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Jens Franke
Jens Franke (born 28 June 1964) is a German mathematician. He has held a chair at the University of Bonn's Hausdorff Center for Mathematics since 1992. Franke's research has covered various problems of number theory, algebraic geometry and analysis on locally symmetric spaces. Franke attended the University of Jena, where he earned his PhD under Hans Triebel in 1986. He was awarded the EMS Prize in 1992, and the Oberwolfach Prize in 1993. In recent years, Franke worked on an implementation of the Number Field Sieve algorithm for prime decomposition In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these factors are further restricted to prime numbers, the process is called prime factorization. When the numbers are suf .... In May 2007, he and his colleague Thorsten Kleinjung announced the factorization of ''M''1039, the 1,039th Mersenne number. References External linksFranke's Website at the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Field Sieve
In number theory, the general number field sieve (GNFS) is the most efficient classical algorithm known for factoring integers larger than . Heuristically, its complexity for factoring an integer (consisting of bits) is of the form :\exp\left( \left(\sqrt + o(1)\right)(\ln n)^(\ln \ln n)^\right) =L_n\left .html"_;"title="frac,\sqrt[3">frac,\sqrt[3right/math> (in_L-notation.html" ;"title="">frac,\sqrt[3right.html" ;"title=".html" ;"title="frac,\sqrt[3">frac,\sqrt[3right">.html" ;"title="frac,\sqrt[3">frac,\sqrt[3right/math> (in L-notation">">frac,\sqrt[3right.html" ;"title=".html" ;"title="frac,\sqrt[3">frac,\sqrt[3right">.html" ;"title="frac,\sqrt[3">frac,\sqrt[3right/math> (in L-notation), where is the natural logarithm. It is a generalization of the special number field sieve: while the latter can only factor numbers of a certain special form, the general number field sieve can factor any number apart from prime powers (which are trivial to factor by taking roots). The pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Decomposition
In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these factors are further restricted to prime numbers, the process is called prime factorization. When the numbers are sufficiently large, no efficient non-quantum integer factorization algorithm is known. However, it has not been proven that such an algorithm does not exist. The presumed difficulty of this problem is important for the algorithms used in cryptography such as RSA public-key encryption and the RSA digital signature. Many areas of mathematics and computer science have been brought to bear on the problem, including elliptic curves, algebraic number theory, and quantum computing. In 2019, Fabrice Boudot, Pierrick Gaudry, Aurore Guillevic, Nadia Heninger, Emmanuel Thomé and Paul Zimmermann factored a 240-digit (795-bit) number (RSA-240) utilizing approximately 900 core-years of computing power. The researchers estimated that a 1024-bit RSA mod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21st-century German Mathematicians
The 1st century was the century spanning AD 1 ( I) through AD 100 ( C) according to the Julian calendar. It is often written as the or to distinguish it from the 1st century BC (or BCE) which preceded it. The 1st century is considered part of the Classical era, epoch, or historical period. The 1st century also saw the appearance of Christianity. During this period, Europe, North Africa and the Near East fell under increasing domination by the Roman Empire, which continued expanding, most notably conquering Britain under the emperor Claudius ( AD 43). The reforms introduced by Augustus during his long reign stabilized the empire after the turmoil of the previous century's civil wars. Later in the century the Julio-Claudian dynasty, which had been founded by Augustus, came to an end with the suicide of Nero in AD 68. There followed the famous Year of Four Emperors, a brief period of civil war and instability, which was finally brought to an end by Vespasian, ninth Roman em ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Related categories * :Year of birth missing (living people) / :Year of birth unknown * :Date of birth missing (living people) / :Date of birth unknown * :Place of birth missing (living people) / :Place of birth unknown * :Year of death missing / :Year of death unknown * :Date of death missing / :Date of death unknown * :Place of death missing / :Place of death unknown * :Missing middle or first names See also * :Dead people * :Template:L, which generates this category or death years, and birth year and sort keys. : {{DEFAULTSORT:Living people 21st-century people People by status ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1964 Births
Events January * January 1 – The Federation of Rhodesia and Nyasaland is dissolved. * January 5 - In the first meeting between leaders of the Roman Catholic and Orthodox churches since the fifteenth century, Pope Paul VI and Patriarch Athenagoras I of Constantinople meet in Jerusalem. * January 6 – A British firm, the Leyland Motor Corp., announces the sale of 450 buses to the Cuban government, challenging the United States blockade of Cuba. * January 9 – ''Martyrs' Day'': Armed clashes between United States troops and Panamanian civilians in the Panama Canal Zone precipitate a major international crisis, resulting in the deaths of 21 Panamanians and 4 U.S. soldiers. * January 11 – United States Surgeon General Luther Terry reports that smoking may be hazardous to one's health (the first such statement from the U.S. government). * January 12 ** Zanzibar Revolution: The predominantly Arab government of Zanzibar is overthrown by African nationalist rebels; a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mersenne Number
