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	(11*2^435879+1)/3337	131211	Lelio R Paula	06/2015
1753	(2^435808+1)/641/6700417	131182	Lelio R Paula	02/2012
1752	(2^435808+1)/4294967297	131182	Serge Batalov	12/2016
1754	2^435773+1875557	131181	Enzo Doria	06/2016
1755	2^435612-2789939	131133	Enzo Doria	12/2015
1756	66^72047-65^72047	131093	Robert Price	09/2013
1757	(5*10^131090+37)/3	131091	Robert Price	03/2018
1758	2^435468+75631	131089	Enzo Doria	04/2016
1759	37^83588-2	131083	Lelio R Paula	08/2015
1760	(4^217720+11)/3	131081	Robert Price	02/2017
1761	2^435202-113193	131009	Enzo Doria	07/2014
1762	floor((sqrt(5)-1)/2*10^130911)	130911	Serge Batalov	06/2017
1763	2^434835-111937	130899	Enzo Doria	05/2014
1764	2^434685+72257	130854	Enzo Doria	04/2016
1765	(7*10^130825+113)/3	130826	Robert Price	02/2018
1766	2^434539-29317	130810	Enzo Doria	07/2015
1767	2^434469-114259	130789	Enzo Doria	01/2015
1768	2^434246+33	130722	Robert Price	11/2015
1769	2^433911-91	130621	Lelio R Paula	06/2017
1770	2^433744-114419	130570	Enzo Doria	02/2015
1771	2^433708+1869451	130560	Enzo Doria	05/2016
1772	2^433710+93	130560	Lelio R Paula	06/2017
1773	(29*2^433547-1)/27	130511	Lelio R Paula	06/2015
1774	4*10^130480+9	130481	Robert Price	05/2015
1775	(23*2^433449-1)/75	130481	Lelio R Paula	06/2015
1776	(23*2^433334-1)/3731	130445	Lelio R Paula	06/2015
1777	2^433023-113497	130353	Enzo Doria	08/2014
1778	2^433002+1179379	130347	Enzo Doria	06/2016
1779	2^432974+19	130339	Robert Price	08/2015
1780	(2^432457-1)/1672739247834685086279697	130159	Tony Prest / Never Odd Or Even	09/2013
1781	2^432217+41	130111	Lelio R Paula	06/2017
1782	(2^216089*(2^216091-1)-339)/25	130098	Makoto Morimoto	03/2017
1783	((2^216091+1066)^2+(2^216091+1066)+41)/47/2069	130095	Makoto Morimoto	05/2016
1784	97^65480-2	130094	Lelio R Paula	05/2017
1785	2^432117-113215	130081	Enzo Doria	07/2014
1786	2^431804+72511	129986	Enzo Doria	04/2016
1787	(3^272141-3^136071+1)/7	129844	Serge Batalov	03/2014
1788	(9*2^431141+1)/17	129787	Lelio R Paula	06/2015
1789	(29*2^430881-1)/21	129709	Lelio R Paula	06/2015
1790	2^430807+1869563	129686	Enzo Doria	05/2016
1791	2^430721-21429	129660	Enzo Doria	07/2013
1792	2^430415-276271	129568	Enzo Doria	07/2015
1793	2^430142-2791721	129486	Enzo Doria	03/2016
1794	2^429568-21017	129313	Enzo Doria	07/2013
1795	2^429194-112685	129201	Enzo Doria	06/2014
1796	2^429145-2780449	129186	Enzo Doria	04/2016
1797	2^428892-113453	129110	Enzo Doria	07/2014
1798	(11*2^428881-7)/15	129106	Renaud Lifchitz	03/2011
1799	2^428727-113959	129060	Enzo Doria	10/2014
1800	(7*2^428725-1)/13	129059	Lelio R Paula	05/2014
1801	(10^129051-31)/3	129051	Serge Batalov	12/2014
1802	2^428564+71161	129011	Enzo Doria	04/2016
1803	2^428502-113285	128992	Enzo Doria	07/2014
1804	2^428421-21373	128968	Enzo Doria	06/2013
1805	L(616787)	128901	Henri Lifchitz	09/2008
1806	91^65772-2	128851	Lelio R Paula	05/2017
1807	2^428022+43	128848	Lelio R Paula	05/2017
1808	2^427999-459397	128841	Enzo Doria	05/2015
1809	2^427993+76847	128839	Enzo Doria	05/2016
1810	2^427824-1851507	128788	Enzo Doria	08/2015
1811	2^427807-21469	128783	Enzo Doria	07/2013
1812	11^123594-240	128710	Enzo Doria	09/2012
