The Smarandache constant is the minimal solution $x_{\min}$ of the generalized Andrica equation: $p_{n+1}^{x}-p_{n}^{x}=1$ where $p_n$ is the n$^{{th}}$ prime number, and $x \in \mathbb{R}$ . The exact value of the Smarandache constant and whether it exists is currently unknown, however according to the generalized Andrica conjecture proposed by Florentin Smarandache the value of the Smarandache constant is $x_{\min}\approx0.5671481302\ldots$

The Smarandache constant should not be confused with a list of sixteen Smarandache constants $s_{1}-s_{16}$ defined as limits of different convergent series involving the Smarandache function.