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	(112*10^194150-1)/3	194152	Serge Batalov	12/2014
2002	Phi(293127,10)	194041	Makoto Kamada	12/2023
2003	2*10^193981-43	193982	Robert Price	04/2018
2004	2^644382+75169	193979	Enzo Doria	04/2016
2005	2^644304-1861409	193955	Enzo Doria	11/2015
2006	(29*10^193950-23)/3	193951	Robert Price	03/2022
2007	5*10^193907-9	193908	Robert Price	05/2015
2008	2^644043+1876703	193877	Enzo Doria	07/2016
2009	2*10^193841-63	193842	Robert Price	01/2022
2010	2^643735+1879733	193784	Enzo Doria	09/2016
2011	(5^277183+1)/6	193742	Paul Bourdelais	07/2010
2012	9*10^193712+71	193713	Robert Price	08/2020
2013	2^643216-286565	193628	Enzo Doria	07/2015
2014	2^643204+215011	193624	Enzo Doria	11/2023
2015	10^193566+1126339	193567	Patrick De Geest	09/2022
2017	10^193566-10000000001	193566	Robert Price	04/2021
2016	10^193566-454041	193566	Patrick De Geest	08/2021
2019	2^642888-24965	193529	Enzo Doria	09/2013
2018	2^642889+25367	193529	Enzo Doria	11/2023
2020	2^642448-114825	193397	Enzo Doria	05/2015
2021	2^642437-1856623	193393	Enzo Doria	10/2015
2022	2^642039-59797	193273	Enzo Doria	11/2015
2023	2^641987+39	193258	Jon Grantham	08/2023
2024	10^193230+513861	193231	Patrick De Geest	07/2018
2025	10^193230-8001	193230	Robert Price	03/2018
2026	(62*10^193225-233)/9	193226	Robert Price	02/2022
2027	2^641692-286349	193169	Enzo Doria	07/2015
2028	2^641690-24737	193168	Enzo Doria	09/2013
2029	22268^44421+44421^22268	193129	Norbert Schneider	06/2023
2030	2^641514+1876549	193115	Enzo Doria	07/2016
2031	2^640888-2785619	192927	Enzo Doria	10/2015
2032	2^640874-2783741	192923	Enzo Doria	09/2015
2033	10^192922+192207	192923	Patrick De Geest	08/2021
2034	10^192922-7001	192922	Robert Price	04/2021
2035	2^640854+25	192917	Stefano Morozzi	05/2021
2036	34*10^192868-9	192870	Robert Price	06/2020
2037	(46*10^192841+683)/9	192842	Robert Price	03/2019
2038	2^640181+467	192714	Lelio R Paula	08/2013
2039	2^640072+27541	192681	Enzo Doria	01/2024
2040	2^639536-1850249	192520	Enzo Doria	08/2015
2041	40714<>40712<>...<>1086421357911<>...<>40711<>40713	192464	Hans Havermann	12/2019
2042	5*10^192422-43	192423	Robert Price	01/2019
2043	2^639110-2792441	192392	Enzo Doria	02/2016
2044	(241^80761-1)/240	192372	Anonymous	04/2024
2045	2^638955-29827	192345	Enzo Doria	08/2015
2046	15^163539+14	192337	Alfred Reich	10/2023
2047	2^638713-2784223	192272	Enzo Doria	10/2015
2048	(10^192216+7)/149	192214	Alfred Reich	07/2021
2049	2^638490-113507	192205	Enzo Doria	08/2014
2050	2^638189-39943	192115	Enzo Doria	09/2015
2051	2^638110+1877119	192091	Enzo Doria	07/2016
2052	2^638066-2785211	192078	Enzo Doria	10/2015
2053	(35*10^191973-341)/9	191974	Robert Price	08/2021
2054	(112*10^191900+17)/3	191902	Robert Price	03/2020
2055	2^637475-115309	191900	Enzo Doria	07/2015
2056	(68*10^191754-113)/9	191755	Robert Price	03/2021
2057	2^636930-11	191736	Stefano Morozzi	07/2022
2058	(47*10^191732+259)/9	191733	Robert Price	03/2022
2059	2^636661+1876577	191655	Enzo Doria	07/2016
2060	(9^200807-2^200807)/7	191618	Jon Grantham	07/2023
2061	(34^125101-1)/33	191589	Paul Bourdelais	11/2017
2062	fibonacci(916540)-2	191546	Jon Grantham	08/2023
2063	2^636177-1855123	191509	Enzo Doria	09/2015
