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 (> 30000)	Who ?	When ?
1751	2^441330+1871959	132854	Enzo Doria	05/2016
1752	2^441063+383	132774	Lelio R Paula	06/2012
1753	2^440846+1870909	132708	Enzo Doria	05/2016
1754	2^440656-113489	132651	Enzo Doria	08/2014
1755	numbpart(14180123587)	132646	Serge Batalov	04/2017
1756	(2^440399-1)/(1621082028116197820931518475633880799)	132538	Dario Alpern	01/2015
1757	(38^83891+1)/39	132529	Robert Price	09/2013
1758	2*10^132493-43	132494	Robert Price	04/2018
1759	2^439931-21	132433	Lelio R Paula	08/2017
1760	47^79201-46^79201	132432	Robert Price	10/2012
1761	2^439897-113653	132423	Enzo Doria	08/2014
1762	(5*2^439822+1)/9	132400	Lelio R Paula	06/2015
1763	(112*10^132337-1)/3	132339	Serge Batalov	12/2014
1764	2^439576-113247	132326	Enzo Doria	07/2014
1765	2^439497-29143	132302	Enzo Doria	07/2015
1766	2^439409-114193	132276	Enzo Doria	12/2014
1767	9*10^132148-7	132149	Robert Price	09/2015
1768	2^438845+1870217	132106	Enzo Doria	05/2016
1769	2^438789+87855	132089	Lelio R Paula	01/2016
1770	2^438774-2786411	132085	Enzo Doria	03/2016
1771	2^438755-1848205	132079	Enzo Doria	07/2015
1772	2^438739-112087	132074	Enzo Doria	06/2014
1773	13907#+(318259#)/(13907#)	131923	Makoto Morimoto	10/2017
1774	L(631181)	131910	Henri Lifchitz	09/2008
1775	(3*2^438121+1)/4308193883	131879	Lelio R Paula	06/2015
1776	2^438079-1863877	131875	Enzo Doria	03/2016
1777	(2^438067+5)/329	131869	Lelio R Paula	06/2015
1778	2^437908-113855	131824	Enzo Doria	09/2014
1779	2^437884-286349	131817	Enzo Doria	07/2015
1780	(11*10^131784-17)/3	131785	Robert Price	06/2018
1781	3^276062-112292	131716	Enzo Doria	07/2014
1782	2^437343+75953	131654	Enzo Doria	04/2016
1783	35^85243-34^85243	131621	Robert Price	05/2012
1784	(68^71713+1)/69	131413	Paul Bourdelais	09/2017
1785	2^436451+1884713	131385	Enzo Doria	03/2017
1786	2^436365+35	131359	Robert Price	11/2015
1787	2^436300+1866871	131340	Enzo Doria	03/2016
1788	(5*10^131223-29)/3	131224	Robert Price	03/2018
1789	(23*2^435891-1)/699	131215	Lelio R Paula	07/2015
1790	(11*2^435879+1)/3337	131211	Lelio R Paula	06/2015
1791	(2^435808+1)/641/6700417	131182	Lelio R Paula	02/2012
1792	(2^435808+1)/4294967297	131182	Serge Batalov	12/2016
1793	2^435773+1875557	131181	Enzo Doria	06/2016
1794	(25*10^131144-7)/9	131145	Robert Price	05/2018
1795	2^435612-2789939	131133	Enzo Doria	12/2015
1796	66^72047-65^72047	131093	Robert Price	09/2013
1797	(5*10^131090+37)/3	131091	Robert Price	03/2018
1798	2^435468+75631	131089	Enzo Doria	04/2016
1799	37^83588-2	131083	Lelio R Paula	08/2015
1800	(4^217720+11)/3	131081	Robert Price	02/2017
1801	2^435202-113193	131009	Enzo Doria	07/2014
1802	floor((sqrt(5)-1)/2*10^130911)	130911	Serge Batalov	06/2017
1803	2^434835-111937	130899	Enzo Doria	05/2014
1804	2^434685+72257	130854	Enzo Doria	04/2016
1805	(7*10^130825+113)/3	130826	Robert Price	02/2018
1806	2^434539-29317	130810	Enzo Doria	07/2015
1807	2^434469-114259	130789	Enzo Doria	01/2015
1808	2^434246+33	130722	Robert Price	11/2015
1809	2^433911-91	130621	Lelio R Paula	06/2017
1810	2^433744-114419	130570	Enzo Doria	02/2015
1812	2^433708+1869451	130560	Enzo Doria	05/2016
1811	2^433710+93	130560	Lelio R Paula	06/2017
