Smarandache constant

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${}^{\text{th}}$ prime number, and $x\in ℝ$. 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 $x_{\min }\approx 0.5671481302\mathrm{\dots }$

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.

Title	Smarandache constant
Canonical name	SmarandacheConstant
Date of creation	2013-03-22 17:17:49
Last modified on	2013-03-22 17:17:49
Owner	dankomed (17058)
Last modified by	dankomed (17058)
Numerical id	17
Author	dankomed (17058)
Entry type	Conjecture
Classification	msc 11A41
Related topic	FlorentinSmarandache