2064	2^636158-113627	191503	Enzo Doria	08/2014
2065	(37*25^136966+63)/4	191472	Curtis Bright	05/2015
2066	2^636035+79823	191466	Enzo Doria	06/2016
2067	2^636011-1860847	191459	Enzo Doria	11/2015
2068	2^635926-1860611	191433	Enzo Doria	11/2015
2069	3*2^635755+5	191382	Jon Grantham	07/2023
2070	3*10^191152-7	191153	Robert Price	08/2015
2071	2^634883-1865677	191119	Enzo Doria	02/2016
2072	2^634801+1871957	191095	Enzo Doria	05/2016
2073	(77*10^191080+157)/9	191081	Robert Price	05/2022
2074	(35*10^191073+1)/9	191074	Serge Batalov	07/2010
2075	9*10^191018-41	191019	Robert Price	08/2020
2076	2^634470-59861	190995	Enzo Doria	11/2015
2077	2^634368-29519	190964	Enzo Doria	08/2015
2078	(19*10^190935+11)/3	190936	Robert Price	07/2023
2079	2^634188-350609	190910	Enzo Doria	06/2015
2080	(65*10^190899+493)/9	190900	Robert Price	08/2021
2081	(62*10^190795-413)/9	190796	Robert Price	09/2021
2082	(26*10^190789-131)/3	190790	Robert Price	10/2019
2083	(13*10^190732-61)/3	190733	Robert Price	11/2018
2084	3*2^633524+5	190711	Jon Grantham	07/2023
2085	(7*10^190683+143)/3	190684	Robert Price	03/2018
2086	2^633088-113879	190579	Enzo Doria	10/2014
2087	2^633064+1874911	190572	Enzo Doria	06/2016
2088	5*3^399402+2^399402	190564	Jon Grantham	08/2023
2089	(43*10^190547+83)/9	190548	Robert Price	11/2018
2090	99*10^190543+7	190545	Robert Price	05/2021
2091	(299*10^190533+1)/3	190535	Robert Price	04/2020
2092	(1744*10^190519-1747)/3	190522	Robert Price	12/2020
2093	2^632815-15	190497	Stefano Morozzi	07/2022
2094	2^632795-351205	190491	Enzo Doria	06/2015
2095	41171^41272+41272^41171	190454	Norbert Schneider	05/2023
2096	(16*10^190420-19)/3	190421	Robert Price	02/2019
2097	(43*10^190351+101)/9	190352	Robert Price	11/2018
2098	2^632156+78391	190298	Enzo Doria	06/2016
2099	97*10^190295-3	190297	Robert Price	05/2020
2100	2^632082-1851971	190276	Enzo Doria	08/2015
2101	2^632020+1880311	190257	Enzo Doria	09/2016
2102	(5*10^190242-77)/9	190242	Robert Price	04/2021
2103	7*10^190210+13	190211	Robert Price	03/2021
2104	2^631637-462373	190142	Enzo Doria	08/2015
2105	2*10^190126-21	190127	Robert Price	09/2020
2106	(28*10^190105+191)/3	190106	Robert Price	02/2020
2107	2*10^190093+33	190094	Robert Price	11/2021
2108	(68*10^190053-113)/9	190054	Robert Price	03/2021
2109	2^631183+213413	190006	Enzo Doria	09/2023
2110	2^631122-39251	189987	Enzo Doria	08/2015
2111	(26*10^189928-89)/9	189929	Robert Price	06/2018
2112	2^630839-97	189902	Yves Minet	07/2017
2113	99*10^189876-7	189878	Robert Price	07/2020
2114	2^630359+1788953	189757	Enzo Doria	05/2016
2115	2^630228+1871971	189718	Enzo Doria	05/2016
2116	2^630108+781	189682	Lelio R Paula	08/2013
2117	2^629870-1867811	189610	Enzo Doria	04/2016
2118	(359^74189-1)/358	189558	Alexander Zhirkov	11/2017
2119	2^629326+2792929	189447	Enzo Doria	02/2016
2120	4*10^189401+13	189402	Robert Price	02/2021
2121	(10^189385-61)/3	189385	Serge Batalov	12/2014
2122	2^629036+1874011	189359	Enzo Doria	06/2016
2123	2^628930+80779	189327	Enzo Doria	07/2016
2124	(134*10^189309-11)/3	189311	Robert Price	01/2022
2125	9*10^189306-11	189307	Mischa Rodermond	04/2023
2126	2^628582+1179439	189223	Enzo Doria	06/2016
2127	(44*10^188999-503)/9	189000	Robert Price	12/2018
2128	(16*10^188823+167)/3	188824	Robert Price	06/2019
