'''
The first two consecutive numbers to have two distinct prime factors are:

14 = 2 × 7
15 = 3 × 5

The first three consecutive numbers to have three distinct prime factors are:

644 = 2² × 7 × 23
645 = 3 × 5 × 43
646 = 2 × 17 × 19.

Find the first four consecutive integers to have four distinct prime factors each. What is the first of these numbers?
'''

import math
import numpy as np

def sieve(n):
    assert n > 1

    ns = [True] * n

    for i in range(2, math.ceil(np.sqrt(n))):
        if ns[i]:
            j = pow(i, 2)

            while j < n:
                ns[j] = False
                j = j + i

    return [i for i,val in enumerate(ns) if val][2:]

def primeFactors(n, primes):
    res = []

    for p in primes:
        if n % p == 0:
            res.append(p)
            while n % p == 0:
                n /= p
    
    return res

def main():
    print("Hello this is Patrick")

    end = 1000000
    primeList = sieve(end)
    primeSet = set(primeList)
    consecs = 0

    for n in range(100000, end):
        if n not in primeSet:
            if len(primeFactors(n, primeList)) == 4:
                consecs += 1
            else:
                consecs = 0
        else:
            consecs = 0
        
        if consecs == 4:
            for i in range(n-3, n+1):
                print(i, primeFactors(i, primeList))
            break

if __name__ == "__main__":
    main()