Python 2, 62 bytes

Wilson's theroem FTW!

f=lambda p,a=1,b=1:p==[]or(a%b<1or b**p.pop(0))*f(p,a*b*b,b+1)

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Python 2, 61 bytes

Wilson's theroem FTW!

f=lambda p,a=1,b=1:p==[]or b**(a%b*p[0])*f(p[a%b:],a*b*b,b+1)

Try it online!

Python 2 , 62 bytes

f=lambda p,a=1,b=1:p==[]or(a%b<1or b**p.pop(0))*f(p,a*b*b,b+1)

Try it online!