1813	2^427504-21503	128692	Enzo Doria	07/2013
1814	2^427420+91	128667	Lelio R Paula	05/2017
1815	2^427269-113635	128621	Enzo Doria	08/2014
1816	2^427130+1877569	128579	Enzo Doria	08/2016
1817	2^427016-115349	128545	Enzo Doria	07/2015
1818	(4*10^128510+137)/3	128511	Robert Price	03/2018
1819	2^426889-112879	128507	Enzo Doria	06/2014
1820	2^426804+1869931	128481	Enzo Doria	05/2016
1821	2^426750+77635	128465	Enzo Doria	05/2016
1822	2^426425-91	128367	Lelio R Paula	05/2017
1823	(15*2^426398-1)/11	128359	Lelio R Paula	05/2014
1824	2^426352+74971	128345	Enzo Doria	04/2016
1825	2^426300-1863689	128330	Enzo Doria	03/2016
1826	2^426293+1881017	128327	Enzo Doria	11/2016
1827	2^426043+35	128252	Robert Price	11/2015
1828	(4*10^128244-19)/3	128245	Robert Price	03/2018
1829	2^425808-459959	128181	Enzo Doria	06/2015
1830	2^425627-113605	128127	Enzo Doria	08/2014
1831	18565^30002-30002^18565	128070	Norbert Schneider	01/2015
1832	(2^425287-9)/2737	128021	Lelio R Paula	05/2015
1833	(3*2^425233-1)/25	128007	Lelio R Paula	05/2014
1834	2^425205+4911	128000	Marek Hubal	02/2017
1835	2^425118-113663	127974	Enzo Doria	08/2014
1836	2^425061+1869761	127957	Enzo Doria	05/2016
1837	2^424918-21141	127914	Enzo Doria	07/2013
1838	2^424864-29489	127897	Enzo Doria	08/2015
1839	(97*10^127858-1)/3	127860	Serge Batalov	12/2014
1840	2^424632-2786639	127827	Enzo Doria	03/2016
1841	2^424577-113755	127811	Enzo Doria	09/2014
1842	(7*2^424512-1)/3	127792	Lelio R Paula	05/2014
1843	11^122629-720	127705	Enzo Doria	11/2012
1844	2^423696-21429	127546	Enzo Doria	07/2013
1845	2^423664-1864559	127536	Enzo Doria	03/2016
1846	3^267267-4	127519	Henri Lifchitz	10/2014
1847	(19^99689+5^99689)/24	127477	Robert Price	09/2013
1848	(21*2^423372+1)/101	127447	Lelio R Paula	05/2014
1849	2^423328-21537	127435	Enzo Doria	07/2013
1850	(2^423165-7)/25	127384	Lelio R Paula	05/2015
1851	(F(5)^182099-F(4)^182099)/F(3)	127282	Wayne Halsdorf	08/2013
1852	(234483*27^88884-145)/26	127230	Curtis Bright	05/2015
1853	2^422515-114997	127190	Enzo Doria	06/2015
1854	5*10^127179-3	127180	Robert Price	07/2015
1855	-516776642557847117490*Bern(37960)/34256837217082767928421792453	127042	Thomas Ritschel	06/2017
1856	(78^67141-1)/77	127036	Paul Bourdelais	09/2017
1857	2^421860-113285	126993	Enzo Doria	07/2014
1858	(2^421827-7)/11	126982	Lelio R Paula	05/2015
1859	11^121910-840	126957	Enzo Doria	12/2012
1860	(71^68539+1)/72	126882	Paul Bourdelais	09/2017
1861	(5*10^126871-119)/3	126872	Robert Price	03/2018
1862	331^50339-10004	126846	Enzo Doria	07/2012
1863	2^421363-2790757	126843	Enzo Doria	03/2016
1864	(106*10^126839-1)/3	126841	Serge Batalov	12/2014
1865	(7*2^421243+1)/39	126807	Lelio R Paula	05/2014
1866	2^421161-286183	126783	Enzo Doria	06/2015
1867	2^420939-113935	126716	Enzo Doria	10/2014
1868	177^56363-2	126703	Lelio R Paula	10/2017
1869	2^420741-113659	126656	Enzo Doria	08/2014
1870	2^420694-21	126642	Lelio R Paula	05/2017
1871	(13*10^126638+437)/9	126639	Robert Price	04/2018
1872	(31*2^420556+1)/7	126601	Lelio R Paula	05/2014
1873	2^420424-59189	126561	Enzo Doria	10/2015
1874	2^420126+71893	126471	Enzo Doria	04/2016
1875	2^419866+1877059	126393	Enzo Doria	07/2016
