Step by Step solution about How to resolve the algorithm Cullen and Woodall numbers step by step in the Ruby programming language

This Ruby code uses Ruby's enumerator and OpenSSL libraries to generate and print Cullen and Woodall numbers and their prime numbers. A step-by-step explanation of the code:

1. It includes the 'openssl' library to work with prime numbers.

2. It defines two enumerator objects, 'cullen' and 'woodall', to generate Cullen and Woodall numbers:

   • The Cullen numbers are generated using the formula n * (1 << n) + 1.
   • The Woodall numbers are generated using the formula n * (1 << n) - 1.

3. It creates two more enumerator objects, 'cullen_primes' and 'woodall_primes', to filter out the prime numbers from the generated Cullen and Woodall numbers. It checks the primality of each generated number using 'OpenSSL::BN.new(number).prime?'.

4. It sets the variable 'num' to 20, which specifies how many of the first Cullen and Woodall numbers to print.

5. It prints the first 20 generated Cullen numbers:

   • cullen.first(num).join(" ") generates an array of the first 20 Cullen numbers and joins them with spaces into a string.

6. It prints the first 20 generated Woodall numbers:

   • woodall.first(num).join(" ") generates an array of the first 20 Woodall numbers and joins them with spaces into a string.

7. It prints the first 5 generated Cullen prime numbers:

   • cullen_primes.first(5).join(", ") generates an array of the first 5 Cullen prime numbers and joins them with commas and spaces into a string.

8. It prints the first 12 generated Woodall prime numbers:

   • woodall_primes.first(12).join(", ") generates an array of the first 12 Woodall prime numbers and joins them with commas and spaces into a string.

When you run this code, it will generate and print sequences of Cullen and Woodall numbers and their prime numbers up to the specified limits.

require 'openssl'

cullen  = Enumerator.new{|y| (1..).each{|n| y << (n*(1<<n) + 1)} }
woodall = Enumerator.new{|y| (1..).each{|n| y << (n*(1<<n) - 1)} }
cullen_primes  = Enumerator.new{|y| (1..).each {|i|y << i if OpenSSL::BN.new(cullen.next).prime?}}
woodall_primes = Enumerator.new{|y| (1..).each{|i|y << i if OpenSSL::BN.new(woodall.next).prime?}} 

num = 20
puts "First #{num} Cullen numbers:\n#{cullen.first(num).join(" ")}"
puts "First #{num} Woodal numbers:\n#{woodall.first(num).join(" ")}"
puts "First 5 Cullen primes:\n#{cullen_primes.first(5).join(", ")}"
puts "First 12 Woodall primes:\n#{woodall_primes.first(12).join(", ")}"