Step by Step solution about How to resolve the algorithm Penta-power prime seeds step by step in the Ruby programming language

This code implements a simple program that generates and displays the first n penta-power prime seeds. A penta-power prime seed is a positive integer n such that n**exp + n + 1 is prime for all exponents exp from 0 to 4.

Implementation Details:

1. Module OpenSSL: The program uses the OpenSSL module to check primality of numbers.
2. pent_pow_primes: This is a lazy enumerator that generates penta-power prime seeds indefinitely. It starts with the integer 1 and keeps checking each integer n to see if it satisfies the penta-power prime conditions.
3. Penta-Power Prime Conditions: For each integer n, the program checks if (0..4).all?{|exp| OpenSSL::BN.new(nexp + n + 1).prime?} is true. This condition ensures that nexp + n + 1 is prime for all exponents exp from 0 to 4.
4. BN.new: This method in OpenSSL is used to create a big number from a given integer.
5. n = 30: The program is configured to display the first n = 30 penta-power prime seeds.
6. .take(n): This method is used to take the first n elements from the pent_pow_primes enumerator.
7. .each_slice(10): This method divides the first n penta-power prime seeds into groups of 10 and iterates over those groups.
8. "%8s"*s.size % s: This string format specifier is used to format each group of 10 penta-power prime seeds into a string with each seed aligned with 8 spaces.

Example Output:

The first 30 penta-power prime seeds:
    1      2      3      4      5      7      8     10     11     12
   13     14     15     16     17     19     20     21     22     23
   24     25     26     28     29     30     31     32     33     34

require 'openssl'

pent_pow_primes = (1..).lazy.select{|n| (0..4).all?{|exp| OpenSSL::BN.new(n**exp + n + 1).prime?} }

n = 30
puts "The first #{n} penta-power prime seeds:"
pent_pow_primes.take(n).each_slice(10){|s| puts "%8s"*s.size % s}