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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
2002	(13*10^135279+437)/9	135280	Robert Price	04/2018
2003	2^449330-35	135262	Lelio R Paula	08/2017
2004	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
2005	(13*10^135184-43)/3	135185	Robert Price	11/2018
2006	2^449049-115309	135178	Enzo Doria	07/2015
2007	(10^135174+191)/3	135174	Robert Price	02/2018
2008	2^449030-15	135172	Lelio R Paula	08/2017
2009	(27*2^448936-1)/11	135144	Lelio R Paula	07/2015
2010	2^448762-351401	135091	Enzo Doria	07/2015
2011	2*10^135083-43	135084	Robert Price	04/2018
2012	5*10^135019+77	135020	Robert Price	12/2018
2013	(10^135011+719)/9	135011	Serge Batalov	12/2014
2014	2^448386-2786261	134978	Enzo Doria	03/2016
2015	(73*10^134939+143)/9	134940	Robert Price	07/2019
2016	2^448113-113949	134896	Enzo Doria	11/2014
2017	2^447888-2786639	134828	Enzo Doria	03/2016
2018	2^447870-396765	134823	Enzo Doria	07/2013
2019	2^447766-21791	134791	Enzo Doria	07/2013
2020	(19*10^134786-49)/3	134787	Robert Price	05/2019
2021	Phi(202173,10)/10064306514895399941409	134758	Makoto Kamada	05/2019
2022	(23*2^447647+1)/155	134755	Lelio R Paula	07/2015
2023	2^447552-1019	134727	Yves Minet	02/2014
2024	(2*10^134720-41)/3	134720	Robert Price	02/2018
2025	2^447437-113569	134692	Enzo Doria	08/2014
2026	2^447426-65	134689	Lelio R Paula	08/2017
2027	2^447357-2797573	134668	Enzo Doria	04/2016
2028	2^447278+93	134645	Lelio R Paula	08/2017
2029	2^447094-113193	134589	Enzo Doria	07/2014
2030	3^282041-9934	134568	Enzo Doria	05/2014
2031	2^447019-109039	134567	Enzo Doria	04/2014
2032	2^446990-22041	134558	Enzo Doria	07/2013
2033	123^64370+122	134528	Karsten Bonath	04/2018
2034	2^446782-39701	134495	Enzo Doria	09/2015
2035	2^446494-16485	134409	Enzo Doria	04/2013
2036	29504^30069-30069^29504	134405	Norbert Schneider	12/2014
2037	2^446441+65	134393	Lelio R Paula	08/2017
2038	(10^134385+719)/9	134385	Serge Batalov	12/2014
2039	(2*10^134364+529)/9	134364	Robert Price	01/2018
2040	(13*2^446187-1)/661	134314	Lelio R Paula	07/2015
2041	(2^446022-7)/339	134264	Lelio R Paula	07/2015
2042	63^74568+2	134174	Lelio R Paula	06/2017
2043	2^445671-22071	134161	Enzo Doria	07/2013
2044	532^49205+49205^532	134129	Norbert Schneider	02/2019
2045	(28*10^134122-1)/9	134123	Serge Batalov	10/2014
2046	2^445515-113859	134114	Enzo Doria	10/2014
2047	(22*10^134111-37)/3	134112	Robert Price	04/2019
2048	2^445328-216917	134058	Enzo Doria	05/2014
2049	2^445202+1874899	134020	Enzo Doria	06/2016
2050	(13*2^445102+1)/17	133989	Lelio R Paula	07/2015
2051	(35*10^133979-593)/9	133980	Robert Price	07/2018
2052	2*10^133955+51	133956	Robert Price	05/2018
2053	2^444964-113639	133948	Enzo Doria	08/2014
2054	28118^30097-30097^28118	133902	Norbert Schneider	01/2015
2055	2^444784-113859	133894	Enzo Doria	10/2014
2056	(89*10^133580+1)/9	133581	Serge Batalov	05/2010
2057	62^74521-61^74521	133571	Robert Price	05/2013
2058	2^443198-1867301	133416	Enzo Doria	03/2016
2059	(19*10^133390+101)/3	133391	Robert Price	09/2019
2060	(71^72043-1)/70	133369	Paul Bourdelais	09/2017
2061	2^442799+1874633	133296	Enzo Doria	06/2016
2062	L(637751)	133283	Henri Lifchitz	09/2008
2063	109^65410-2	133269	Lelio R Paula	10/2017
