# Consecutive Integers and Prime Factors

Question

Find three consecutive integers greater than 2000, such that each integer is a product of exactly three distinct prime numbers.

Solution

A simple way for the above would be to list down the prime factors for the numbers above 2000 & note that the numbers 2013, 2014 & 2015 are a possible answer.

Put the list like this in working:

2001 = 3 x 23 x 29

2002 = 2 x 7 x 11 x 13

Etc.

Until

2013 = 3 x 11 x 61

2014 = 2 x 19 x 53

2015 = 5 x 13 x 31

QED