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If $p$ is prime, then it is $p$-smooth and $p$-rough because both inequalities are not strict. $k$-rough is thus not $k-1$-smooth.
Also, a link to http://planetmath.org/encyclopedia/Addition.html is spurious.

Parting words from the person who closed the correction: 
If $p$ is prime, then it is $p$-smooth and $p$-rough because both inequalities are not strict. $k$-rough is thus not $k-1$-smooth. Also, a link to http://planetmath.org/encyclopedia/Addition.html is spurious. You're right on both counts.
Status: Accepted
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