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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. 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 s; they continue to be of importance in the computational search for large prime numbers. Proth also formulated Gilbreath's conjecture
Gilbreath's conjecture is a conjecture in number theory regarding the sequences generated by applying the forward differenc ...
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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 76 (2019). 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 , the new village was rebuilt near the old village. The old vill ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Verdun
Verdun (, , , ; official name before 1970 ''Verdun-sur-Meuse'') is a large city in the Meuse department in Grand Est, northeastern France. It is an arrondissement of the department. 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 its name to a major battle of the First World War. Geography Verdun is situated on both banks of the river Meuse, in the northern part of the Meuse department. It is connected by rail to Jarny. The A4 autoroute Paris–Metz–Strasbourg passes south of the town. History Verdun (''Verodunum'', a latinisation of a place name meaning "strong fort" in Gaulish) was founded by the Gauls. It has been the seat of the bishop of Verdun since the 4th century, with interruptions.A History of Food, Maguelonne Toussaint-Samat, Blackwell Publishing 1992, p.567 In 486, following the decisive Frankish victory at the Battle of Soissons, the city (amon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
France
France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of Overseas France, overseas regions and territories in the Americas and the Atlantic Ocean, Atlantic, Pacific Ocean, Pacific and Indian Oceans. Its Metropolitan France, metropolitan area extends from the Rhine to the Atlantic Ocean and from the Mediterranean Sea to the English Channel and the North Sea; overseas territories include French Guiana in South America, Saint Pierre and Miquelon in the North Atlantic, the French West Indies, and many islands in Oceania and the Indian Ocean. Due to its several coastal territories, France has the largest exclusive economic zone in the world. France borders Belgium, Luxembourg, Germany, Switzerland, Monaco, Italy, Andorra, and Spain in continental Europe, as well as the Kingdom of the Netherlands, Netherlands, Suriname, and Brazil in the Americas via its overseas territories in French Guiana and Saint Martin (island), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proth's Theorem
In number theory, Proth's theorem is a primality test for Proth numbers. It states that if ''p'' is a Proth number, of the form ''k''2''n'' + 1 with ''k'' odd and ''k'' < 2''n'', and if there exists an ''a'' for which : then ''p'' is . In this case ''p'' is called a Proth prime. This is a practical test because if ''p'' is prime, any chosen ''a'' has about a 50 percent chance of working, furthermore, since the calculation is ''mod p'', only values of ''a'' smaller than ''p'' have to be taken into consideration. In practice, however, a of ... [...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 prim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proth Prime
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 prim ... [...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 false. 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 numbers maintained by Chris Caldwell at the University of Tennessee at Martin. 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 5,000th prime has around 412,000 digits.. Retrieved on 2018-02-12. 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 subsequent years, the whole top-5,000 has consisted of gigantic primes (primes with at least 10,000 decimal digits). Primes of special forms are kept on the current lists if they are titanic and in the top-20 or top-5 for their form. See also *List of prime numbers This is a list of articles about pri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1852 Births
Year 185 ( CLXXXV) was a common year starting on Friday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Lascivius and Atilius (or, less frequently, year 938 '' Ab urbe condita''). The denomination 185 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Empire * Nobles of Britain demand that Emperor Commodus rescind all power given to Tigidius Perennis, who is eventually executed. * Publius Helvius Pertinax is made governor of Britain and quells a mutiny of the British Roman legions who wanted him to become emperor. The disgruntled usurpers go on to attempt to assassinate the governor. * Tigidius Perennis, his family and many others are executed for conspiring against Commodus. * Commodus drains Rome's treasury to put on gladiatorial spectacles and confiscates property to su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1879 Deaths
Events January–March * 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. * 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 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 proposes the global adoption of standard time. * March 3 – United States Geological Survey is founded. * March 11 – The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
