The video derives the Prime Number Theorem by treating the number of primes up to x as the area under the density curve. It simplifies this by assuming constant density, multiplying the size x by the density estimate 1/ln(x) to get x/ln(x).
Conditions: Uses the asymptotic density approximation 1/ln(x).; The derivation assumes density is constant over the range for simplification.
The video derives the Prime Number Theorem by treating the number of primes up to x as the area under the density curve. It simplifies this by assuming constant density, multiplying the size x by the density estimate 1/ln(x) to get x/ln(x).
Conditions: Uses the asymptotic density approximation 1/ln(x).; The derivation assumes density is constant over the range for simplification.
Prime density up to x is defined as the ratio of the number of primes found to the search size x. The video expresses this operationally as # PRIMES divided by SIZE.
Conditions: x is a positive integer search bound.; Density is computed by dividing the prime count by the search size.
Prime density up to x is defined as the ratio of the number of primes found to the search size x. The video expresses this operationally as # PRIMES divided by SIZE.
Conditions: x is a positive integer search bound.; Density is computed by dividing the prime count by the search size.