def problem_7():
"""What is the 10 001st prime number?"""
# Upper bound on nth prime:
# http://www.ams.org/journals/mcom/1999-68-225/S0025-5718-99-01037-6/S0025-5718-99-01037-6.pdf
n = 10001
num_primes = 0
for lim in xrange(0, n * int(log(n) + log(log(n))), 1000):
p = helper.get_primes(lim + 1000, lower=lim)
if num_primes + len(p) >= 10001:
return p[n - num_primes - 1]
num_primes += len(p)
def problem_10():
"""Find the sum of all the primes below two million"""
return sum(helper.get_primes(2000000))