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

This Ruby code finds and yields the "anti-primes" sequence, a series of numbers with an increasing number of divisors. It uses Ruby's built-in Prime module and the Enumerator class to generate the sequence lazily and efficiently. Here's a step-by-step explanation:

1. Loading Prime Module:

   • The code requires the Prime module, which provides methods for working with prime numbers.

2. Defining num_divisors method:

   • This method takes a number n and calculates the number of divisors of n. It uses the prime_division method to get the prime factorization of n. The number of divisors is calculated by multiplying the exponents of each prime factor plus one.

3. Defining anti_primes Enumerator:

   • This is the core of the code. It creates an infinite enumerator (lazy sequence generator) using Enumerator.new. Within the block passed to the enumerator, the following steps occur:
     • max is initialized to 0, representing the maximum number of divisors found so far.
     • The first anti-prime, 1, is yielded using y << 1.
     • Starting from 2, numbers are checked in increments of 2 using 2.step(nil,2). The nil argument indicates that the process should continue indefinitely.
     • For each candidate number, the number of divisors, num, is calculated using the num_divisors method.
     • If num is greater than max, it means a new anti-prime is found. The candidate is yielded using y << candidate, and max is updated to the new value of num.

4. Printing Anti-primes:

   • The code uses the take(20) method on the anti_primes enumerator to get the first 20 anti-primes. These numbers are then joined into a string and printed using puts.

This code efficiently generates an infinite sequence of anti-primes, allowing you to explore the sequence as needed without having to store all the values in memory.

require 'prime'
def num_divisors(n)
  n.prime_division.inject(1){|prod, (_p,n)| prod * (n + 1) } 
end

anti_primes = Enumerator.new do |y| # y is the yielder
  max = 0
  y << 1                            # yield 1
  2.step(nil,2) do |candidate|      # nil is taken as Infinity
     num = num_divisors(candidate)
     if  num > max
       y << candidate               # yield the candidate
       max = num
     end
  end
end

puts anti_primes.take(20).join(" ")