Legendre's Constant

The number 1.08366 in Legendre's guess at the Prime Number Theorem

$$\pi(n)\sim{n\over \ln n-1.08366}.$$

This expression is correct to leading term only.

References

Le Lionnais, F. Les nombres remarquables. Paris: Hermann, p. 147, 1983.

Wagon, S. Mathematica in Action. New York: W. H. Freeman, pp. 28-29, 1991.