Wolfram Language (Mathematica), 5252 45 bytes
ToExpression@*StringReplace[{"["->"Prime[",""->"1">"Prime[1"}]
Input uses brackets.
Transforms the input into a Mathematica expression that computes the result. We do this simply by replacing [
with Prime[
inserting 1
into every postition except in front of those [Prime[1
we already replaced. This works because concatenation is multiplication in Mathematica.