# Distinct primes factors

# 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 prime factors.

# What is the first of these numbers?

# Solution by Sam Gerber

def distinct_prime_factors(n)

first = 2 ** n

loop do

result = true

(first + n - 1).step(first, -1) do |number|

unless prime_factors(number).uniq.count == n

first = number + 1

result = false

break

end

end

return first if result

end

end

# This method returns the prime factors of a number in an array.

def prime_factors(number)

return [] if number < 2

return [number] if number < 4

factors = []

factor = 2

while factor < number

break if number % factor == 0

factor += 1

end

factors << factor

factors.concat(prime_factors(number / factor))

factors.sort

end

puts "solution"

puts distinct_prime_factors(4)