Importance: High ✭✭✭
 Author(s):
 Subject: Number Theory » Analytic Number Theory
 Keywords: constant Euler irrational Mascheroni rational transcendental
Let $\gamma:=\lim_{n\rightarrow\infty}\left(\sum_{k=1}^n\left(\frac{1}{k}\right)-\ln(n)\right)$. The number $\gamma$ has not been proved algebraic or transcendental. In fact, it is not even known whether $\gamma$ is irrational.