  Let $b \ge 2$ be an integer. Not much is known on the representation in base
$b$ of prime numbers or of numbers whose prime factors belong to a given,
finite set. Among other results, we establish that any sufficiently large
integer which is not a multiple of $b$ and has only small (in a suitable sense)
prime factors has at least four nonzero digits in its representation in base
$b$.

Number Theory