def problem27():
# b must be prime in order for (0) to be prime
primes = eratosthenes_primes(1000)
_a, _b, _np = None, None, None
# Only consider odd values for a
for a in xrange(-999, 1000, 2):
for b in primes:
# Since n**2 + a*n + b must be prime, then 1 + a + b must be prime, so a must be greater than -b - 1
if a > -b - 1:
n = 0
while True:
num = n ** 2 + a * n + b
if num < 0:
break
if not is_prime(num):
break
n += 1
if n > _np:
_a, _b, _np = a, b, n
return _a, _b, _np, _a * _b
def problem10():
return sum(eratosthenes_primes(2000000))