Python - 203 Characters
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/x=input();y=x-1;w=x+y;A=[];R=range;k,j,s,t=R(4) \
| for i in R(2,w*w): |
| A+=[(x,y)]*all(i%d for d in R(2,i)) |
| if i==s:j,k,s,t=k,-j,s+t/2,t+1 |
| x+=j;y+=k |
| for y in R(w):print"".join(" *"[(x,y)in A]for x in R(w)) |
\_________________________________________________________/
\ ^__^
\ (oo)\_______
(__)\ )\/\
||----w |
|| ||
x=input();y=x-1;w=x+y
A=[];R=range;k,j,s,t=R(4)
for i in R(2,w*w):
A+=[(x,y)]*all(i%d for d in R(2,i))
if i==s:j,k=k,-j;s,t=s+t/2,t+1
x+=j;y+=k
for y in R(w):print"".join(" *"[(x,y)in A]for x in R(w))
How it works
The idea is to fill A with x,y coords that need to be printed as '*'
The algorithm starts at the cell corresponding to 2, so the special case of testing 1 for primality is avoided.
x,y is the cell of interest
j,k keep track of whether we need to inc or dec x or y to get to the next cell
s is the value of i at the next corner
t keeps track of the increment to s
all(i%d for d in R(2,i)) does the primality check
The last line is rather clumsy. It iterates over all the cells and decides whether to place a space or an asterisk
