Step by Step solution about How to resolve the algorithm Truncatable primes step by step in the Ruby programming language

The provided Ruby code defines methods to determine whether a given number is left-truncatable or right-truncatable and uses these methods to find the first left- and right-truncatable prime numbers within a range.

1. left_truncatable? and right_truncatable? Methods:

• left_truncatable? checks if a number n is left-truncatable, meaning all its truncations (removing digits from the left) are prime.
• right_truncatable? does the same, but for truncations from the right.

2. truncatable? Method:

   • truncatable? implements the core logic for checking whether a number is truncatable.
   • It takes a number n and a block trunc_func that defines how to truncate n.
   • It checks if n contains any zeros (which would make it non-prime), then iteratively truncates n using trunc_func.
   • If n becomes zero, the number is truncatable. If n is not prime at any point, it is not truncatable.

3. Usage:

   • The code requires the prime library for prime number handling.
   • It generates a list of prime numbers up to 1 million in reverse order.
   • It uses the detect method to find the first prime number that is left-truncatable and right-truncatable within the list.

4. Expected Output:

   • The first left-truncatable prime within the range is 3797, which can be truncated from the left to yield 797, 97, and 7.
   • The first right-truncatable prime within the range is 53, which can be truncated from the right to yield 5, 3, and 0.

def left_truncatable?(n)
  truncatable?(n) {|i| i.to_s[1..-1].to_i}
end


def right_truncatable?(n)
  truncatable?(n) {|i| i/10}
end

def truncatable?(n, &trunc_func)
  return false if n.to_s.include? "0"
  loop do
    n = trunc_func.call(n)
    return true if n.zero?
    return false unless Prime.prime?(n)
  end
end

require 'prime'
primes = Prime.each(1_000_000).to_a.reverse

p primes.detect {|p| left_truncatable? p}
p primes.detect {|p| right_truncatable? p}