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R. E. Powers
Ralph Ernest Powers (April 27, 1875 – January 31, 1952) was an American amateur mathematician who worked on prime numbers. He is credited with discovering the Mersenne primes and , in 1911 and 1914 respectively. In 1934 he verified that the Mersenne number is composite. Life Powers was born in Fountain, Colorado Territory. Details of his life are little-known,Obituary by D. H. Lehmer though he appears to have been an employee of the . Soon after P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Numbers
A prime number (or a prime) is a natural number greater than 1 that is not a 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 because the only ways of writing it as a product, or , involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order. The property of being prime is called primality. A simple but slow method of checking the primality of a given number n, called trial division, tests whether n is a multiple of any integer between 2 and \sqrt. Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error, and the AKS primality test, which alway ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mersenne Prime
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. If is a composite number then so is . Therefore, an equivalent definition of the Mersenne primes is that they are the prime numbers of the form for some prime . The exponents which give Mersenne primes are 2, 3, 5, 7, 13, 17, 19, 31, ... and the resulting Mersenne primes are 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, ... . Numbers of the form without the primality requirement may be called Mersenne numbers. Sometimes, however, Mersenne numbers are defined to have the additional requirement that be prime. The smallest composite Mersenne number with prime exponent ''n'' is . Mersenne primes were studied in antiquity because of their close connection to perfect numbers: the Euclid–Euler theorem as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fountain, Colorado
The City of Fountain is a home rule municipality located in El Paso County, Colorado, United States. The city population was 29,802 at the 2020 United States Census, a +15.31% increase since the 2010 United States Census. Fountain is a part of the Colorado Springs, CO Metropolitan Statistical Area and the Front Range Urban Corridor. Fountain is located south of downtown Colorado Springs and just east of Fort Carson. Fountain and the Colorado Springs suburbs Security and Widefield make up the "Fountain Valley" community. History Fountain was built in 1859 as a railroad shipping center for local ranches and farms. The town was named for Fountain Creek and was incorporated in 1900. A train wreck, "The Blast", as it is now known, occurred in Fountain during the spring of 1888. Just after three in the morning on May 14, 1888, a freight train carrying eighteen tons of explosives and a passenger train collided in the city. The accident killed three people: Charles F. Smith, a Fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Derrick Henry Lehmer
Derrick Henry "Dick" Lehmer (February 23, 1905 – May 22, 1991), almost always cited as D.H. Lehmer, was an American mathematician significant to the development of computational number theory. Lehmer refined Édouard Lucas' work in the 1930s and devised the Lucas–Lehmer test for Mersenne primes. His peripatetic career as a number theorist, with him and his wife taking numerous types of work in the United States and abroad to support themselves during the Great Depression, fortuitously brought him into the center of research into early electronic computing. Early life Lehmer was born in Berkeley, California, to Derrick Norman Lehmer, a professor of mathematics at the University of California, Berkeley, and Clara Eunice Mitchell. He studied physics and earned a Bachelor degree from UC Berkeley, and continued with graduate studies at the University of Chicago. He and his father worked together on Lehmer sieves. Marriage During his studies at Berkeley, Lehmer met Emma Markov ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Denver And Rio Grande Western Railroad
The Denver & Rio Grande Western Railroad , often shortened to ''Rio Grande'', D&RG or D&RGW, formerly the Denver & Rio Grande Railroad, was an American Class I railroad company. The railroad started as a narrow-gauge line running south from Denver, Colorado, in 1870. It served mainly as a transcontinental bridge line between Denver, and Salt Lake City, Utah. The Rio Grande was also a major origin of coal and mineral traffic. The Rio Grande was the epitome of mountain railroading, with a motto of ''Through the Rockies, not around them'' and later ''Main line through the Rockies'', both referring to the Rocky Mountains. The D&RGW operated the highest mainline rail line in the United States, over the Tennessee Pass in Colorado, and the famed routes through the Moffat Tunnel and the Royal Gorge. At its height, in 1889, the D&RGW had the largest narrow-gauge railroad network in North America with of track interconnecting the states of Colorado, New Mexico, and Utah. Known fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PrimePages
