The distribution and density of these zeros affect the error term in the Prime Number Theorem. If the Riemann Hypothesis holds, it implies a tighter error bound in the Prime Number Theorem. I The expression provided combines the prime number theorem approximation, x / log(x), with an error term, + (x)/(math.log(x)**(2)). Prime Number Theorem (x / log(x)) This part of the expression estimates the number of prime numbers less than or equal to a specific value (x). It states that the number of primes is approximately equal to x divided by the natural logarithm of (ln(x) or log(x) with base-e). Error Term + (x)/(math.log(x)**(2)) This term represents the deviation from the exact number of primes predicted by the prime number theorem. The actual number of primes might be slightly higher or lower than the estimated value due to the complexities of prime distribution. Combined Expression X=(x / math.log(x)) + (x)/(math.log(x)**(2)) This expression combines the prime number theorem's approximation with a potential error term. It suggests that the actual number of primes might be around the value given by x / log(x) , with an additional correction based on x divided by logarithm x raised to the exponential of 2 .

The Riemann Hypothesis proposes a specific location (the critical line) for the non-trivial zeros of the Riemann zeta function. This paper argues that the aperiodicity observed in the distribution of these non-trivial zeros and the distribution of primes numbers is a fundamental property. A periodic zeta function would significantly alter