Python 3, 125125 110 bytes
lambda s:eval(s.replace("][""]","]*[""1]*").replace("[","p[").replace("[]","[1]""p[1*")+"1")
p=2,
k=P=1
while k<1e4:
if P%k:p+=k,
P*=k*k;k+=1
Uses xnor's implementation of the Wilson Theorem method to generate primes. Substitutes ()
with []
.