Legendre gave an estimate for π(n) the number of primes n of:
π(n) = n / ( log(n) - 1.08366 )
while Gauss's estimate is in terms of the logarithmic integral:
π(n) = ∫( 1 / log(t) ) dt where the range of integration is from 2 to n.
The statement that the density of primes is 1/log(n) is known as the Prime Number Theorem.
Prof. Ashay Dharwadker