1876	F(604711)	126377	Henri Lifchitz	02/2005
1877	2^419757+72707	126360	Enzo Doria	04/2016
1878	2^419720-21569	126349	Enzo Doria	07/2013
1879	2^419637+29	126324	Henri Lifchitz	02/2006
1880	2^419612+1876741	126316	Enzo Doria	07/2016
1881	2^419520+2793271	126289	Enzo Doria	03/2016
1882	(2^419447-5)/369	126264	Lelio R Paula	05/2014
1883	2^419328-1859939	126231	Enzo Doria	03/2016
1884	2^419282-1851507	126217	Enzo Doria	08/2015
1885	2^419251+1866143	126208	Enzo Doria	03/2016
1886	11^121185+2	126202	Robert Price	05/2014
1887	(23*2^419036-1)/1393	126141	Lelio R Paula	05/2014
1888	2^418851+23	126087	Robert Price	09/2015
1889	(2^418849-9)/2681	126083	Lelio R Paula	05/2014
1890	2^418829+167	126081	Lelio R Paula	01/2012
1891	(31*2^418782-1)/75891	126063	Lelio R Paula	05/2014
1892	(19*2^418754-1)/15	126058	Lelio R Paula	05/2014
1893	2^418319-109501	125927	Enzo Doria	04/2014
1894	2^418316-112373	125926	Enzo Doria	06/2014
1895	2^417968+1869811	125821	Enzo Doria	06/2016
1896	2^417902+63	125802	Lelio R Paula	09/2015
1897	(10^125792-91)/9	125792	Serge Batalov	12/2014
1898	2^417704+77011	125742	Enzo Doria	05/2016
1899	(10^125706+149)/3	125706	Serge Batalov	12/2014
1900	2^417419-115309	125656	Enzo Doria	07/2015
1901	2^417300+77281	125620	Enzo Doria	05/2016
1902	2^417095-1657	125559	Yves Minet	07/2014
1903	2^416773-25	125462	Lelio R Paula	09/2015
1904	(289511#+292834)/(2^3*146417)	125444	Makoto Morimoto	10/2017
1905	(11*2^416691+1)/43	125436	Lelio R Paula	05/2014
1906	(21*2^416566-1)/17	125399	Lelio R Paula	05/2014
1907	2^416530+1870429	125389	Enzo Doria	05/2016
1908	2^416490+1875109	125376	Enzo Doria	09/2016
1909	2^416416-114929	125354	Enzo Doria	05/2015
1910	(172*10^125292-1)/9	125294	Serge Batalov	12/2014
1911	2^416134+1865899	125269	Enzo Doria	03/2016
1912	(9*2^415992+1)/13560845	125220	Lelio R Paula	05/2014
1913	(23^91943-1)/22	125201	Robert Price	01/2012
1914	43125^27010-106	125185	Enzo Doria	08/2012
1915	2^415765-112603	125158	Enzo Doria	06/2014
1916	2^415290-113591	125015	Enzo Doria	08/2014
1917	2^415276-460919	125011	Enzo Doria	06/2015
1918	2^415259+77243	125006	Enzo Doria	05/2016
1919	2^415144-3683	124971	Yves Minet	10/2011
1920	2^414874+79	124890	Lelio R Paula	01/2015
1921	(2^414765+7)/1389	124854	Lelio R Paula	05/2014
1922	2^414618+79459	124813	Enzo Doria	06/2016
1923	2^414432-1846709	124757	Enzo Doria	07/2015
1924	2*10^124751-51	124752	Robert Price	04/2018
1925	(13*2^414274-1)/153	124708	Lelio R Paula	05/2014
1927	2^414032-5	124637	Henri Lifchitz	07/2006
1926	2^414032+1872331	124637	Enzo Doria	05/2016
1928	14120^30009-30009^14120	124533	Norbert Schneider	02/2015
1929	64^68909-63^68909	124463	Robert Price	07/2013
1930	2^413387+76253	124442	Enzo Doria	04/2016
1931	287117#+391613	124424	Nicolas PALAU	01/2017
1932	(4*10^124420+83)/3	124421	Robert Price	02/2018
1933	(27*2^413207-1)/108335	124385	Lelio R Paula	05/2014
1934	2^412868-120599	124286	Paul Bourdelais	02/2012
1935	45^75145-2	124231	Lelio R Paula	08/2015
1936	2^412645-112213	124219	Enzo Doria	06/2014
1937	2^412248+74611	124100	Enzo Doria	04/2016
1938	2^412192-3329	124083	Yves Minet	12/2014
1939	(25*2^412191-1)/23	124082	Lelio R Paula	05/2014
