# Pépin's Test/Mistake

## Source Work

The Dictionary
$257$

## Mistake

Such tests are easily performed today on computers using this criterion, which is similar to Lucas's test for the primality of Mersenne numbers: $F_n$ is prime if and only if it divides $3^{1/x \paren {F_n - 1} } + 1$.

## Correction

That last expression should read $3^{\frac 1 2 \paren {F_n - 1} } + 1$, or more neatly: $3^{\paren {F_n - 1} / 2} + 1$.

This misprint was not present in the $1986$ edition of Curious and Interesting Numbers.