def problem_10():
"""
The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
Find the sum of all the primes below two million.
"""
return sum(elib.primes_to(2000000))
def smallest_divisible_by(dividers):
max_divider = max(list(dividers))
primes = elib.primes_to(max_divider)
#min to start with
min = reduce(lambda x, y: x* y, primes, 1)
act = min
while True:
for d in dividers:
if act % d != 0:
act += min
break
else:
return act
def problem_35():
"""
The number, 197, is called a circular prime because all rotations of the digits:
197, 971, and 719, are themselves prime.
There are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and 97.
How many circular primes are there below one million?
"""
primes = set(elib.primes_to(1000000))
circulars = 0
for prime in primes:
is_circular = True
for rotation in elib.digit_rotator(prime):
if rotation not in primes:
is_circular = False
break
if is_circular:
circulars += 1
return circulars
def gen_coefs(min_limit, max_limit):
return ((a, b) for a in xrange(min_limit, max_limit)
for b in elib.primes_to(max_limit))
