Euler problem 47

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?

Performance improvements:
Suppose we have to check number 80 for prime divisibility. The first prime can only be 2 because the next prime 3 will yield to a greater number (3 * 3 * 3 * 3 > 80). 
Stop prime division when maximum prime number is reached yield to 20 x faster code execution. The maximum prime depends on primes already found.


number  = x * x * x * x  ( x = maximum prime number )
number  = 2 * x * x * x  
number  = 2 * 3 * x * x  
number  = 2 * 3 * 5 * x  

Problem47 =      134043 elapsed time:  117 ms. Test Passed.