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In number theory, the Green–Tao theorem, proved by Ben Green and Terence Tao in 2004, states that the sequence of prime numbers contains arbitrarily long arithmetic progressions. In other words, for every natural number k {\displaystyle k} , there exist arithmetic progressions of primes with k {\displaystyle k} terms.
Terence Chi-Shen Tao FAA FRS (Chinese: 陶哲軒; born 17 July 1975) is an Australian-American mathematician, Fields medalist, and professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins Chair in the College of Letters and Sciences.
Ben Joseph Green FRS (born 27 February 1977) is a British mathematician, specialising in combinatorics and number theory. He is the Waynflete Professor of Pure Mathematics at the University of Oxford .
Terence Tao gave this "rough" statement of the problem: [1]. Parity problem.If A is a set whose elements are all products of an odd number of primes (or are all products of an even number of primes), then (without injecting additional ingredients), sieve theory is unable to provide non-trivial lower bounds on the size of A.
Green Bay "Jeopardy!" champ Ben Chan was honored by the Wisconsin Assembly with Joint Resolution 114 at the Capitol in February. He's pictured with Rep. Kristina Shelton (D-Green Bay), who ...
This work was further developed by Ben Green and Terence Tao, leading to the Green–Tao theorem. In 2003, Gowers established a regularity lemma for hypergraphs, [15] analogous to the Szemerédi regularity lemma for graphs. In 2005, he introduced [16] the notion of a quasirandom group.
Terence Tao summed up the advantage of the hyperreal framework by noting that it allows one to rigorously manipulate things such as "the set of all small numbers", or to rigorously say things like "η 1 is smaller than anything that involves η 0 ", while greatly reducing epsilon management issues by automatically concealing many of the ...
Benjamin Richard Green (1807/8–1876), English watercolour painter and author; Benjamin Green (c. 1811–1858), English architect who partnered with his father as John and Benjamin Green; Ben Charles Green (1905–1983), American federal jurist; Ben K. Green (1912–1974), American writer about Southwestern horses