1813	(29*2^433547-1)/27	130511	Lelio R Paula	06/2015
1814	4*10^130480+9	130481	Robert Price	05/2015
1815	(23*2^433449-1)/75	130481	Lelio R Paula	06/2015
1816	(23*2^433334-1)/3731	130445	Lelio R Paula	06/2015
1817	2^433023-113497	130353	Enzo Doria	08/2014
1818	2^433002+1179379	130347	Enzo Doria	06/2016
1819	2^432974+19	130339	Robert Price	08/2015
1820	(2^432457-1)/1672739247834685086279697	130159	Tony Prest / Never Odd Or Even	09/2013
1821	2^432217+41	130111	Lelio R Paula	06/2017
1822	(2^216089*(2^216091-1)-339)/25	130098	Makoto Morimoto	03/2017
1823	((2^216091+1066)^2+(2^216091+1066)+41)/47/2069	130095	Makoto Morimoto	05/2016
1824	97^65480-2	130094	Lelio R Paula	05/2017
1825	2^432117-113215	130081	Enzo Doria	07/2014
1826	2^431804+72511	129986	Enzo Doria	04/2016
1827	(3^272141-3^136071+1)/7	129844	Serge Batalov	03/2014
1828	(9*2^431141+1)/17	129787	Lelio R Paula	06/2015
1829	(29*2^430881-1)/21	129709	Lelio R Paula	06/2015
1830	2^430807+1869563	129686	Enzo Doria	05/2016
1831	2^430721-21429	129660	Enzo Doria	07/2013
1832	2^430415-276271	129568	Enzo Doria	07/2015
1833	2^430142-2791721	129486	Enzo Doria	03/2016
1834	2^429568-21017	129313	Enzo Doria	07/2013
1835	2^429194-112685	129201	Enzo Doria	06/2014
1836	2^429145-2780449	129186	Enzo Doria	04/2016
1837	2^428892-113453	129110	Enzo Doria	07/2014
1838	(11*2^428881-7)/15	129106	Renaud Lifchitz	03/2011
1839	2^428727-113959	129060	Enzo Doria	10/2014
1840	(7*2^428725-1)/13	129059	Lelio R Paula	05/2014
1841	(10^129051-31)/3	129051	Serge Batalov	12/2014
1842	2^428564+71161	129011	Enzo Doria	04/2016
1843	2^428502-113285	128992	Enzo Doria	07/2014
1844	2^428421-21373	128968	Enzo Doria	06/2013
1845	L(616787)	128901	Henri Lifchitz	09/2008
1846	91^65772-2	128851	Lelio R Paula	05/2017
1847	2^428022+43	128848	Lelio R Paula	05/2017
1848	2^427999-459397	128841	Enzo Doria	05/2015
1849	2^427993+76847	128839	Enzo Doria	05/2016
1850	2^427824-1851507	128788	Enzo Doria	08/2015
1851	2^427807-21469	128783	Enzo Doria	07/2013
1852	11^123594-240	128710	Enzo Doria	09/2012
1853	2^427504-21503	128692	Enzo Doria	07/2013
1854	2^427420+91	128667	Lelio R Paula	05/2017
1855	2^427269-113635	128621	Enzo Doria	08/2014
1856	2^427130+1877569	128579	Enzo Doria	08/2016
1857	2^427016-115349	128545	Enzo Doria	07/2015
1858	(4*10^128510+137)/3	128511	Robert Price	03/2018
1859	2^426889-112879	128507	Enzo Doria	06/2014
1860	2^426804+1869931	128481	Enzo Doria	05/2016
1861	2^426750+77635	128465	Enzo Doria	05/2016
1862	2^426425-91	128367	Lelio R Paula	05/2017
1863	(15*2^426398-1)/11	128359	Lelio R Paula	05/2014
1864	2^426352+74971	128345	Enzo Doria	04/2016
1865	2^426300-1863689	128330	Enzo Doria	03/2016
1866	2^426293+1881017	128327	Enzo Doria	11/2016
1867	2^426043+35	128252	Robert Price	11/2015
1868	(4*10^128244-19)/3	128245	Robert Price	03/2018
1869	2^425808-459959	128181	Enzo Doria	06/2015
1870	2^425627-113605	128127	Enzo Doria	08/2014
1871	18565^30002-30002^18565	128070	Norbert Schneider	01/2015
1872	(2^425287-9)/2737	128021	Lelio R Paula	05/2015
1873	(3*2^425233-1)/25	128007	Lelio R Paula	05/2014
1874	2^425205+4911	128000	Marek Hubal	02/2017
1875	2^425118-113663	127974	Enzo Doria	08/2014
