def euler_37():
primes = lib.prime_gen()
candidates = itertools.chain(*[itertools.product(['1', '2', '3', '5', '7', '9'], repeat=n) for n in range(2, 11)])
truncatable_primes = (int(''.join(n)) for n in candidates if is_truncatable_prime((''.join(n))))
return sum(list(itertools.islice(truncatable_primes, 11)))
def num_factors_via_prime(n):
primes = lib.prime_gen()
current_prime = next(primes)
x = n
pfacts = defaultdict(int)
while not is_prime(n):
while (n % current_prime) == 0:
n = n // current_prime
pfacts[current_prime] += 1
current_prime = next(primes)
if n != 1:
pfacts[n] += 1
return reduce(operator.mul, (x + 1 for x in pfacts.values()), 1)
def euler_35(m):
primes = itertools.takewhile(lambda x: x < m, (n for n in lib.prime_gen()))
circular_primes = filter(circular_filter, primes)
return len(list(circular_primes))
consecutive = 0
while True:
n = next(i)
if len(prime_factors(n).keys()) >= 4:
consecutive += 1
if consecutive == 1:
possible_retval = n
if consecutive == 4:
return possible_retval
else:
consecutive = 0
pregenned_primes = []
primes = lib.prime_gen()
def prime_factors(n):
retval = defaultdict(int)
for p in pregenned_primes:
while n % p == 0:
n /= p
retval[p] += 1
if n == 1:
return retval
while n > 1:
p = next(primes)
pregenned_primes.append(p)