def prime_factors(n):
"""Yield primes which evenly divide n."""
sqrt_n = n ** 0.5
for p in primes():
if p > sqrt_n:
return
if not n % p:
yield p
def first_factor(n):
"""Find the smallest positive integer that evenly divides n."""
sqrt_n = n ** 0.5
for p in primes():
if p > sqrt_n:
# n must be prime
return n
if not n % p:
return p
def nth_prime(n):
"""Find the nth prime number."""
return next(islice(primes(), n - 1, None))
