 In the second edition of his book on number theory (1808) he then made a more precise conjecture, with and .Carl Friedrich Gauss considered the same question at age 15 or 16 "in the year 1792 or 1793", according to his own recollection in 1849.In 1838 Peter Gustav Lejeune Dirichlet came up with his own approximating function, the logarithmic integral (under the slightly different form of a series, which he communicated to Gauss).