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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.
Any given arithmetic progression of primes has a finite length. In 2004, Ben J. Green and Terence Tao settled an old conjecture by proving the Green–Tao theorem: The primes contain arbitrarily long arithmetic progressions. [1] It follows immediately that there are infinitely many AP-k for any k.
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 .
The Green–Tao theorem, proved by Ben Green and Terence Tao in 2004, [3] states that the sequence of prime numbers contains arbitrarily long arithmetic progressions. In other words, there exist arithmetic progressions of primes, with k terms, where k can be any natural number. The proof is an extension of Szemerédi's theorem.
A family of conjectures () was made by Ben Green and Terence Tao, concerning the Möbius function of prime number theory and -step nilsequences. Here the underlying Lie group G {\displaystyle G} is assumed simply connected and nilpotent with length at most s {\displaystyle s} .
Police say a TikTok video post has led to the capture of a Florida man who was on the run for more than three years after he allegedly lured his estranged girlfriend to a cemetery where he killed her.
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