|
François Proth
François Proth (22 March 1852 – 21 January 1879) was a French self-taught mathematician farmer who lived in Vaux-devant-Damloup near Verdun, France France, officially the French Republic, is a country located primarily in Western Europe. Overseas France, Its overseas regions and territories include French Guiana in South America, Saint Pierre and Miquelon in the Atlantic Ocean#North Atlan .... He stated four primality-related theorems. The most famous of these, Proth's theorem, can be used to test whether a Proth number (a number of the form ''k''2''n'' + 1 with ''k'' odd and ''k'' < 2''n'') is prime. The numbers passing this test are called Proth primes; they continue to be of importance in the computational search for large prime numbers. Proth also formulated [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vaux-devant-Damloup
Vaux-devant-Damloup (, literally ''Vaux before Damloup'') is a former commune in the Meuse department in Grand Est in north-eastern France. It had a population of 77 (2022). On 1 January 2019, it was merged into the new commune Douaumont-Vaux. 19 December 2018 is partially located within the territory of the commune (the other part is in Damloup). It was one of the French villages destroyed during World War I. The new villag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Verdun
Verdun ( , ; ; ; official name before 1970: Verdun-sur-Meuse) is a city in the Meuse (department), Meuse departments of France, department in Grand Est, northeastern France. It is an arrondissement of the department. In 843, the Treaty of Verdun, which divided the Carolingian Empire into three kingdoms—considered the foundation of Germany and France—was signed there. An episcopal principality of the Holy Roman Empire since the 10th century, Verdun was subjugated by France in 1552, during the "Voyage to Austrasia". Along with the other free cities of the Empire, Metz and Toul, it formed the province of the Three Bishoprics, which was attached to the Kingdom of France in 1648 by the Treaty of Münster (1648), Treaty of Münster. Verdun is the biggest city in Meuse, although the capital of the department is Bar-le-Duc, which is slightly smaller than Verdun. It is well known for giving Battle of Verdun, its name to the longest battle in modern history in the World War I, Fir ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
France
France, officially the French Republic, is a country located primarily in Western Europe. Overseas France, Its overseas regions and territories include French Guiana in South America, Saint Pierre and Miquelon in the Atlantic Ocean#North Atlantic, North Atlantic, the French West Indies, and List of islands of France, many islands in Oceania and the Indian Ocean, giving it Exclusive economic zone of France, one of the largest discontiguous exclusive economic zones in the world. Metropolitan France shares borders with Belgium and Luxembourg to the north; Germany to the northeast; Switzerland to the east; Italy and Monaco to the southeast; Andorra and Spain to the south; and a maritime border with the United Kingdom to the northwest. Its metropolitan area extends from the Rhine to the Atlantic Ocean and from the Mediterranean Sea to the English Channel and the North Sea. Its Regions of France, eighteen integral regions—five of which are overseas—span a combined area of and hav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proth's Theorem
In number theory, Proth's theorem is a theorem which forms the basis of a primality test for Proth numbers (sometimes called Proth Numbers of the First Kind). For ''Proth Numbers of the Second Kind'', see Riesel numbers. It states that for any integer ''p'' that is a Proth number (of the first kind) - an integer of the form ''k''2''n'' + 1 with ''k'' odd and ''k'' < 2''n'' - and if there exists an integer ''a'' for which Euler's criterion is ''-1'', thus: : then ''p'' is . In this case, ''p'' is called a Proth prime. The is also true: if ''p'' is composite then no such ''a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proth Number
