This equation computes the estimated count of prime numbers that are less than some input integer.  The value is an estimate and this estimate grows more accurate as you try it for larger and larger input integers.

• Input: x - some number
• Output: y - estimated number of primes less than the number x

Notes

See this video for a full explanation of the Prime Number Theorem as it describes the asymptotic distribution of prime numbers.

The probability that a chosen integer is a prime number is equivalent to the relative density of prime number amongst all integers and this can be shown to be:  probability = 1/ln(N).  Therefore an approximation of the number of primes existing between 0 and N is the total number of integers in this interval, N, multiplied by the probability that some number of N are primes, `1/ln(N)`