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 ass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thorsten Kleinjung
Thorsten (Thorstein, Torstein, Torsten) is a Scandinavian given name. The Old Norse name was ''Þórsteinn''. It is a compound of the theonym ''Þór'' (''Thor'') and ''steinn'' "stone", which became ''Thor'' and ''sten'' in Old Danish and Old Swedish. The name is one of a group of Old Norse names containing the theonym ''Thor'', besides other such as ''Þórarin, Þórhall, Þórkell, Þórfinnr, Þórvald, Þórvarðr, Þórolf'', most of which, however, do not survive as modern names given with any frequency. The name is attested in medieval Iceland, e.g. Þorsteinn rauður Ólafsson (c. 850 – 880), Þōrsteinn Eirīkssonr (late 10th century), and in literature such as '' Draumr Þorsteins Síðu-Hallssonar''. The Old English equivalent of the Scandinavian and Norman name is ''Thurstan'', attested after the Norman conquest of England in the 11th century as the name of a medieval archbishop of York (died 1140), of an abbot of Pershore (1080s) and of an abbot of Glast ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Bonn
The Rhenish Friedrich Wilhelm University of Bonn (german: Rheinische Friedrich-Wilhelms-Universität Bonn) is a public research university located in Bonn, North Rhine-Westphalia, Germany. It was founded in its present form as the ( en, Rhine University) on 18 October 1818 by Frederick William III, as the linear successor of the ( en, Academy of the Prince-elector of Cologne) which was founded in 1777. The University of Bonn offers many undergraduate and graduate programs in a range of subjects and has 544 professors. The University of Bonn is a member of the U15 (German universities), German U15 association of major research-intensive universities in Germany and has the title of "University of Excellence" under the German Universities Excellence Initiative; it is consistently ranked amongst the best German universities in the world rankings and is one of the most research intensive universities in Germany. Bonn has 6 Clusters of Excellence, the most of any German university; t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Jena
The University of Jena, officially the Friedrich Schiller University Jena (german: Friedrich-Schiller-Universität Jena, abbreviated FSU, shortened form ''Uni Jena''), is a public research university located in Jena, Thuringia, Germany. The university was established in 1558 and is counted among the ten oldest universities in Germany. It is affiliated with six Nobel Prize winners, most recently in 2000 when Jena graduate Herbert Kroemer won the Nobel Prize for physics. In the 2023 Times Higher Education World University Rankings, the university was awarded 189th place in the world. It was renamed after the poet Friedrich Schiller who was teaching as professor of philosophy when Jena attracted some of the most influential minds at the turn of the 19th century. With Karl Leonhard Reinhold, Johann Gottlieb Fichte, G. W. F. Hegel, F. W. J. Schelling and Friedrich Schlegel on its teaching staff, the university was at the centre of the emergence of German idealism and early Romanti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hans Triebel
Hans may refer to: __NOTOC__ People * Hans (name), a masculine given name * Hans Raj Hans, Indian singer and politician ** Navraj Hans, Indian singer, actor, entrepreneur, cricket player and performer, son of Hans Raj Hans ** Yuvraj Hans, Punjabi actor and singer, son of Hans Raj Hans * Hans clan, a tribal clan in Punjab, Pakistan Places * Hans, Marne, a commune in France * Hans Island, administrated by Greenland and Canada Arts and entertainment * ''Hans'' (film) a 2006 Italian film directed by Louis Nero * Hans (Frozen), the main antagonist of the 2013 Disney animated film ''Frozen'' * ''Hans'' (magazine), an Indian Hindi literary monthly * ''Hans'', a comic book drawn by Grzegorz Rosiński and later by Zbigniew Kasprzak Other uses * Clever Hans, the "wonder horse" * ''The Hans India'', an English language newspaper in India * HANS device, a racing car safety device *Hans, the ISO 15924 code for Simplified Chinese script See also *Han (other) *Hans im Glück, a Germa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analysis
Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384–322 B.C.), though ''analysis'' as a formal concept is a relatively recent development. The word comes from the Ancient Greek ἀνάλυσις (''analysis'', "a breaking-up" or "an untying;" from ''ana-'' "up, throughout" and ''lysis'' "a loosening"). From it also comes the word's plural, ''analyses''. As a formal concept, the method has variously been ascribed to Alhazen, René Descartes (''Discourse on the Method''), and Galileo Galilei. It has also been ascribed to Isaac Newton, in the form of a practical method of physical discovery (which he did not name). The converse of analysis is synthesis: putting the pieces back together again in new or different whole. Applications Science The field of chemistry uses analysis in thr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
