Step by Step solution about How to resolve the algorithm Sequence of primes by trial division step by step in the Kotlin programming language

1. Introduction:

This Kotlin code determines whether a given integer n is a prime number and prints all prime numbers below 2000.

2. isPrime Function:

The isPrime function checks if the input integer n is prime. It uses a probabilistic algorithm that is fast but not guaranteed to be correct. Here's how it works:

• If n is less than 2, it's not prime because 0 and 1 are not prime.
• If n is even (except for 2), it's not prime.
• If n is divisible by 3 (except for 3), it's not prime.
• The main loop starts with d = 5 and increments by 2 and 4 in each iteration. The loop checks if n is divisible by d or d + 2. If any of these divisions result in 0, n is not prime.
• If the loop completes without finding any divisors, n is prime.

3. main Function:

The main function is the entry point of the program. It uses a for loop to iterate through numbers from 3 to 1999 in steps of 2 (i.e., only odd numbers). For each i, it checks if it's prime using the isPrime function. If i is prime, it prints its value and increments a counter. When the counter reaches 15, it starts a new line.

4. Output:

The program outputs all prime numbers below 2000 in a multi-column format, with 15 primes printed on each line.

// version 1.0.6

fun isPrime(n: Int): Boolean {
    if (n < 2) return false 
    if (n % 2 == 0) return n == 2
    if (n % 3 == 0) return n == 3
    var d : Int = 5
    while (d * d <= n) {
        if (n % d == 0) return false
        d += 2
        if (n % d == 0) return false
        d += 4
    }
    return true
}

fun main(args: Array<String>) {
    // print all primes below 2000 say
    var count = 1
    print("    2")
    for (i in 3..1999 step 2)
        if (isPrime(i)) {
            count++ 
            print("%5d".format(i))
            if (count % 15 == 0) println()
        }
}