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	2^576016-113919	173399	Enzo Doria	11/2014
2002	2^575911-1849387	173367	Enzo Doria	08/2015
2003	515^63898+63898^515	173280	Norbert Schneider	12/2022
2004	2^575614+9	173278	Stefano Morozzi	04/2021
2005	(16*10^173251+107)/3	173252	Robert Price	03/2019
2006	2^575196-114053	173152	Enzo Doria	11/2014
2007	7*10^173135-53	173136	Robert Price	06/2020
2008	(301*10^173047+23)/9	173049	Robert Price	06/2021
2009	2^574591-115387	172970	Enzo Doria	07/2015
2010	(202*10^172940-13)/9	172942	Robert Price	01/2020
2011	45^104608+104608^45	172940	Norbert Schneider	06/2021
2012	2^574328+81121	172890	Enzo Doria	07/2016
2013	(115*10^172862-1)/3	172864	Serge Batalov	12/2014
2014	3*10^172812+13	172813	Robert Price	07/2018
2015	4*5^247217-9	172798	Lelio R Paula	10/2015
2016	6*10^172772-31	172773	Robert Price	07/2020
2017	69061#+(467617#)/(69061#)	172766	Makoto Morimoto	10/2017
2018	(34*10^172693-547)/9	172694	Robert Price	03/2021
2019	5*10^172692+57	172693	Robert Price	12/2018
2020	2^573668-2782319	172692	Enzo Doria	09/2015
2021	2^573444-1855109	172624	Enzo Doria	09/2015
2022	(14*10^172532-29)/3	172533	Robert Price	09/2021
2023	3^361608+2	172531	Robert Price	08/2014
2024	(54^99563+1)/55	172481	Paul Bourdelais	11/2017
2025	2^572592-114893	172368	Enzo Doria	05/2015
2026	4*10^172354-39	172355	Robert Price	09/2020
2027	37535^37674+37674^37535	172338	Norbert Schneider	05/2022
2028	(11*10^172322-119)/9	172323	Robert Price	11/2021
2029	5^246497-4^246497	172295	Jean-Louis Charton	11/2008
2030	(38^109037-1)/37	172254	Paul Bourdelais	10/2017
2031	(4*10^172241+89)/3	172242	Robert Price	08/2021
2032	3*10^172219+73	172220	Robert Price	08/2018
2033	A352736(15)	172032	Kellen Shenton	05/2022
2034	(36^110503+1)/37	171975	Lelio R Paula	04/2017
2035	8*10^171934+71	171935	Robert Price	05/2022
2036	(11*10^171933+601)/9	171934	Robert Price	02/2022
2037	(22*10^171929-73)/3	171930	Robert Price	04/2019
2038	(49*10^171892-319)/9	171893	Robert Price	10/2021
2039	4*10^171891-63	171892	Robert Price	10/2018
2040	67*10^171882-9	171884	Robert Price	03/2021
2041	2^570980-2782289	171883	Enzo Doria	09/2015
2042	(25*10^171849-37)/3	171850	Robert Price	10/2019
2043	10^171832+387909	171833	Patrick De Geest	08/2021
2044	10^171832-10001	171832	Robert Price	02/2021
2046	(2^(12*47563+13)-9)/7	171818	Kevin Acres	11/2013
2045	(2^570769-9)/7	171818	Stefano Morozzi	08/2022
2047	(74*10^171651-29)/9	171652	Robert Price	06/2022
2048	(536*10^171601-23)/9	171603	Robert Price	02/2020
2049	7*10^171535-99	171536	Robert Price	06/2019
2050	(28*10^171534+101)/3	171535	Robert Price	09/2020
2051	2^569563-1854607	171456	Enzo Doria	09/2015
2052	3*10^171391+59	171392	Robert Price	08/2018
2053	(13*10^171306-37)/3	171307	Robert Price	01/2019
2054	8*10^171296+87	171297	Robert Price	10/2019
2055	(55^98419-1)/54	171284	Paul Bourdelais	12/2017
2056	(29*10^171275+67)/3	171276	Robert Price	12/2019
2057	(457*10^171248-7)/9	171250	Robert Price	09/2022
2058	(194*10^171193+1)/3	171195	Robert Price	01/2022
2059	2^568642+1876129	171179	Enzo Doria	07/2016
2060	4*10^171146-47	171147	Robert Price	10/2021
2061	(19*10^170970+131)/3	170971	Robert Price	06/2020
2062	(46*10^170932+143)/9	170933	Robert Price	01/2019
