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

The provided code is written in Julia programming language and it is designed to perform operations on pentagonal power prime seeds. Here's a detailed explanation of what the code does:

1. Importing Libraries:

   • using Primes, Printf: This line imports the Primes module for working with prime numbers and the Printf module for formatted printing.

2. Function ispenta:

   • This function determines if a given number n is a pentagonal power prime seed. It does this by checking if n^i + n + 1 is prime for i in the range 0 to 4.
   • If all these values are prime, it returns true, indicating that n is a pentagonal power prime seed.

3. Function firstpenta:

   • This function generates the first m pentagonal power prime seeds.
   • It uses the countfrom iterator to generate an infinite sequence of positive integers starting from 1.
   • The filter iterator is then used to filter out non-pentagonal power prime seeds using the ispenta function.
   • Finally, the take iterator is used to limit the sequence to the first m elements, which are collected into an array.

4. Function table_display:

   • This function displays a table of numbers arranged in a grid with a specified number of columns.
   • It takes two arguments: an array of numbers and the desired number of columns.
   • It iterates through the array and prints each number in a table format, ensuring that there are num_columns numbers per row.

5. Function stretch_penta:

   • This function generates pentagonal power prime seeds until it reaches a specified goal.
   • It uses the same approach as the firstpenta function to generate pentagonal power prime seeds using iterators.
   • However, it uses the takewhile iterator to continue generating seeds until the last seed exceeds the goal.
   • The collected seeds are returned as an array.

6. Function run_rosetta:

   • This function serves as the main entry point for the program.
   • It calls the firstpenta function to generate the first 30 pentagonal power prime seeds and displays them in a table using table_display.
   • It then calls the stretch_penta function to generate pentagonal power prime seeds until they exceed 20,000,000.
   • For every million milestone (1,000,000, 2,000,000, etc.), it finds the index of the first seed that exceeds the milestone and prints the seed value and its index.

7. Program Execution Check:

   • The last part of the code checks if the program is being executed as the main script (abspath(PROGRAM_FILE) == @__FILE__).
   • If so, it calls the run_rosetta function to execute the program's main functionality.

using Primes, Printf

function ispenta(n)
    all(0:4) do i
        isprime(n^i + n + 1)
    end
end

function firstpenta(m, T=BigInt)
    nums = Iterators.countfrom(T(1))
    pentas = Iterators.filter(ispenta, nums)
    firstn = Iterators.take(pentas, m)
    return collect(firstn)
end

function table_display(nums, num_columns)
    num_elements = length(nums)
    num_rows = div(num_elements, num_columns)
    remaining_elements = num_elements % num_columns

    for i in 1:num_rows
        for j in 1:num_columns
            index = (i - 1) * num_columns + j
            print(nums[index], "\t")
        end
        println()
    end

    for i in 1:remaining_elements
        index = num_rows * num_columns + i
        print(nums[index], "\t")
    end
    println()
end

function stretch_penta(goal, T=BigInt)
    nums = Iterators.countfrom(T(1))
    pentas = Iterators.filter(ispenta, nums)
    firstn = Iterators.takewhile(<=(goal), pentas)
    return collect(firstn)
end

function run_rosetta()
    fp = firstpenta(30)
    println("First 30 Penta power prime seeds:")
    table_display(fp, 10)
    
    sp = stretch_penta(20000000)
    milestones = 1000000 .* (1:10)
    for milestone in milestones
        index = findfirst(>(milestone), sp)
        @printf "First element over %9i: %9i, index:%4i\n" milestone sp[index] index
    end
end

if abspath(PROGRAM_FILE) == @__FILE__
    run_rosetta()
end