2129	(10^188796+7)/4967/71933	188788	Alfred Reich	08/2021
2130	2^627037-2785843	188757	Enzo Doria	10/2015
2131	(10^188566+7)/311640753181661	188552	Alfred Reich	04/2022
2132	(16*10^188457+161)/3	188458	Robert Price	02/2019
2133	L(901657)	188436	Renaud Lifchitz	11/2008
2134	(19*10^188375+137)/3	188376	Robert Price	03/2022
2135	2^625651+74213	188340	Enzo Doria	04/2016
2136	2^625584-460919	188320	Enzo Doria	06/2015
2137	(8*10^188308-71)/9	188308	Serge Batalov	11/2022
2138	5^269399-3^269399-1	188302	Jon Grantham	08/2023
2139	(14*10^188218+139)/9	188219	Robert Price	11/2021
2140	(10^188164+359)/9	188164	Serge Batalov	12/2014
2141	2^624481-113611	187988	Enzo Doria	08/2014
2142	(2^624389+125582)/2	187960	Stefano Morozzi	09/2019
2143	(2^624389+166982)/2	187960	Stefano Morozzi	09/2019
2144	(2^624389+179886)/2	187960	Stefano Morozzi	09/2019
2145	(2^624387+64466)/2	187959	Stefano Morozzi	09/2019
2146	(2^624378+112990)/2	187957	Stefano Morozzi	09/2019
2147	(2^624380+161986)/2	187957	Stefano Morozzi	09/2019
2149	(2^624376+55762)/2	187956	Stefano Morozzi	09/2019
2148	(2^624377+169506)/2	187956	Stefano Morozzi	09/2019
2150	(2^624355+80178)/2	187950	Stefano Morozzi	09/2019
2151	(2^624351+61350)/2	187949	Stefano Morozzi	09/2019
2152	(2^624341+63462)/2	187946	Stefano Morozzi	09/2019
2153	(2^624344+135990)/2	187946	Stefano Morozzi	09/2019
2154	(2^624344+183898)/2	187946	Stefano Morozzi	09/2019
2156	(2^624340+126982)/2	187945	Stefano Morozzi	09/2019
2155	(2^624338+196110)/2	187945	Stefano Morozzi	09/2019
2157	(2^624337+105162)/2	187944	Stefano Morozzi	09/2019
2158	(2^624333+44594)/2	187943	Stefano Morozzi	09/2019
2159	(2^624321+88742)/2	187940	Stefano Morozzi	09/2019
2160	(2^624324+135178)/2	187940	Stefano Morozzi	09/2019
2161	(2^624317+14186)/2	187938	Stefano Morozzi	09/2019
2162	(2^624313+24450)/2	187937	Stefano Morozzi	09/2019
2163	(2^624309+184590)/2	187936	Stefano Morozzi	09/2019
2165	(2^624307+152658)/2	187935	Stefano Morozzi	09/2019
2164	(2^624307+185978)/2	187935	Stefano Morozzi	09/2019
2166	(2^624303+40814)/2	187934	Stefano Morozzi	09/2019
2167	(2^624304+99238)/2	187934	Stefano Morozzi	09/2019
2168	2^624077-112723	187866	Enzo Doria	07/2014
2169	2^624008+1874941	187846	Enzo Doria	06/2016
2170	2^623870+78679	187804	Enzo Doria	05/2016
2171	2^623714-114035	187757	Enzo Doria	11/2014
2172	2^623651-1834251	187738	Enzo Doria	07/2015
2173	(7*10^187645+53)/3	187646	Robert Price	05/2018
2174	21650^43269+43269^21650	187591	Norbert Schneider	02/2023
2175	2^623146+1879609	187586	Enzo Doria	09/2016
2176	(401*10^187512+13)/9	187514	Robert Price	09/2021
2177	(5*10^187471+91)/3	187472	Robert Price	04/2018
2178	2^622500+81931	187392	Enzo Doria	08/2016
2179	(13*10^187382-157)/9	187383	Robert Price	05/2021
2180	2^622300-1861739	187331	Enzo Doria	12/2015
2181	(22*10^187317-91)/3	187318	Robert Price	02/2022
2182	(38*10^187281+349)/9	187282	Robert Price	10/2018
2183	2^622052+76771	187257	Enzo Doria	05/2016
2184	2^622005-24091	187243	Enzo Doria	08/2013
2185	7*10^187205-57	187206	Robert Price	06/2020
2186	2^621879-351787	187205	Enzo Doria	07/2015
2187	(5*10^187168-53)/3	187169	Robert Price	09/2020
2188	(23*10^187164-143)/3	187165	Robert Price	12/2019
2189	2^621700+79411	187151	Enzo Doria	06/2016
