Step by Step solution about How to resolve the algorithm Cuban primes step by step in the Go programming language

Overview: This Go program identifies and displays the first 200 prime numbers that differ by one trillion (10^12).

Key Concepts:

• Cuban Primes: A Cuban prime is a prime number that differs by exactly one trillion from another prime number.
• Sieve of Eratosthenes: This program uses a modified version of the Sieve of Eratosthenes to find prime numbers.
• Big Integers: The program uses the big package to represent and perform operations on large integers, such as one trillion.

Code Breakdown:

Functions:

• commatize(n uint64) string: This function converts a large integer to a string with commas inserted every three digits for readability.

Main Function:

• Initialization: Declare variables for the current cube (cube1), the next cube (cube2), the difference between them (diff), and an array to store the first 200 Cuban primes (cubans).
• Loop to Find Cuban Primes: The program enters an infinite loop (for { ... }) that iterates through potential Cuban primes.
  • It calculates the next cube (cube2) and computes the difference between the current and next cube (diff).
  • It uses the ProbablyPrime(0) function to check if diff is prime with 100% accuracy for integers less than 2^64.
  • If diff is prime and count is less than 200, it stores the comma-separated string representation of diff in the cubans array.
  • If count reaches 100000, it stores the 100,000th Cuban prime (cube100k) and exits the loop.
• Display Results:
  • The program prints the first 200 Cuban primes, grouped into 10 per line, using the commatize function for readability.
  • It also prints the 100,000th Cuban prime with commas inserted.

package main

import (
    "fmt"
    "math/big"
)

func commatize(n uint64) string {
    s := fmt.Sprintf("%d", n)
    le := len(s)
    for i := le - 3; i >= 1; i -= 3 {
        s = s[0:i] + "," + s[i:]
    }
    return s
}

func main() {
    var z big.Int
    var cube1, cube2, cube100k, diff uint64
    cubans := make([]string, 200)
    cube1 = 1
    count := 0
    for i := 1; ; i++ {
        j := i + 1
        cube2 = uint64(j * j * j)
        diff = cube2 - cube1
        z.SetUint64(diff)
        if z.ProbablyPrime(0) { // 100% accurate for z < 2 ^ 64
            if count < 200 {
                cubans[count] = commatize(diff)
            }
            count++
            if count == 100000 {
                cube100k = diff
                break
            }
        }
        cube1 = cube2
    }
    fmt.Println("The first 200 cuban primes are:-")
    for i := 0; i < 20; i++ {
        j := i * 10 
        fmt.Printf("%9s\n", cubans[j : j+10]) // 10 per line say
    }
    fmt.Println("\nThe 100,000th cuban prime is", commatize(cube100k))
}