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Vaughan's identity has been used to simplify the proof of the Bombieri–Vinogradov theorem and to study Kummer sums (see the references and external links below).; In Chapter 25 of Davenport, one application of Vaughan's identity is to estimate an important prime-related exponential sum of Vinogradov defined by
This is a list of articles about prime numbers.A prime number (or prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. By Euclid's theorem, there are an infinite number of prime numbers.
William John Ellison. William John Ellison (1943 - 16 March 2022 [1]) was a British mathematician who worked on number theory.. Ellison studied at the University of Cambridge, where he earned his bachelor's degree and then, after spending the academic year 1969/70 at the University of Michigan, his PhD in 1970 under John Cassels with thesis Waring's and Hilbert's 17th Problems. [2]
Visualization of 6 as a perfect number Logarithmic graph of the number of digits of the largest known prime number by year, nearly all of which have been Mersenne primes ...
In number theory, Dirichlet's theorem, also called the Dirichlet prime number theorem, states that for any two positive coprime integers a and d, there are infinitely many primes of the form a + nd, where n is also a positive integer.
A natural number (1, 2, 3, 4, 5, 6, etc.) is called a prime number (or a prime) if it is greater than 1 and cannot be written as the product of two smaller natural ...
Several variations on Euclid's proof exist, including the following: The factorial n! of a positive integer n is divisible by every integer from 2 to n, as it is the product of all of them.
Green and Tao's proof has three main components: Szemerédi's theorem, which asserts that subsets of the integers with positive upper density have arbitrarily long arithmetic progressions.