# Euler Solution 47

### From ProgSoc Wiki

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 primes factors. What is the first of these numbers?

# Solutions for Problem 47

## Python by Althalus

Runtime: 16 seconds

import time, math start_time = time.time() def isPrime(num): for i in range(2,int(math.sqrt(num))+1): if num%i == 0: return False return True def getPrimeFactors(num): numbers=[] for i in range(2,int(math.sqrt(num))+1): if num%i == 0: if isPrime(i): numbers.append(i) if isPrime(num/i): numbers.append(num/i) return numbers i=10 numbers= [] while len(numbers) != 4: if len(getPrimeFactors(i)) == 4: numbers.append(i) if len(numbers) == 4: if not (numbers[0]+1 == numbers[1] and numbers[1]+1 == numbers[2] \ and numbers[2]+1 == numbers[3]): numbers = [numbers[1],numbers[2],numbers[3]] i+=1 print (numbers) run_time = time.time() - start_time print (run_time)