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Project Euler 47「異なる素因数」

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クッソ遅い。死ぬほど遅い。
20分強かかります。。。

Problem 47 「異なる素因数」

それぞれ2つの異なる素因数を持つ連続する2つの数が最初に現れるのは:

14 = 2 × 7
15 = 3 × 5

それぞれ3つの異なる素因数を持つ連続する3つの数が最初に現れるのは:

644 = 2^2 × 7 × 23
645 = 3 × 5 × 43
646 = 2 × 17 × 19

最初に現れるそれぞれ4つの異なる素因数を持つ連続する4つの数を求めよ. その最初の数はいくつか?

from itertools import count

def hoge(target):
    cnt = 0
    for n in count(1):
        if not is_prime(n) and is_four_prime_factors(n, target):
            cnt += 1
            if cnt == target: return n - (target - 1)
        else:
            cnt = 0

def is_four_prime_factors(n, target):
    primes = set()
    for m in get_prime(n):
        if n == 1 or len(primes) > target: break
        while True:
            if n % m == 0:
                primes.add(m)
                n = n / m
            else:
                break
    return True if len(primes) == target else False

def get_prime(n):
    yield 2
    for m in range(3, n // 2 +1):
        if is_prime(m): yield m

def is_prime(n):
    if n < 2: return False
    if n == 2: return True
    if n % 2 == 0: return False
    return all(n % i != 0 for i in range(3, int(n ** 0.5) + 1, 2))

print(hoge(4))

どうやったら早くなるんや。。。

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