A Proth number is a natural number ''N'' of the form N = k \times 2^n+1 where ''k'' and ''n'' are positive integers, ''k'' is odd and 2^n > k. A Proth prime is a Proth number that is prime. They are named after the French mathematician François Proth. The first few Proth primes are :3, 5, 13, 17, 41, 97, 113, 193, 241, 257, 353, 449, 577, 641, 673, 769, 929, 1153, 1217, 1409, 1601, 2113, 2689, 2753, 3137, 3329, 3457, 4481, 4993, 6529, 7297, 7681, 7937, 9473, 9601, 9857 (). It is still an open question whether an infinite number of Proth primes exist. It was shown in 2022 that the reciprocal sum of Proth primes converges to a real number near 0.747392479, substantially less than the value of 1.093322456 for the reciprocal sum of Proth numbers. The primality of Proth numbers can be tested more easily than many other numbers of similar magnitude. Definition A Proth number takes the form N=k 2^n +1 where ''k'' and ''n'' are positive integers, k is odd and 2^n>k. A Proth prime i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gilbreath's Conjecture
Gilbreath's conjecture is a conjecture in number theory regarding the sequences generated by applying the forward difference operator to consecutive prime numbers and leaving the results unsigned, and then repeating this process on consecutive terms in the resulting sequence, and so forth. The statement is named after Norman L. Gilbreath who, in 1958, presented it to the mathematical community after observing the pattern by chance while doing arithmetic on a napkin.. In 1878, eighty years before Gilbreath's discovery, François Proth had, however, published the same observations along with an attempted proof, which was later shown to be incorrect. Motivating arithmetic Gilbreath observed a pattern while playing with the ordered sequence of prime numbers :2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ... Computing the absolute value of the difference between term ''n'' + 1 and term ''n'' in this sequence yields the sequence :1, 2, 2, 4, 2, 4, 2, 4, 6, 2, ... If the same ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Pages
The PrimePages is a website about prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...s originally created by Chris Caldwell at the University of Tennessee at Martin who maintained it from 1994 to 2023. The site maintains the list of the "5,000 largest known primes", selected smaller primes of special forms, and many "top twenty" lists for primes of various forms. The PrimePages has articles on primes and primality testing. It includes "The Prime Glossary" with articles on hundreds of glosses related to primes, and "Prime Curios!" with thousands of curios about specific numbers. The database started as a list of "titanic primes" (primes with at least 1000 decimal digits) by Samuel Yates in 1984. On March 11, 2023, the PrimePages moved from primes.utm.edu to t5k.or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1852 Births
Events January–March * January 14 – President Napoleon III, Louis-Napoléon Bonaparte proclaims a French Constitution of 1852, new constitution for the French Second Republic. * January 15 – Nine men representing various Jewish charitable organizations come together to form what will become Mount Sinai Hospital, New York, Mount Sinai Hospital in New York City. * January 17 – The United Kingdom recognizes the independence of the South African Republic, Transvaal. * February 3 – Battle of Caseros, Argentina: The Argentine provinces of Entre Ríos Province, Entre Rios and Corrientes, allied with Brazil and members of Colorado Party (Uruguay), Colorado Party of Uruguay, defeat Buenos Aires troops under Juan Manuel de Rosas. * February 11 – The first British public toilet for women opens in Bedford Street, London. * February 14 – The Great Ormond Street Hospital for Sick Children, London, admits its first patient. * February 15 – ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1879 Deaths
Events January * January 1 ** The Specie Resumption Act takes effect. The United States Note is valued the same as gold, for the first time since the American Civil War. ** Brahms' Violin Concerto (Brahms), Violin Concerto is premiered in Leipzig with Joseph Joachim as soloist and the composer conducting. * January 11 – The Anglo-Zulu War begins. * January 22 – Anglo-Zulu War – Battle of Isandlwana: A force of 1,200 British soldiers is wiped out by over 20,000 Zulu warriors. * January 23 – Anglo-Zulu War – Battle of Rorke's Drift: Following the previous day's defeat, a smaller British force of 140 successfully repels an attack by 4,000 Zulus. February * February 3 – Mosley Street in Newcastle upon Tyne (England) becomes the world's first public highway to be lit by the electric incandescent light bulb invented by Joseph Swan. * February 8 – At a meeting of the Royal Canadian Institute, engineer and inventor Sandford Fleming first prop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
