In this work, prime number theorem is proven using analytic methods. For this purpose elementary theory of infinite products is introduced and the Riemann zeta function is used. We derive the Euler product formula and find a meromorphic extension of the zeta function to the right half of the complex plane and the expression for its logarithmic derivative. We also define the Mangoldt and psi function and use them to find an equivalent formulation of the prime number theorem. Finally, the prime number theorem is proved using complex analytic methods.
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