Step by Step solution about How to resolve the algorithm Sequence of primorial primes step by step in the Ruby programming language

Explanation:

The provided Ruby code finds and prints the first 20 primorial primes.

A primorial prime is a prime number that is the result of multiplying the first n prime numbers. For example, the first primorial prime is 2 because it is the product of the first prime number (2).

Detailed Breakdown:

1. Initialization:

   • i is initialized to 1, which represents the index of the prime number in the sequence.
   • urutan is initialized to 1, which represents the number of primorial primes found so far.
   • primorial_number is initialized to 1, which represents the product of the first n prime numbers.

2. Loading Required Modules:

   • require 'prime' imports the Prime module, which provides methods for generating and manipulating prime numbers.
   • require 'openssl' imports the OpenSSL module, which provides a fast Miller-Rabin primality test, which is used to check if a number is prime.

3. Generating Prime Array:

   • prime_array = Prime.first(500) creates an array containing the first 500 prime numbers.

4. Main Loop: The loop continues until urutan is greater than 20.

5. Calculating Primorial Number:

   • primorial_number *= prime_array[i-1] multiplies the current primorial number by the i-th prime number in the array.

6. Checking for Primorial Prime:

   • (primorial_number - 1).prime_fasttest? checks if the primorial number minus 1 is prime.
   • (primorial_number + 1).prime_fasttest? checks if the primorial number plus 1 is prime.

7. Printing Primorial Prime: If either the primorial number minus 1 or plus 1 is prime, it means the primorial number is a primorial prime. In that case, it prints the time taken and the index of the primorial prime found.

8. Incrementing Counters:

   • urutan += 1 increments the number of primorial primes found.
   • i += 1 increments the index of the prime number.

# Sequence of primorial primes

require 'prime' # for creating prime_array
require 'openssl' # for using fast Miller–Rabin primality test (just need 10.14 seconds to complete)
 
i, urutan, primorial_number = 1, 1, OpenSSL::BN.new(1)
start = Time.now
prime_array = Prime.first (500)

until urutan > 20
  primorial_number *= prime_array[i-1] 
  if (primorial_number - 1).prime_fasttest? || (primorial_number + 1).prime_fasttest?
    puts "#{Time.now - start} \tPrimorial prime #{urutan}: #{i}"
    urutan += 1
  end 
  i += 1
end