  In this note we introduce the notion of $(b,d)$-geprofi sets and study their
basic properties. These are sets of $bd$ points in $\mathbb{P}^4$ whose
projection from a general point to a hyperplane is a full intersection, i.e.,
the intersection of a curve of degree $b$ and a surface of degree $d$. We show
that such nontrivial sets exist if and only if $b\geq 4$ and $d\geq 2$.
Somewhat surprisingly, for infinitely many values of $b$ and $d$ there exist
such sets in linear general position. The note contains open questions and
problems.
