Python - 176
This one starts with a big long list of newline characters and replaces all of them except for the ones that are needed at the end of the lines.
Starting at the centre, the algorithm peeps around the lefthand corner at each step. If there is a newline character there, turn left otherwise keep going forward.
w=input()*2;v=w-1;a=['\n']*v*w;p=w/2*v-1;d=0;z=[w,-1,-w,1]
for i in range(v*v):a[p]=' *'[i and all((i+1)%f for f in range(2,i))];d=d%4-(a[p+z[d-1]]<' ');p+=z[d]
print"".join(a)
Python - 177
Using a string avoids "join" but ends up one byte longer since the string is immutable
w=input()*2;v=w-1;a='\n'*v*w;p=w/2*v-1;d=0;z=[w,-1,-w,1]
for i in range(v*v):a=a[:p]+' *'[i and all((i+1)%f for f in range(2,i))]+a[p+1:];d=d%4-(a[p+z[d-1]]<' ');p+=z[d]
print a
