 For example, the th prime number is , and ()log() rounds to , a relative error of about 6.4%.As outlined below, the prime number theorem is also equivalent to
where and are the first and the second Chebyshev functions respectively.Based on the tables by Anton Felkel and Jurij Vega, Adrien-Marie Legendre conjectured in 1797 or 1798 that is approximated by the function , where and are unspecified constants.