def check(digits):
"""
>>> from utility import digits_of
>>> check(digits_of(1406357289))
True
>>> check(digits_of(1406357298))
False
"""
digits = digits[1:] # ignore the first number
for prime, number in zip(primes, tuplewise(3, digits)):
number = from_digits(number)
if not number % prime == 0:
return False
return True
import itertools
from utility import prime_factorization, tuplewise
def factor_counts():
for n in itertools.count():
yield len(set(prime_factorization(n)))
size = 4
for n, counts in enumerate(tuplewise(size, factor_counts())):
if all(c >= size for c in counts):
print(n)
break
