  Let $\mathbb{F}_p$ be the field of residue classes modulo a prime number $p$
and let $A$ be a non-empty subset of $\mathbb{F}_p.$ In this paper we give an
explicit version of the sum-product estimate of Bourgain, Katz, Tao and
Bourgain, Glibichuk, Konyagin on the size of $\max\{|A+A|, |AA|\}.$ In
particular, our result implies that if $1<|A|\le p^{7/13}(\log p)^{-4/13},$
then $$ \max\{|A+A|, |AA|\}\gg \frac{|A|^{15/14}}{(\log|A|)^{2/7}} . $$
