 Both Legendre's and Dirichlet's formulas imply the same conjectured asymptotic equivalence of and stated above, although it turned out that Dirichlet's approximation is considerably better if one considers the differences instead of quotients.In two papers from 1848 and 1850, the Russian mathematician Pafnuty Chebyshev attempted to prove the asymptotic law of distribution of prime numbers.His work is notable for the use of the zeta function , for real values of the argument "", as in works of Leonhard Euler, as early as 1737.