2064	2^442688-113489	133263	Enzo Doria	08/2014
2065	(7*2^442640-1)/783	133246	Lelio R Paula	07/2015
2066	(9*2^442463+1)/17441	133192	Lelio R Paula	07/2015
2067	2^442437-1849993	133187	Enzo Doria	08/2015
2068	2^442430-2791721	133185	Enzo Doria	03/2016
2069	(13*2^442428-1)/309	133183	Lelio R Paula	07/2015
2070	(25*2^442379-1)/71	133169	Lelio R Paula	07/2015
2071	(2^441799+78557)/5	132995	Lelio R Paula	07/2015
2072	2^441781-2787883	132990	Enzo Doria	03/2016
2073	(3*2^441685+1)/749	132959	Lelio R Paula	07/2015
2074	2^441618+37	132941	Lelio R Paula	08/2017
2075	2^441521-113575	132912	Enzo Doria	08/2014
2076	7*10^132884-99	132885	Robert Price	06/2019
2077	2^441396-65	132874	Lelio R Paula	08/2017
2078	2^441330+1871959	132854	Enzo Doria	05/2016
2079	2^441063+383	132774	Lelio R Paula	06/2012
2080	(22*10^132746+53)/3	132747	Robert Price	07/2019
2081	2^440846+1870909	132708	Enzo Doria	05/2016
2082	2^440656-113489	132651	Enzo Doria	08/2014
2083	numbpart(14180123587)	132646	Serge Batalov	04/2017
2084	(19*10^132550+191)/3	132551	Robert Price	05/2019
2085	(2^440399-1)/(1621082028116197820931518475633880799)	132538	Dario Alpern	01/2015
2086	(38^83891+1)/39	132529	Robert Price	09/2013
2087	2*10^132493-43	132494	Robert Price	04/2018
2088	2^439931-21	132433	Lelio R Paula	08/2017
2089	47^79201-46^79201	132432	Robert Price	10/2012
2090	2^439897-113653	132423	Enzo Doria	08/2014
2091	(5*2^439822+1)/9	132400	Lelio R Paula	06/2015
2092	(112*10^132337-1)/3	132339	Serge Batalov	12/2014
2093	2^439576-113247	132326	Enzo Doria	07/2014
2094	2^439497-29143	132302	Enzo Doria	07/2015
2095	2^439409-114193	132276	Enzo Doria	12/2014
2096	(44*10^132233-233)/9	132234	Robert Price	01/2019
2097	9*10^132148-7	132149	Robert Price	09/2015
2098	(47*10^132125-119)/9	132126	Robert Price	05/2019
2099	2^438845+1870217	132106	Enzo Doria	05/2016
2100	2^438789+87855	132089	Lelio R Paula	01/2016
2101	2^438774-2786411	132085	Enzo Doria	03/2016
2102	2^438755-1848205	132079	Enzo Doria	07/2015
2103	2^438739-112087	132074	Enzo Doria	06/2014
2104	13907#+(318259#)/(13907#)	131923	Makoto Morimoto	10/2017
2105	L(631181)	131910	Henri Lifchitz	09/2008
2106	(47*10^131886-119)/9	131887	Robert Price	05/2019
2107	(3*2^438121+1)/4308193883	131879	Lelio R Paula	06/2015
2108	2^438079-1863877	131875	Enzo Doria	03/2016
2109	(2^438067+5)/329	131869	Lelio R Paula	06/2015
2110	2^437908-113855	131824	Enzo Doria	09/2014
2111	2^437884-286349	131817	Enzo Doria	07/2015
2112	(11*10^131784-17)/3	131785	Robert Price	06/2018
2113	3^276062-112292	131716	Enzo Doria	07/2014
2114	2^437343+75953	131654	Enzo Doria	04/2016
2115	35^85243-34^85243	131621	Robert Price	05/2012
2116	(68^71713+1)/69	131413	Paul Bourdelais	09/2017
2117	2^436451+1884713	131385	Enzo Doria	03/2017
2118	2^436365+35	131359	Robert Price	11/2015
2119	2^436300+1866871	131340	Enzo Doria	03/2016
2120	(7*10^131339+179)/3	131340	Robert Price	09/2018
2121	(37*10^131270+341)/9	131271	Robert Price	08/2018
2122	(5*10^131223-29)/3	131224	Robert Price	03/2018
2123	(23*2^435891-1)/699	131215	Lelio R Paula	07/2015
2124	(11*2^435879+1)/3337	131211	Lelio R Paula	06/2015
2126	(2^435808+1)/641/6700417	131182	Lelio R Paula	02/2012
