# Problem 47

^{4}/ Nov 2008

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

14 = 2 x 7

15 = 3 x 5

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

644 = 2² x 7 x 23

645 = 3 x 5 x 43

646 = 2 x 17 x 19.

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

project euler用に素数primes、素因数分解factorsのモジュールNumberを用意した。

import Number import Data.List consecutive m n =all((==m).toInteger.length).map (nub.factors)$[n..(n+m-1)] p047 = find (consecutive 4) [1..] main = print p047