Step 1: Straight chain amines.
1. n-Butylamine: CH$_3$–CH$_2$–CH$_2$–CH$_2$–NH$_2$
2. Isobutylamine: (CH$_3$)$_2$CH–CH$_2$–NH$_2$
Step 2: Branched chain amines.
3. sec-Butylamine: CH$_3$–CH(NH$_2$)–CH$_2$–CH$_3$
4. tert-Butylamine: (CH$_3$)$_3$C–NH$_2$
Step 3: Count unique structures.
Thus, four distinct primary amines are possible.
\[
\boxed{4}
\]
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