2125	(2^435808+1)/4294967297	131182	Serge Batalov	12/2016
2129	2^435773+1875557	131181	Enzo Doria	06/2016
2128	(16*10^131180+167)/3	131181	Robert Price	06/2019
2127	(26*10^131180-77)/3	131181	Robert Price	11/2019
2130	(25*10^131144-7)/9	131145	Robert Price	05/2018
2131	2^435612-2789939	131133	Enzo Doria	12/2015
2132	66^72047-65^72047	131093	Robert Price	09/2013
2133	(5*10^131090+37)/3	131091	Robert Price	03/2018
2134	2^435468+75631	131089	Enzo Doria	04/2016
2135	37^83588-2	131083	Lelio R Paula	08/2015
2136	(4^217720+11)/3	131081	Robert Price	02/2017
2137	2^435202-113193	131009	Enzo Doria	07/2014
2138	9*10^130998-19	130999	Robert Price	07/2019
2139	floor((sqrt(5)-1)/2*10^130911)	130911	Serge Batalov	06/2017
2140	2^434835-111937	130899	Enzo Doria	05/2014
2141	2^434685+72257	130854	Enzo Doria	04/2016
2142	(7*10^130825+113)/3	130826	Robert Price	02/2018
2143	2^434539-29317	130810	Enzo Doria	07/2015
2144	2^434469-114259	130789	Enzo Doria	01/2015
2145	2^434246+33	130722	Robert Price	11/2015
2146	2^433911-91	130621	Lelio R Paula	06/2017
2147	2^433744-114419	130570	Enzo Doria	02/2015
2149	2^433708+1869451	130560	Enzo Doria	05/2016
2148	2^433710+93	130560	Lelio R Paula	06/2017
2150	(29*2^433547-1)/27	130511	Lelio R Paula	06/2015
2151	4*10^130480+9	130481	Robert Price	05/2015
2152	(23*2^433449-1)/75	130481	Lelio R Paula	06/2015
2153	(23*2^433334-1)/3731	130445	Lelio R Paula	06/2015
2154	2^433023-113497	130353	Enzo Doria	08/2014
2155	2^433002+1179379	130347	Enzo Doria	06/2016
2156	2^432974+19	130339	Robert Price	08/2015
2157	(2^432457-1)/1672739247834685086279697	130159	Tony Prest / Never Odd Or Even	09/2013
2158	2^432217+41	130111	Lelio R Paula	06/2017
2159	(2^216089*(2^216091-1)-339)/25	130098	Makoto Morimoto	03/2017
2160	((2^216091+1066)^2+(2^216091+1066)+41)/47/2069	130095	Makoto Morimoto	05/2016
2161	97^65480-2	130094	Lelio R Paula	05/2017
2162	4*10^130088-89	130089	Robert Price	11/2018
2163	2^432117-113215	130081	Enzo Doria	07/2014
2164	2^431804+72511	129986	Enzo Doria	04/2016
2165	(3^272141-3^136071+1)/7	129844	Serge Batalov	03/2014
2166	(47*10^129789-119)/9	129790	Robert Price	05/2019
2167	(9*2^431141+1)/17	129787	Lelio R Paula	06/2015
2168	(29*2^430881-1)/21	129709	Lelio R Paula	06/2015
2169	2^430807+1869563	129686	Enzo Doria	05/2016
2170	2^430721-21429	129660	Enzo Doria	07/2013
2171	2^430415-276271	129568	Enzo Doria	07/2015
2172	2^430142-2791721	129486	Enzo Doria	03/2016
2173	(7*10^129472-13)/3	129473	Robert Price	07/2018
2174	2^429568-21017	129313	Enzo Doria	07/2013
2175	(11*10^129239-179)/3	129240	Robert Price	09/2018
2176	2^429194-112685	129201	Enzo Doria	06/2014
2177	2^429145-2780449	129186	Enzo Doria	04/2016
2178	2^428892-113453	129110	Enzo Doria	07/2014
2179	(11*2^428881-7)/15	129106	Renaud Lifchitz	03/2011
2180	2^428727-113959	129060	Enzo Doria	10/2014
2181	(7*2^428725-1)/13	129059	Lelio R Paula	05/2014
2182	(10^129051-31)/3	129051	Serge Batalov	12/2014
2183	2^428564+71161	129011	Enzo Doria	04/2016
2184	2^428502-113285	128992	Enzo Doria	07/2014
2185	2^428421-21373	128968	Enzo Doria	06/2013
2186	L(616787)	128901	Henri Lifchitz	09/2008
2187	91^65772-2	128851	Lelio R Paula	05/2017
2188	2^428022+43	128848	Lelio R Paula	05/2017
2189	2^427999-459397	128841	Enzo Doria	05/2015