2063	(79*10^170901-1)/3	170903	Robert Price	02/2020
2064	(58*10^170842+221)/9	170843	Robert Price	02/2017
2065	(29*10^170830+583)/9	170831	Robert Price	06/2021
2066	3*10^170800+73	170801	Robert Price	08/2018
2067	(29*10^170799-119)/9	170800	Robert Price	12/2021
2068	11^164009-270	170798	Enzo Doria	10/2012
2069	2*10^170767+41	170768	Robert Price	05/2018
2070	3^357706-112358	170670	Enzo Doria	07/2014
2071	TheodorusPrime(170657)	170657	Eric W. Weisstein	08/2013
2072	2^566871+1876163	170646	Enzo Doria	07/2016
2073	(10657#+(404267#)/(10657#))/(1675379)	170624	Makoto Morimoto	10/2017
2074	2^566496+7	170533	Donovan Johnson	07/2006
2075	(7^201653+1)/8	170416	Paul Bourdelais	02/2010
2076	7*10^170348+33	170349	Robert Price	06/2020
2077	2^565183-352021	170138	Enzo Doria	07/2015
2078	2^565143-114457	170125	Enzo Doria	02/2015
2079	2^564976-49869	170075	Enzo Doria	10/2015
2080	(7*10^169944+23)/3	169945	Robert Price	06/2020
2081	(37*10^169943+251)/9	169944	Robert Price	09/2021
2082	2^564526-351401	169940	Enzo Doria	07/2015
2083	4*10^169759+19	169760	Robert Price	10/2018
2084	(2^563903-13)/5	169752	Stefano Morozzi	08/2022
2085	21^128327-20^128327	169677	Jean-Louis Charton	11/2014
2086	2^563583+89	169656	Stefano Morozzi	04/2021
2087	(4*10^169559+83)/3	169560	Robert Price	02/2018
2088	(194*10^169461-17)/3	169463	Robert Price	09/2020
2089	2^562749+2793047	169405	Enzo Doria	02/2016
2090	(154*10^169337-1)/9	169339	Serge Batalov	12/2014
2091	(109*10^169337+11)/3	169339	Robert Price	06/2022
2092	(56*10^169311+691)/9	169312	Robert Price	05/2019
2093	2^562369-29503	169290	Enzo Doria	08/2015
2094	(17*10^169283+19)/9	169284	Robert Price	03/2021
2095	10^169074-5000000001	169074	Robert Price	09/2022
2096	8*10^169071+59	169072	Robert Price	11/2021
2097	(10^169044+173)/3	169044	Robert Price	05/2021
2098	(22*10^169019+383)/9	169020	Robert Price	05/2018
2099	(64*10^168935+143)/9	168936	Robert Price	05/2021
2100	(22*10^168906+47)/3	168907	Robert Price	06/2021
2101	5*10^168807+87	168808	Robert Price	02/2019
2102	(77*10^168803-149)/9	168804	Robert Price	03/2022
2103	4*10^168788-47	168789	Robert Price	10/2021
2104	(154*10^168781+17)/9	168783	Robert Price	06/2022
2105	(418*10^168751-31)/9	168753	Robert Price	05/2022
2106	(29*10^168711+691)/9	168712	Robert Price	08/2021
2107	2^560405-39943	168699	Enzo Doria	09/2015
2108	(397*10^168634+17)/9	168636	Robert Price	03/2022
2109	89*10^168614-7	168616	Robert Price	04/2020
2110	(23*10^168608-83)/3	168609	Robert Price	08/2019
2111	(94*10^168541+11)/3	168543	Robert Price	04/2020
2112	2^559686-350471	168483	Enzo Doria	06/2015
2113	2^559672-1855889	168479	Enzo Doria	09/2015
2114	(5*10^168379-473)/9	168379	Robert Price	01/2018
2115	2^559000-59939	168276	Enzo Doria	11/2015
2116	(16*10^168181+41)/3	168182	Robert Price	03/2019
2117	(19*10^168173+77)/3	168174	Robert Price	05/2019
2118	(74*10^168170+529)/9	168171	Robert Price	02/2022
2119	2^558640-114149	168168	Enzo Doria	12/2014
2120	2^558498-1849277	168125	Enzo Doria	08/2015
2121	2^558476-1850249	168119	Enzo Doria	08/2015
2122	(7*10^168067+71)/3	168068	Robert Price	05/2018
2123	2^558150-1852211	168020	Enzo Doria	08/2015
2124	2^558125-113661	168013	Enzo Doria	09/2014
2125	393^64747-392^64747	167980	Jean-Louis Charton	08/2012
