The function li(x), also known as the logarithmic integral, is defined as the integral from 2 to x of the function \( \frac{1}{\log(t)} \) dt. This function is important in number theory as it serves as an asymptotic approximation to the prime counting function, which counts the number of primes less than or equal to a given number x. Understanding li(x) is crucial for analyzing the distribution of prime numbers and is central to proving key results such as the Prime Number Theorem.
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