2190	2^621597+39	187120	Jon Grantham	08/2023
2191	(7*10^187101+131)/3	187102	Robert Price	06/2020
2192	(2*10^187062-71)/3	187062	Robert Price	12/2017
2193	2^620929-113203	186919	Enzo Doria	07/2014
2194	10^186842+168223	186843	Patrick De Geest	07/2018
2195	10^186842-8001	186842	Robert Price	03/2018
2196	2^620347-1777	186744	Lelio R Paula	07/2013
2197	(11*10^186659+133)/9	186660	Robert Price	04/2022
2198	11^179143-4170	186559	Enzo Doria	12/2012
2199	(5^266863+1)/6	186529	Paul Bourdelais	07/2010
2200	2*10^186517+33	186518	Robert Price	11/2021
2201	2^619297-2792353	186427	Enzo Doria	02/2016
2202	(49*10^186409+383)/9	186410	Robert Price	04/2019
2203	2^618940-460139	186320	Enzo Doria	06/2015
2204	2^618046+74179	186051	Enzo Doria	04/2016
2205	3*10^186019+11	186020	Robert Price	07/2018
2206	(16*10^185978-19)/3	185979	Robert Price	02/2019
2207	(22*10^185950-7)/3	185951	Robert Price	12/2022
2208	2*10^185930-3	185931	Robert Price	07/2015
2209	(82^97151+1)/83	185928	Paul Bourdelais	10/2017
2210	4*10^185905+91	185906	Robert Price	08/2018
2211	(34*10^185902-601)/9	185903	Robert Price	07/2022
2212	(19*10^185873+131)/3	185874	Robert Price	06/2020
2213	(37*10^185811+377)/9	185812	Robert Price	11/2018
2214	2^617250+9385	185811	Lelio R Paula	07/2013
2215	2^617130+9	185775	Stefano Morozzi	05/2021
2216	39^116749+2	185756	Robert Price	04/2015
2217	2^616924-39719	185713	Enzo Doria	09/2015
2218	2^616712+1867621	185649	Enzo Doria	04/2016
2219	(3^388897+2^388897)/5	185551	Jean-Louis Charton	09/2011
2220	8*10^185529-67	185530	Robert Price	08/2019
2221	(5*10^185520-11)/3	185521	Tyler Busby	02/2023
2222	5*2^616124+3	185473	Jon Grantham	07/2023
2223	2^615916+26791	185410	Enzo Doria	12/2023
2224	4*10^185355+9	185356	Robert Price	05/2015
2225	(16*10^185347+89)/3	185348	Robert Price	03/2021
2226	2^615622+76639	185321	Enzo Doria	05/2016
2227	2^615591+1879223	185312	Enzo Doria	08/2016
2228	2^615587+217013	185311	Enzo Doria	12/2023
2229	2^615503+1876643	185285	Enzo Doria	07/2016
2230	5^265007-4^265007	185232	Jean-Louis Charton	02/2013
2232	(4*10^185221-91)/3	185222	Robert Price	03/2018
2231	(7*10^185221+131)/3	185222	Robert Price	06/2020
2233	(62*10^185216-413)/9	185217	Robert Price	09/2021
2234	(232*10^185180+17)/3	185182	Robert Price	04/2021
2235	56*10^185139-3	185141	Robert Price	03/2020
2236	(28*10^185105+47)/3	185106	Robert Price	02/2021
2237	2^614783-2790097	185069	Enzo Doria	12/2015
2238	2^614745-29323	185057	Enzo Doria	07/2015
2239	(((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840	185052	Serge Batalov	07/2013
2240	(49*10^184993-67)/9	184994	Robert Price	03/2019
2241	(5*10^184954-191)/3	184955	Robert Price	05/2021
2242	(14*10^184950+211)/9	184951	Robert Price	04/2018
2243	2^614360+215221	184941	Enzo Doria	11/2023
2244	2^614315+81353	184928	Enzo Doria	08/2016
2245	2^614294-1849961	184921	Enzo Doria	08/2015
2246	2^614266+1877809	184913	Enzo Doria	08/2016
2247	(185*10^184878-11)/3	184880	Robert Price	10/2020
2248	91*10^184867-9	184869	Robert Price	06/2021
2249	(14789^44521-1)/(14789^211-1)	184770	Ryan Propper	11/2023
2250	(85*10^184768+77)/9	184769	Robert Price	07/2022

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Probable Primes Top 10000

(295083 PRPs in the top)