1876	2^425061+1869761	127957	Enzo Doria	05/2016
1877	2^424918-21141	127914	Enzo Doria	07/2013
1878	2^424864-29489	127897	Enzo Doria	08/2015
1879	(97*10^127858-1)/3	127860	Serge Batalov	12/2014
1880	2^424632-2786639	127827	Enzo Doria	03/2016
1881	2^424577-113755	127811	Enzo Doria	09/2014
1882	(7*2^424512-1)/3	127792	Lelio R Paula	05/2014
1883	11^122629-720	127705	Enzo Doria	11/2012
1884	2^423696-21429	127546	Enzo Doria	07/2013
1885	2^423664-1864559	127536	Enzo Doria	03/2016
1886	3^267267-4	127519	Henri Lifchitz	10/2014
1887	(19^99689+5^99689)/24	127477	Robert Price	09/2013
1888	(21*2^423372+1)/101	127447	Lelio R Paula	05/2014
1889	2^423328-21537	127435	Enzo Doria	07/2013
1890	(2^423165-7)/25	127384	Lelio R Paula	05/2015
1891	(F(5)^182099-F(4)^182099)/F(3)	127282	Wayne Halsdorf	08/2013
1892	(234483*27^88884-145)/26	127230	Curtis Bright	05/2015
1893	2^422515-114997	127190	Enzo Doria	06/2015
1894	5*10^127179-3	127180	Robert Price	07/2015
1895	-516776642557847117490*Bern(37960)/34256837217082767928421792453	127042	Thomas Ritschel	06/2017
1896	(78^67141-1)/77	127036	Paul Bourdelais	09/2017
1897	2^421860-113285	126993	Enzo Doria	07/2014
1898	(2^421827-7)/11	126982	Lelio R Paula	05/2015
1899	11^121910-840	126957	Enzo Doria	12/2012
1900	(71^68539+1)/72	126882	Paul Bourdelais	09/2017
1901	(5*10^126871-119)/3	126872	Robert Price	03/2018
1902	331^50339-10004	126846	Enzo Doria	07/2012
1903	2^421363-2790757	126843	Enzo Doria	03/2016
1904	(106*10^126839-1)/3	126841	Serge Batalov	12/2014
1905	(7*2^421243+1)/39	126807	Lelio R Paula	05/2014
1906	2^421161-286183	126783	Enzo Doria	06/2015
1907	2^420939-113935	126716	Enzo Doria	10/2014
1908	177^56363-2	126703	Lelio R Paula	10/2017
1909	2^420741-113659	126656	Enzo Doria	08/2014
1910	2^420694-21	126642	Lelio R Paula	05/2017
1911	(13*10^126638+437)/9	126639	Robert Price	04/2018
1912	(31*2^420556+1)/7	126601	Lelio R Paula	05/2014
1913	2^420424-59189	126561	Enzo Doria	10/2015
1914	2^420126+71893	126471	Enzo Doria	04/2016
1915	2^419866+1877059	126393	Enzo Doria	07/2016
1916	F(604711)	126377	Henri Lifchitz	02/2005
1917	2^419757+72707	126360	Enzo Doria	04/2016
1918	2^419720-21569	126349	Enzo Doria	07/2013
1919	2^419637+29	126324	Henri Lifchitz	02/2006
1920	2^419612+1876741	126316	Enzo Doria	07/2016
1921	2^419520+2793271	126289	Enzo Doria	03/2016
1922	(2^419447-5)/369	126264	Lelio R Paula	05/2014
1923	2^419328-1859939	126231	Enzo Doria	03/2016
1924	2^419282-1851507	126217	Enzo Doria	08/2015
1925	2^419251+1866143	126208	Enzo Doria	03/2016
1926	11^121185+2	126202	Robert Price	05/2014
1927	(23*2^419036-1)/1393	126141	Lelio R Paula	05/2014
1928	2^418851+23	126087	Robert Price	09/2015
1929	(2^418849-9)/2681	126083	Lelio R Paula	05/2014
1930	2^418829+167	126081	Lelio R Paula	01/2012
1931	(31*2^418782-1)/75891	126063	Lelio R Paula	05/2014
1932	(19*2^418754-1)/15	126058	Lelio R Paula	05/2014
1933	2^418319-109501	125927	Enzo Doria	04/2014
1934	2^418316-112373	125926	Enzo Doria	06/2014
1935	(26*10^125886-413)/9	125887	Robert Price	05/2018
1936	2^417968+1869811	125821	Enzo Doria	06/2016
1937	2^417902+63	125802	Lelio R Paula	09/2015
1938	(10^125792-91)/9	125792	Serge Batalov	12/2014
