  Let $v\geq 2$ be a fixed integer, and let $x \geq 1$ and $z \geq x$ be large
numbers. The exact asymptotic formula for the number of Wieferich primes $p$
such that $ v^{p-1} \equiv 1 \bmod p^2$ in the short interval $[x,x+z]$ is
proposed in this note. The search conducted on the last 100 years have produced
two primes $p<x=10^{15}$ such that $2^{p-1} -1\equiv 0 \bmod p^2$. The
probabilistic and theoretical information within predicts the existence of
another base $v=2$ prime on the interval $[10^{15},10^{40}]$. Furthermore, a
result for the upper bound on the number of Wieferich primes is used to
demontrate that the subset of nonWieferich primes has density 1.
