The logarithmic integral, denoted as $$ ext{Li}(x) $$, is a special function defined as the integral of the logarithm function, which is often used in number theory, particularly in estimating the distribution of prime numbers. It approximates the number of primes less than or equal to a given number and plays a crucial role in the analytic proof of the Prime Number Theorem. The logarithmic integral is expressed mathematically as $$ ext{Li}(x) = rac{1}{ ext{ln}(t)}dt $$ from 2 to x.
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