003.py

from math import sqrt, ceil, trunc

# Sieve of Eratosthenes
def seive(max):
  nums = range(max + 1)
	nums[0] = None
	nums[1] = None
	for i in range(2, max + 1):
		if nums[i]:
			c = i * 2
			while c <= max:
				nums[c] = None
				c += i
			yield i


val = 600851475143
#val = 13195
max_factor = trunc(ceil(sqrt(val)))
primes = [i for i in seive(max_factor)]

for i in range(len(primes) - 1, -1, -1):
	if val % primes[i] == 0:
		print primes[i]
		break

007.py

# prime generator based on a modification of the Seive of Eratosthenes 
# that allows it to generate an infinite series of primes
def primes():
  d = {}  
	q = 2  
	while True:
		if q not in D:
			yield q        
			d[q * q] = [q]
		else:
			for p in D[q]:
				d.setdefault(p + q, []).append(p)
			del d[q]
		q += 1

p = primes()
for i in range(10000):
	p.next()

print "%d" % p.next()