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?
require 'mathn'
tmp, $c = Array.new, 646
loop do
$c += 1
if $c.prime_division.none?{|div| ($c-1).prime_division.detect{|d| d==div}} && $c.prime_division.size==4 && ($c-1).prime_division.size==4
tmp << $c
else
tmp.clear
end
break if tmp.size == 3
end
p tmp.first-1
require 'prime'
N = 4
a = (1..N).to_a
loop do
break if a.all?{|e| e.prime_division.size == N}
a.push a.shift+N
end
p a