2126	(13*10^167911+179)/3	167912	Robert Price	11/2018
2127	(26*10^167861-167)/3	167862	Robert Price	10/2019
2128	39^105456+2	167788	Robert Price	04/2015
2129	(28^115877-1)/27	167691	Paul Bourdelais	12/2017
2130	6*10^167662-13	167663	Robert Price	07/2022
2131	10^167639+121911	167640	Patrick De Geest	07/2018
2132	10^167639-8001	167639	Robert Price	03/2018
2133	2^556504-462059	167525	Enzo Doria	07/2015
2134	(88*10^167522-637)/9	167523	Robert Price	11/2020
2135	5*10^167510+9	167511	Robert Price	08/2015
2136	7*10^167437-93	167438	Robert Price	08/2020
2137	11^160663+6	167314	Paul Bourdelais	02/2021
2138	(7*10^167308-493)/9	167308	Robert Price	04/2021
2139	2^555343+1874333	167175	Enzo Doria	06/2016
2140	2^555210-461261	167135	Enzo Doria	07/2015
2141	9*10^166996+59	166997	Robert Price	01/2020
2142	(68*10^166976-329)/9	166977	Robert Price	03/2021
2143	(64*10^166901+683)/9	166902	Robert Price	06/2022
2144	2^554372+1880527	166883	Enzo Doria	11/2016
2145	2^554299+72173	166861	Enzo Doria	04/2016
2146	(185*10^166837+7)/3	166839	Robert Price	03/2020
2147	(14*10^166813+139)/9	166814	Robert Price	11/2021
2148	2^554037-2797063	166782	Enzo Doria	03/2016
2149	(49*10^166721-139)/9	166722	Robert Price	03/2019
2150	2*10^166646+69	166647	Robert Price	06/2020
2151	2^553484-29819	166616	Enzo Doria	08/2015
2152	(188*10^166611+7)/3	166613	Robert Price	03/2020
2153	2^553383-2784217	166585	Enzo Doria	10/2015
2154	2^553069+76427	166491	Enzo Doria	05/2016
2155	2*10^166458+51	166459	Robert Price	05/2018
2156	589^60089-588^60089	166454	Jean-Louis Charton	09/2012
2157	11^159756-2424	166369	Mike Oakes	06/2010
2158	2^552649-361275	166364	Enzo Doria	05/2014
2159	2^552628-113669	166358	Enzo Doria	09/2014
2160	(19*10^166325+137)/3	166326	Robert Price	03/2022
2161	10^166324+550603	166325	Patrick De Geest	07/2018
2162	10^166324-801	166324	Robert Price	02/2018
2163	(85*10^166297-1)/3	166299	Robert Price	02/2020
2164	8*10^166227+87	166228	Robert Price	10/2019
2165	2^552137+1879397	166210	Enzo Doria	09/2016
2166	(103*10^166126+11)/3	166128	Robert Price	01/2021
2167	(22*10^166077+179)/3	166078	Robert Price	02/2022
2168	(23^121949-1)/22	166061	Paul Bourdelais	10/2017
2169	2^551542+19249	166031	Payam Samidoost	08/2002
2170	2^551535-23821	166029	Enzo Doria	08/2013
2171	2^551507-23557	166021	Enzo Doria	08/2013
2172	10^165947-7000000001	165947	Robert Price	12/2021
2173	4*10^165938-47	165939	Robert Price	10/2021
2174	7*10^165916-3	165917	Robert Price	08/2015
2175	(29*10^165796+67)/3	165797	Robert Price	12/2019
2176	81^86837-80^86837	165728	Robert Price	01/2015
2177	(71*10^165716-17)/9	165717	Serge Batalov	01/2023
2178	(71*10^165663-539)/9	165664	Robert Price	07/2019
2179	2^550270-69551	165648	Enzo Doria	12/2015
2180	(202*10^165569-13)/9	165571	Robert Price	01/2020
2181	2^550000-23625	165567	Enzo Doria	08/2013
2182	2^549675-1852057	165469	Enzo Doria	08/2015
2183	(529*10^165394-7)/9	165396	Robert Price	08/2021
2184	-tau(103^14938)	165374	Nik Lygeros / Olivier Rozier	10/2013
2185	(28*10^165358-1)/9	165359	Serge Batalov	10/2014
2186	2^549278+1879669	165350	Enzo Doria	09/2016
2187	(7*10^165350-439)/9	165350	Robert Price	02/2018
2188	2^549252-351269	165342	Enzo Doria	06/2015
2189	67*10^165327-9	165329	Robert Price	03/2021
