I'd say the flexibility to not need to know how big of a prime you'll need is the main draw.
The programming flexibility is indeed the win.
def primes ():
yield 2
yield 3
f = {}
n = 5
for p in primes():
if p == 2:
continue
p2 = p*p
while n < p2:
if n in f:
double_p = f.pop(n)
m = n + double_p
while m in f:
m += double_p
f[m] = double_p
else:
yield n
n += 2
f[n] = 2*pTo do that it recursively contains a second prime generator that only produces up to the square root. Which contains one that produces up to the fourth root. And so on until you get down to 3. The work and memory for those recursive generators is a rounding error compared to the initial prime generator. The work and memory saved by not keeping unnecessary primes is a significant win.