  We study the skein algebras of surfaces associated to the exceptional Lie
group $G_2,$ using Kuperberg webs. We identify two 2-variable polynomials,
$P_n(x,y)$ and $Q_n(x,y),$ and use threading operations along knots to
construct a family of central elements in the $G_2$ skein algebra of a surface,
$\mathcal{S}_q^{G_2}(\Sigma),$ when the quantum parameter $q$ is a
$2n\text{-th}$ root of unity. We verify these elements are central using
elementary skein-theoretic arguments. We also obtain a result about the
uniqueness of the so-called transparent polynomials $P_n$ and $Q_n.$ Our
methods involve a detailed study of the skein modules of the annulus and the
twice-marked annulus.
