/2019
2200	2*10^136057-43	136058	Robert Price	04/2018
2201	(2^451956-5)/181	136051	Lelio R Paula	07/2015
2202	2^451947-22165	136050	Enzo Doria	07/2013
2203	2^451787-21805	136002	Enzo Doria	07/2013
2204	2^451734-112817	135986	Enzo Doria	06/2014
2205	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
2206	2^451705-21879	135977	Enzo Doria	07/2013
2207	2^451560-112349	135934	Enzo Doria	06/2014
2208	2^451530+45	135925	Lelio R Paula	08/2017
2209	(25*10^135906-73)/3	135907	Robert Price	09/2019
2210	2^451450-21743	135900	Enzo Doria	07/2013
2211	2^450805+65	135706	Lelio R Paula	08/2017
2212	2*10^135663+69	135664	Robert Price	06/2020
2213	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
2214	(313007#+121876)/(230469424867)	135559	Makoto Morimoto	08/2020
2215	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
2216	2^449944-113247	135447	Enzo Doria	07/2014
2217	2^449770-113247	135395	Enzo Doria	07/2014
2218	2^449637-21471	135355	Enzo Doria	07/2013
2219	2^449571-75	135335	Lelio R Paula	08/2017
2220	(14*10^135301-53)/3	135302	Robert Price	12/2018
2221	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
2222	(13*10^135279+437)/9	135280	Robert Price	04/2018
2223	2^449330-35	135262	Lelio R Paula	08/2017
2224	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
2225	(13*10^135184-43)/3	135185	Robert Price	11/2018
2226	2^449049-115309	135178	Enzo Doria	07/2015
2227	(10^135174+191)/3	135174	Robert Price	02/2018
2228	2^449030-15	135172	Lelio R Paula	08/2017
2229	(27*2^448936-1)/11	135144	Lelio R Paula	07/2015
2230	2^448762-351401	135091	Enzo Doria	07/2015
2231	2*10^135083-43	135084	Robert Price	04/2018
2232	k(198476)	135054	Robert Price	07/2020
2233	5*10^135019+77	135020	Robert Price	12/2018
2234	(10^135011+719)/9	135011	Serge Batalov	12/2014
2235	2^448386-2786261	134978	Enzo Doria	03/2016
2236	(73*10^134939+143)/9	134940	Robert Price	07/2019
2237	2^448113-113949	134896	Enzo Doria	11/2014
2238	2^447888-2786639	134828	Enzo Doria	03/2016
2239	2^447870-396765	134823	Enzo Doria	07/2013
2240	2^447766-21791	134791	Enzo Doria	07/2013
2241	(19*10^134786-49)/3	134787	Robert Price	05/2019
2242	Phi(202173,10)/10064306514895399941409	134758	Makoto Kamada	05/2019
2243	(23*2^447647+1)/155	134755	Lelio R Paula	07/2015
2244	2^447552-1019	134727	Yves Minet	02/2014
2245	(2*10^134720-41)/3	134720	Robert Price	02/2018
2246	2^447437-113569	134692	Enzo Doria	08/2014
2247	2^447426-65	134689	Lelio R Paula	08/2017
2248	2^447357-2797573	134668	Enzo Doria	04/2016
2249	2^447278+93	134645	Lelio R Paula	08/2017
2250	2^447094-113193	134589	Enzo Doria	07/2014

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Probable Primes Top 10000

(271000 PRPs in the top)