My attempt at figuring out what's special about 277777788888899? (see: https://hive.blog/math/@inertia/my-attempt-at-figuring-out-what-s-special-about-277777788888899)

per.rb

def per(n, s)

  # Summary of the current test by showing the numbere bing tested followed by
  # the number of digits.
  puts("#{n} (digits: #{n.to_s.size})")

  # Increment the step.
  s = s + 1

  # Check if we've reached the last step.
  if n.to_s.size < 2
    puts('Done.  Steps: %d' % s)

    exit(s)
  end

  # Make a new result by multiplying each digit.
  r = 1
  n.to_s.split('').each do |m|
    r = r * m.to_i
  end

  # Recursively try the new result.
  per(r, s)
end

# If you have a number you want to try, pass it as the argument.  Otherwise,
# we'll pick a random number.
n = if ARGV.length == 0
  puts 'Trying random number.'

  # But not *too* random.  We avoid random numbers that have zeros and fives.
  while rnd = rand(10**15)
    break unless (rnd.to_s.split('') & ['0', '5']).any?
  end

  # Here is the random number we're going to try this time.
  rnd
else
  ARGV[0].to_i
end

# Initial check.
per(n, 0)