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Carl Pomerance
Carl Bernard Pomerance (born 1944 in Joplin, Missouri) is an American number theorist. He attended college at Brown University and later received his Ph.D. from Harvard University in 1972 with a dissertation proving that any odd perfect number has at least seven distinct prime factors. He joined the faculty at the University of Georgia, becoming full professor in 1982. He subsequently worked at Lucent Technologies for a number of years, and then became a distinguished Professor at Dartmouth College. Contributions He has over 120 publications, including co-authorship with Richard Crandall of ''Prime numbers: a computational perspective'' (Springer-Verlag, first edition 2001, second edition 2005), and with Paul Erdős. He is the inventor of one of the integer factorization methods, the quadratic sieve algorithm, which was used in 1994 for the factorization of RSA-129. He is also one of the discoverers of the Adleman–Pomerance–Rumely primality test. Awards and honors He has won ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joplin, Missouri
Joplin is a city in Jasper County, Missouri, Jasper and Newton County, Missouri, Newton counties in the southwestern corner of the U.S. state of Missouri. The bulk of the city is in Jasper County, while the southern portion is in Newton County. Joplin is the largest city located within both Jasper and Newton Counties - even though it is not the county seat of either county (Carthage, Missouri, Carthage is the seat of Jasper County while Neosho, Missouri, Neosho is the seat of Newton County). With a population of 51,762 as of the 2020 United States Census, 2020 census, Joplin is the List of cities in Missouri, 13th most-populous city in the state. The city covers an area of 35.69 square miles (92.41 km2) on the outer edge of the Ozarks, Ozark Mountains. Joplin is the main hub of the three-county Joplin-Miami, MO-OK MSA, Joplin-Miami, Missouri-Oklahoma Metro area, which is home to 210,077 people making it the 5th largest metropolitan area in Missouri. In May 2011, the city was 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RSA-129
In mathematics, the RSA numbers are a set of large semiprimes (numbers with exactly two prime factors) that were part of the RSA Factoring Challenge. The challenge was to find the prime factors of each number. It was created by RSA Laboratories in March 1991 to encourage research into computational number theory and the practical difficulty of factoring large integers. The challenge was ended in 2007. RSA Laboratories (which is an acronym of the creators of the technique; Rivest, Shamir and Adleman) published a number of semiprimes with 100 to 617 decimal digits. Cash prizes of varying size, up to US$200,000 (and prizes up to $20,000 awarded), were offered for factorization of some of them. The smallest RSA number was factored in a few days. Most of the numbers have still not been factored and many of them are expected to remain unfactored for many years to come. , the smallest 23 of the 54 listed numbers have been factored. While the RSA challenge officially ended in 2007, people ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1944 Births
Events Below, the events of World War II have the "WWII" prefix. January * January 2 – WWII: ** Free France, Free French General Jean de Lattre de Tassigny is appointed to command First Army (France), French Army B, part of the Sixth United States Army Group in North Africa. ** Landing at Saidor: 13,000 US and Australian troops land on Papua New Guinea, in an attempt to cut off a Japanese retreat. * January 8 – WWII: Philippine Commonwealth troops enter the province of Ilocos Sur in northern Luzon and attack Japanese forces. * January 11 ** President of the United States Franklin D. Roosevelt proposes a Second Bill of Rights for social and economic security, in his State of the Union address. ** The Nazi German administration expands Kraków-Płaszów concentration camp into the larger standalone ''Konzentrationslager Plaszow bei Krakau'' in occupied Poland. * January 12 – WWII: Winston Churchill and Charles de Gaulle begin a 2-day conference in Marrakech ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bulletin Of The American Mathematical Society
The ''Bulletin of the American Mathematical Society'' is a quarterly mathematical journal published by the American Mathematical Society. Scope It publishes surveys on contemporary research topics, written at a level accessible to non-experts. It also publishes, by invitation only, book reviews and short ''Mathematical Perspectives'' articles. History It began as the ''Bulletin of the New York Mathematical Society'' and underwent a name change when the society became national. The Bulletin's function has changed over the years; its original function was to serve as a research journal for its members. Indexing The Bulletin is indexed in Mathematical Reviews, Science Citation Index, ISI Alerting Services, CompuMath Citation Index, and Current Contents/Physical, Chemical & Earth Sciences. See also *'' Journal of the American Mathematical Society'' *''Memoirs of the American Mathematical Society'' *''Notices of the American Mathematical Society'' *'' Proceedings of the American M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ruth–Aaron Pair
In mathematics, a Ruth–Aaron pair consists of two consecutive integers (e.g., 714 and 715) for which the sums of the prime factors of each integer are equal: :714 = 2 × 3 × 7 × 17, :715 = 5 × 11 × 13, and : 2 + 3 + 7 + 17 = 5 + 11 + 13 = 29. There are different variations in the definition, depending on how many times to count primes that appear multiple times in a factorization. The name was given by Carl Pomerance for Babe Ruth and Hank Aaron, as Ruth's career regular-season home run total was 714, a record which Aaron eclipsed on April 8, 1974, when he hit his 715th career home run. Pomerance was a mathematician at the University of Georgia at the time Aaron (a member of the nearby Atlanta Braves) broke Ruth's record, and the student of one of Pomerance's colleagues noticed that the sums of the prime factors of 714 and 715 were equal. Examples If only distinct prime factors are counted, the first few Ruth–Aaron pairs are: :( 5, 6), ( 24, 25), ( 49, 50), ( 77, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carmichael Numbers
In number theory, a Carmichael number is a composite number n, which in modular arithmetic satisfies the congruence relation: :b^n\equiv b\pmod for all integers b. The relation may also be expressed in the form: :b^\equiv 1\pmod. for all integers b which are relatively prime to n. Carmichael numbers are named after American mathematician Robert Daniel Carmichael, Robert Carmichael, the term having been introduced by N. G. W. H. Beeger, Nicolaas Beeger in 1950 (Øystein Ore had referred to them in 1948 as numbers with the "Fermat property", or "''F'' numbers" for short). They are infinite in number. They constitute the comparatively rare instances where the strict converse of Fermat's Little Theorem does not hold. This fact precludes the use of that theorem as an absolute test of Prime numbers, primality. The Carmichael numbers form the subset ''K''1 of the Knödel numbers. Overview Fermat's little theorem states that if ''p'' is a prime number, then for any integer ''b'', the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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