Title: Fractal curves from prime trigonometric series,
Abstract: We study the convergence of the parameter family of series
$$V_{\alpha,\beta}(t)=\sum_{p}p^{-\alpha}\exp(2\pi i p^{\beta}t),\quad
\alpha,\beta \in \mathbb{R}_{>0},\; t \in [0,1)$$ defined over prime numbers
$p$, and subsequently, their differentiability properties. The visible fractal
nature of the graphs as a function of $\alpha,\beta$ is analyzed in terms of
Hölder continuity, self similarity and fractal dimension, backed with
numerical results. We also discuss the link of this series to random walks and
consequently, explore numerically its random properties.