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mersenne Primes
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. If is a composite number then so is . Therefore, an equivalent definition of the Mersenne primes is that they are the prime numbers of the form for some prime . The exponents which give Mersenne primes are 2, 3, 5, 7, 13, 17, 19, 31, ... and the resulting Mersenne primes are 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, ... . Numbers of the form without the primality requirement may be called Mersenne numbers. Sometimes, however, Mersenne numbers are defined to have the additional requirement that be prime. The smallest composite Mersenne number with prime exponent ''n'' is . Mersenne primes were studied in antiquity because of their close connection to perfect numbers: the Euclid–Euler theorem as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Raphael M
Raffaello Sanzio da Urbino, better known as Raphael (; or ; March 28 or April 6, 1483April 6, 1520), was an Italian painter and architect of the High Renaissance. His work is admired for its clarity of form, ease of composition, and visual achievement of the Neoplatonic ideal of human grandeur. Together with Leonardo da Vinci and Michelangelo, he forms the traditional trinity of great masters of that period. His father was court painter to the ruler of the small but highly cultured city of Urbino. He died when Raphael was eleven, and Raphael seems to have played a role in managing the family workshop from this point. He trained in the workshop of Perugino, and was described as a fully trained "master" by 1500. He worked in or for several cities in north Italy until in 1508 he moved to Rome at the invitation of the pope, to work on the Vatican Palace. He was given a series of important commissions there and elsewhere in the city, and began to work as an architect. He was st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continued Fraction Factorization
In number theory, the continued fraction factorization method (CFRAC) is an integer factorization algorithm. It is a general-purpose algorithm, meaning that it is suitable for factoring any integer ''n'', not depending on special form or properties. It was described by D. H. Lehmer and R. E. Powers in 1931, and developed as a computer algorithm by Michael A. Morrison and John Brillhart in 1975. The continued fraction method is based on Dixon's factorization method. It uses convergents in the regular continued fraction expansion of :\sqrt,\qquad k\in\mathbb. Since this is a quadratic irrational In mathematics, a quadratic irrational number (also known as a quadratic irrational, a quadratic irrationality or quadratic surd) is an irrational number that is the solution to some quadratic equation with rational coefficients which is irreducibl ..., the continued fraction must be periodic (unless ''n'' is square, in which case the factorization is obvious). It has a time complexity o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1875 Births
Events January–March * January 1 – The Midland Railway of England abolishes the Second Class passenger category, leaving First Class and Third Class. Other British railway companies follow Midland's lead during the rest of the year (Third Class is renamed Second Class in 1956). * January 5 – The Palais Garnier, one of the most famous opera houses in the world, is inaugurated in Paris. * January 12 – Guangxu becomes the 11th Qing Dynasty Emperor of China at the age of 3, in succession to his cousin. * January 14 – The newly proclaimed King Alfonso XII of Spain (Queen Isabella II's son) arrives in Spain to restore the monarchy during the Third Carlist War. * February 3 – Third Carlist War – Battle of Lácar: Carlist commander Torcuato Mendíri secures a brilliant victory, when he surprises and routs a Government force under General Enrique Bargés at Lácar, east of Estella, nearly capturing newly crowned King Alfonso XII. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1952 Deaths
Year 195 ( CXCV) was a common year starting on Wednesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Scrapula and Clemens (or, less frequently, year 948 ''Ab urbe condita''). The denomination 195 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 * Emperor Septimius Severus has the Roman Senate deify the previous emperor Commodus, in an attempt to gain favor with the family of Marcus Aurelius. * King Vologases V and other eastern princes support the claims of Pescennius Niger. The Roman province of Mesopotamia rises in revolt with Parthian support. Severus marches to Mesopotamia to battle the Parthians. * The Roman province of Syria is divided and the role of Antioch is diminished. The Romans annexed the Syrian cities of Edessa and Nisibis. Severus re-establish his ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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