Find the upper bound and lower bound of the number of prime numbers less than x

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In 1962, Rosser in a paper proposed this formula to estimate the number of primes:

$$0.6x/\ln x < \pi(2x)-\pi(x) < 1.4x/\ln x.$$

How can this formula be used to estimate upper bound and the lower bound of the number of 512-bit prime numbers?