|Gamma, the Euler–Mascheroni constant.
The number γ has not been proved algebraic or transcendental. In fact, it is not even known whether γ is irrational. Continued fraction analysis reveals that if γ is rational, its denominator must be greater than 10242080. The ubiquity of γ revealed by the large number of equations makes the irrationality of γ a major open question in mathematics.