1940	F(593689)	124074	Henri Lifchitz	01/2005
1941	(11*2^412161+1)/19	124073	Lelio R Paula	05/2014
1942	2^411884-113279	123990	Enzo Doria	07/2014
1943	(2^411832+1)/257	123972	Lelio R Paula	05/2014
1944	2^411790-1853531	123962	Enzo Doria	08/2015
1945	(5^177337+1)/6	123953	Paul Bourdelais	11/2008
1946	2^411711-113257	123938	Enzo Doria	07/2014
1947	(23*2^411675-1)/3	123928	Lelio R Paula	05/2014
1948	2^411325-351103	123822	Enzo Doria	06/2015
1949	2^411052+1872481	123739	Enzo Doria	05/2016
1950	2^410997+39	123723	Lelio R Paula	05/2014
1951	2^410596-39	123602	Lelio R Paula	05/2014
1952	2^410540-115079	123585	Enzo Doria	06/2015
1953	(7*10^123563+107)/3	123564	Robert Price	02/2018
1954	(3*2^410392-1)/9229	123537	Lelio R Paula	05/2014
1955	2^410206-113081	123485	Enzo Doria	07/2014
1956	(25*2^410192+1)/10397	123478	Lelio R Paula	04/2014
1957	2^409909-189	123395	Enzo Doria	05/2014
1958	2^409896-109043	123391	Enzo Doria	04/2014
1959	2^409890+75409	123390	Enzo Doria	04/2016
1960	133^58076-2	123345	Lelio R Paula	10/2017
1961	F(590041)	123311	Henri Lifchitz	01/2005
1962	2^409566-113501	123292	Enzo Doria	08/2014
1963	2^409533+77747	123282	Enzo Doria	05/2016
1964	2^409436-112799	123253	Enzo Doria	06/2014
1965	2^409225+1873787	123189	Enzo Doria	06/2016
1966	2^409174+73009	123174	Enzo Doria	04/2016
1967	2^409058-112685	123139	Enzo Doria	06/2014
1968	2^408778+77689	123055	Enzo Doria	05/2016
1969	2^408690-75	123028	Lelio R Paula	11/2013
1970	2^408574-2787341	122994	Enzo Doria	03/2016
1971	Phi(157825,10)	122961	Maksym Voznyy	06/2015
1972	(13*2^408283+1)/1665	122904	Lelio R Paula	05/2014
1973	(11*2^408100-1)/35	122850	Lelio R Paula	04/2014
1974	(2^407821-lucasV(1,2,407821)+1)/2	122767	Mike Oakes	11/2016
1975	(21*2^407604-1)/215	122701	Lelio R Paula	04/2014
1976	(21*2^407433-1)/13	122650	Lelio R Paula	04/2014
1977	(73*10^122592-1)/9	122593	Robert Price	01/2015
1978	2^407179-112075	122574	Enzo Doria	06/2014
1979	(21*2^407131+1)/207517523	122552	Lelio R Paula	04/2014
1980	(66^67349+1)/67	122543	Paul Bourdelais	09/2017
1981	2^407008-1867919	122522	Enzo Doria	04/2016
1982	11^117642-300	122512	Enzo Doria	10/2012
1983	(F(397700+1)^2+L(397700+1)^2)/2	122509	Henri Lifchitz	10/2017
1984	2^406949+72197	122504	Enzo Doria	04/2016
1985	2^406826-65	122467	Lelio R Paula	11/2013
1986	2^406821-2797363	122466	Enzo Doria	04/2016
1987	2^406758-17	122447	Lelio R Paula	11/2013
1988	(30^82883-1)/29	122427	Robert Price	12/2011
1989	(2^406583-1)/813167	122388	Jens K. Andersen	02/2009
1990	97^61575-2	122336	Lelio R Paula	12/2014
1991	2^406298+2799109	122308	Enzo Doria	04/2016
1992	(27*2^406241-1)/10277	122289	Lelio R Paula	04/2014
1993	2^406229-1849993	122288	Enzo Doria	08/2015
1994	3*10^122274+7	122275	Robert Price	07/2015
1995	2^406117+1876577	122254	Enzo Doria	07/2016
1996	3^256199-2^256199	122238	Mike Oakes	06/2005
1997	2^405992-78557	122216	Jorge Menendez	03/2018
1998	2^405774+179149	122151	Enzo Doria	06/2016
1999	2^405514-3311	122072	Yves Minet	12/2014
2000	2^405514-115511	122072	Enzo Doria	07/2015

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PRP Records

Probable Primes Top 10000

(205869 PRPs in the top)