1939	(32*10^125751-77)/9	125752	Robert Price	06/2018
1940	2^417704+77011	125742	Enzo Doria	05/2016
1941	(10^125706+149)/3	125706	Serge Batalov	12/2014
1942	2^417419-115309	125656	Enzo Doria	07/2015
1943	2^417300+77281	125620	Enzo Doria	05/2016
1944	2^417095-1657	125559	Yves Minet	07/2014
1945	2^416773-25	125462	Lelio R Paula	09/2015
1946	(289511#+292834)/(2^3*146417)	125444	Makoto Morimoto	10/2017
1947	(11*2^416691+1)/43	125436	Lelio R Paula	05/2014
1948	2^416641-2*416641+1	125422	Robert Price	05/2018
1949	(21*2^416566-1)/17	125399	Lelio R Paula	05/2014
1950	2^416530+1870429	125389	Enzo Doria	05/2016
1951	2^416490+1875109	125376	Enzo Doria	09/2016
1952	2^416416-114929	125354	Enzo Doria	05/2015
1953	(172*10^125292-1)/9	125294	Serge Batalov	12/2014
1954	2^416134+1865899	125269	Enzo Doria	03/2016
1955	(9*2^415992+1)/13560845	125220	Lelio R Paula	05/2014
1956	(23^91943-1)/22	125201	Robert Price	01/2012
1957	43125^27010-106	125185	Enzo Doria	08/2012
1958	2^415765-112603	125158	Enzo Doria	06/2014
1959	2^415290-113591	125015	Enzo Doria	08/2014
1960	2^415276-460919	125011	Enzo Doria	06/2015
1961	2^415259+77243	125006	Enzo Doria	05/2016
1962	2^415144-3683	124971	Yves Minet	10/2011
1963	2^414874+79	124890	Lelio R Paula	01/2015
1964	(2^414765+7)/1389	124854	Lelio R Paula	05/2014
1965	2^414618+79459	124813	Enzo Doria	06/2016
1966	2^414432-1846709	124757	Enzo Doria	07/2015
1967	2*10^124751-51	124752	Robert Price	04/2018
1968	(13*2^414274-1)/153	124708	Lelio R Paula	05/2014
1970	2^414032-5	124637	Henri Lifchitz	07/2006
1969	2^414032+1872331	124637	Enzo Doria	05/2016
1971	14120^30009-30009^14120	124533	Norbert Schneider	02/2015
1972	64^68909-63^68909	124463	Robert Price	07/2013
1973	2^413387+76253	124442	Enzo Doria	04/2016
1974	287117#+391613	124424	Nicolas PALAU	01/2017
1975	(4*10^124420+83)/3	124421	Robert Price	02/2018
1976	(27*2^413207-1)/108335	124385	Lelio R Paula	05/2014
1977	2^412868-120599	124286	Paul Bourdelais	02/2012
1978	45^75145-2	124231	Lelio R Paula	08/2015
1979	2^412645-112213	124219	Enzo Doria	06/2014
1980	2^412248+74611	124100	Enzo Doria	04/2016
1981	(22*10^124096-13)/9	124097	Robert Price	06/2018
1982	2^412192-3329	124083	Yves Minet	12/2014
1983	(25*2^412191-1)/23	124082	Lelio R Paula	05/2014
1984	F(593689)	124074	Henri Lifchitz	01/2005
1985	(11*2^412161+1)/19	124073	Lelio R Paula	05/2014
1986	2^411884-113279	123990	Enzo Doria	07/2014
1987	(2^411832+1)/257	123972	Lelio R Paula	05/2014
1988	(26*10^123970-89)/9	123971	Robert Price	06/2018
1989	2^411790-1853531	123962	Enzo Doria	08/2015
1990	(5^177337+1)/6	123953	Paul Bourdelais	11/2008
1991	2^411711-113257	123938	Enzo Doria	07/2014
1992	(23*2^411675-1)/3	123928	Lelio R Paula	05/2014
1993	2^411325-351103	123822	Enzo Doria	06/2015
1994	2^411052+1872481	123739	Enzo Doria	05/2016
1995	2^410997+39	123723	Lelio R Paula	05/2014
1996	2^410596-39	123602	Lelio R Paula	05/2014
1997	2^410540-115079	123585	Enzo Doria	06/2015
1998	(7*10^123563+107)/3	123564	Robert Price	02/2018
1999	(3*2^410392-1)/9229	123537	Lelio R Paula	05/2014
2000	2^410206-113081	123485	Enzo Doria	07/2014

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PRP Records

Probable Primes Top 10000

(212140 PRPs in the top)