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sing recent explicit asymptotic zeroï¿½??free region and computations of zeros of the Riemann zeta function, obtained by Mossinghoff & Trudgian and Gourdon, respectively, we give an improvement for estimates of some functions related to distribution of primes, such as prime
counting function, intervals containing at least one prime, Chebyshevï¿½??s ï¿½? and ï¿½? functions.
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