from tools import number_theory

def num_factor(num):
    factor = []
    if not num % 2:
        factor.append(2)
        while not num % 2:
            num //= 2
    p = 3
    while p * p < num:
        if not num % p:
            factor.append(p)
            while not num % p:
                num //= p
        p += 2
    if 1 < num:
        factor.append(num)
    return factor

def find(count, a, b):
    seq = 0
    a += 1
    while b + seq >= count + a:
        if len(num_factor(a)) == count:
            seq += 1
        else:
            seq = 0
        if seq == count:
            return a - count + 1
        a += 1

def search(count, limit):
    prime = list(number_theory.make_prime(limit))
    for i in range(len(prime) - 1):
        get = find(count, prime[i], prime[i + 1])
        if get:
            return get

print(search(4, 200000))