The probability that two elements 
and 
of a symmetric group
generate the entire group tends to 3/4 as 
(Netto 1964, p. 90). The conjecture was proven
by Dixon (1969).
Netto's Conjecture
See also
Permutation Group, Symmetric GroupExplore with Wolfram|Alpha
References
Dixon, J. D. "The Probability of Generating the Symmetric Group." Math. Z. 110, 199-205, 1969.Le Lionnais, F. Les nombres remarquables. Paris: Hermann, p. 31, 1983.Netto, E. The Theory of Substitutions. New York: Chelsea, p. 90, 1964.Referenced on Wolfram|Alpha
Netto's ConjectureCite this as:
Weisstein, Eric W. "Netto's Conjecture." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NettosConjecture.html