2191	(14*10^165282+73)/3	165283	Robert Price	12/2018
2190	(8*10^165283-629)/9	165283	Robert Price	01/2022
2192	2^549049+2797607	165281	Enzo Doria	04/2016
2193	(218*10^165258+7)/9	165260	Robert Price	06/2022
2194	(7*10^165239+107)/3	165240	Robert Price	02/2018
2195	(44^100511-1)/43	165184	Paul Bourdelais	11/2017
2196	(7*10^165134+107)/3	165135	Robert Price	02/2018
2197	(301*10^165082+23)/9	165084	Robert Price	06/2021
2198	(23*10^165060-83)/3	165061	Robert Price	08/2019
2199	7*10^165023-27	165024	Robert Price	11/2022
2200	(76*10^164984+77)/9	164985	Robert Price	10/2019
2201	(4*10^164929-211)/9	164929	Robert Price	03/2022
2202	10^164878-500001	164878	Robert Price	03/2022
2203	9*10^164791-89	164792	Robert Price	04/2020
2204	2^547178-1856501	164717	Enzo Doria	10/2015
2205	11^158160-60	164707	Enzo Doria	07/2012
2206	(26*10^164643-167)/3	164644	Robert Price	10/2019
2207	(10^164643+83)/3	164643	Robert Price	08/2021
2208	2^546398-59201	164483	Enzo Doria	10/2015
2209	2^546332-114893	164463	Enzo Doria	05/2015
2210	(65*10^164427+277)/9	164428	Robert Price	08/2021
2211	2^545958+1876189	164350	Enzo Doria	07/2016
2212	2^545878-49841	164326	Enzo Doria	10/2015
2213	(10^164284+77)/3	164284	Robert Price	01/2018
2214	2^545668-4019	164263	Yves Minet	04/2017
2215	10^164216+780639	164217	Patrick De Geest	08/2021
2217	10^164216-50000000001	164216	Robert Price	12/2020
2216	10^164216-891051	164216	Patrick De Geest	08/2021
2218	(1353^238539617^9)/10^247183	164151	Hans Havermann	07/2017
2219	(16*10^164122+197)/3	164123	Robert Price	04/2019
2220	2^545185+76757	164118	Enzo Doria	05/2016
2221	2^545076-114329	164085	Enzo Doria	01/2015
2222	(2*10^164043-143)/3	164043	Robert Price	03/2018
2223	(29^112153+1)/30	164011	Lelio R Paula	03/2017
2224	2^544757+1874777	163989	Enzo Doria	06/2016
2225	2^544444-457199	163894	Enzo Doria	01/2015
2226	2^544264-343529	163840	Enzo Doria	07/2015
2227	7*10^163780+9	163781	Robert Price	09/2015
2228	2^543989+2793047	163758	Enzo Doria	02/2016
2229	(28*10^163709+113)/3	163710	Robert Price	03/2020
2230	(23*10^163523+301)/9	163524	Robert Price	06/2021
2231	(68*10^163521-329)/9	163522	Robert Price	03/2021
2232	35820^35899+35899^35820	163489	Norbert Schneider	11/2021
2233	2^542870-69551	163421	Enzo Doria	12/2015
2234	2^542395+72533	163278	Enzo Doria	04/2016
2235	2^542072-3683	163180	Yves Minet	03/2017
2236	(682*10^163106-7)/9	163108	Robert Price	08/2021
2237	2^541779-1867357	163092	Enzo Doria	04/2016
2238	(29*10^163056+313)/9	163057	Robert Price	04/2021
2239	8*10^162924+9	162925	Robert Price	12/2015
2240	2^540905+81557	162829	Enzo Doria	08/2016
2241	2^540628-2939	162746	Yves Minet	09/2014
2242	919^54919-918^54919	162743	Jean-Louis Charton	01/2013
2243	(203*10^162689+1)/3	162691	Robert Price	03/2020
2244	3*10^162620-59	162621	Robert Price	09/2018
2245	3^340694-112960	162553	Enzo Doria	07/2014
2246	2^539807-114081	162499	Enzo Doria	12/2014
2247	414^62093+62093^414	162498	Norbert Schneider	03/2022
2248	2^539654-114893	162453	Enzo Doria	05/2015
2249	9*10^162449-71	162450	Robert Price	11/2020
2250	2^539617-1851583	162441	Enzo Doria	08/2015

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Probable Primes Top 10000

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