2190	2^427993+76847	128839	Enzo Doria	05/2016
2191	2^427824-1851507	128788	Enzo Doria	08/2015
2192	2^427807-21469	128783	Enzo Doria	07/2013
2193	11^123594-240	128710	Enzo Doria	09/2012
2194	2^427504-21503	128692	Enzo Doria	07/2013
2195	2^427420+91	128667	Lelio R Paula	05/2017
2196	(68*10^128645-257)/9	128646	Robert Price	07/2019
2197	2^427269-113635	128621	Enzo Doria	08/2014
2198	2^427130+1877569	128579	Enzo Doria	08/2016
2199	2^427016-115349	128545	Enzo Doria	07/2015
2200	(4*10^128510+137)/3	128511	Robert Price	03/2018
2201	2^426889-112879	128507	Enzo Doria	06/2014
2202	2^426804+1869931	128481	Enzo Doria	05/2016
2203	2^426750+77635	128465	Enzo Doria	05/2016
2204	2^426425-91	128367	Lelio R Paula	05/2017
2205	(15*2^426398-1)/11	128359	Lelio R Paula	05/2014
2206	2^426352+74971	128345	Enzo Doria	04/2016
2207	4*10^128343-21	128344	Robert Price	09/2018
2208	2^426300-1863689	128330	Enzo Doria	03/2016
2209	2^426293+1881017	128327	Enzo Doria	11/2016
2210	2^426043+35	128252	Robert Price	11/2015
2211	(4*10^128244-19)/3	128245	Robert Price	03/2018
2212	2^425808-459959	128181	Enzo Doria	06/2015
2213	2^425627-113605	128127	Enzo Doria	08/2014
2214	(22*10^128094+53)/3	128095	Robert Price	07/2019
2215	(86*10^128086-221)/9	128087	Robert Price	09/2019
2216	18565^30002-30002^18565	128070	Norbert Schneider	01/2015
2217	(2^425287-9)/2737	128021	Lelio R Paula	05/2015
2218	(3*2^425233-1)/25	128007	Lelio R Paula	05/2014
2219	2^425205+4911	128000	Marek Hubal	02/2017
2220	2^425118-113663	127974	Enzo Doria	08/2014
2221	2^425061+1869761	127957	Enzo Doria	05/2016
2222	746^44541+44541^746	127955	Norbert Schneider	07/2019
2223	2^424918-21141	127914	Enzo Doria	07/2013
2224	2^424864-29489	127897	Enzo Doria	08/2015
2225	(97*10^127858-1)/3	127860	Serge Batalov	12/2014
2226	2^424632-2786639	127827	Enzo Doria	03/2016
2227	2^424577-113755	127811	Enzo Doria	09/2014
2228	(7*2^424512-1)/3	127792	Lelio R Paula	05/2014
2229	(56*10^127752+691)/9	127753	Robert Price	05/2019
2230	11^122629-720	127705	Enzo Doria	11/2012
2231	2^423696-21429	127546	Enzo Doria	07/2013
2232	2^423664-1864559	127536	Enzo Doria	03/2016
2233	3^267267-4	127519	Henri Lifchitz	10/2014
2234	(19^99689+5^99689)/24	127477	Robert Price	09/2013
2235	(21*2^423372+1)/101	127447	Lelio R Paula	05/2014
2236	2^423328-21537	127435	Enzo Doria	07/2013
2237	(2^423165-7)/25	127384	Lelio R Paula	05/2015
2238	(F(5)^182099-F(4)^182099)/F(3)	127282	Wayne Halsdorf	08/2013
2239	(16*10^127259+197)/3	127260	Robert Price	04/2019
2240	(26*10^127240+61)/3	127241	Robert Price	10/2019
2241	(234483*27^88884-145)/26	127230	Curtis Bright	05/2015
2242	2^422515-114997	127190	Enzo Doria	06/2015
2243	5*10^127179-3	127180	Robert Price	07/2015
2244	(44*10^127169-233)/9	127170	Robert Price	01/2019
2245	5*10^127153+77	127154	Robert Price	12/2018
2246	736^44335+44335^736	127104	Norbert Schneider	07/2019
2247	-516776642557847117490*Bern(37960)/34256837217082767928421792453	127042	Thomas Ritschel	06/2017
2248	(78^67141-1)/77	127036	Paul Bourdelais	09/2017
2249	2^421860-113285	126993	Enzo Doria	07/2014
2250	(2^421827-7)/11	126982	Lelio R Paula	05/2015

Find by discoverer :

PRP Records

Probable Primes Top 10000

(255312 PRPs in the top)