Definition:Coprime/Notation

Definition
Let $a$ and $b$ be coprime integers, that is, such that $\gcd \left\{{a, b}\right\} = 1$.

Then the notation $a \perp b$ is preferred on.

If $\gcd \left\{{a, b}\right\} \ne 1$, the notation $a \not \!\! \mathop{\perp} b$ can be used.

As stated in, section $4.5$:


 * This concept is so important in practice, we ought to have a special notation for it; but, alas, number theorists haven't agreed on a very good one yet. Therefore we cry: "HEAR US, O MATHEMATICIANS OF THE WORLD! LET US NOT WAIT ANY LONGER! WE CAN MAKE MANY POPULAR FORMULAS CLEARER BY ADOPTING A NEW NOTATION NOW! LET US AGREE TO WRITE '$m \perp n$' AND TO SAY "$m$ is prime to $n$," IF $m$ AND $n$ ARE RELATIVELY PRIME.

Can't say it more clearly than that.