The Elliott-Halberstam conjecture is a significant hypothesis in number theory, specifically in the field of analytic number theory, dealing with the distribution of prime numbers in arithmetic progressions. It was formulated by the mathematicians Paul Elliott and Harold Halberstam in the 1960s. The conjecture asserts that there is a specific form of "density" of primes in arithmetic progressions that can be used to improve results concerning the distribution of primes.
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