Step by Step solution about How to resolve the algorithm Twin primes step by step in the Kotlin programming language

Kotlin Code Explanation:

This Kotlin code is designed to find and count pairs of twin prime numbers (prime numbers that differ by 2) within a given range. Here's a detailed explanation:

Main Function:

• The main() function is the entry point of the program.
• It starts by prompting the user to enter the maximum size (upper bound) of the search range.
• It then initializes the search range:
  • max stores the user-provided upper bound.
  • counter keeps track of the number of twin prime pairs found.
  • x represents the current number being checked for primality.

Prime Number Checking:

• The findPrime() function is used to check if a given number x is prime.
• It uses a simple primality test: it checks if x is divisible by any number in the range [2, sqrt(x)].
• If no divisors are found, x is considered prime; otherwise, it's not.

Twin Prime Pair Search:

• The while loop iterates through numbers starting from 3 (x) up to the specified max value.
• For each x, it calculates the upper bound for the primality test using x.sqrt().add(BigInteger.ONE) (to prevent overflow when squaring the number).
• It checks two conditions:
  • If x + 2 is within the search range (x.add(BigInteger.TWO) <= max), it's a potential candidate as the second prime in the pair.
  • It checks if both x and x + 2 are prime by calling the findPrime() function.
• If both conditions are true, it increments the counter to track the found twin prime pair.
• x is then incremented by 1 to check the next potential pair.

Output:

• After the loop completes, the program prints the total number of twin prime pairs found within the specified search range.

import java.math.BigInteger
import java.util.*

fun main() {
    val input = Scanner(System.`in`)
    println("Search Size: ")
    val max = input.nextBigInteger()
    var counter = 0
    var x = BigInteger("3")
    while (x <= max) {
        val sqrtNum = x.sqrt().add(BigInteger.ONE)
        if (x.add(BigInteger.TWO) <= max) {
            counter += if (findPrime(
                    x.add(BigInteger.TWO),
                    x.add(BigInteger.TWO).sqrt().add(BigInteger.ONE)
                ) && findPrime(x, sqrtNum)
            ) 1 else 0
        }
        x = x.add(BigInteger.ONE)
    }
    println("$counter twin prime pairs.")
}

fun findPrime(x: BigInteger, sqrtNum: BigInteger?): Boolean {
    var divisor = BigInteger.TWO
    while (divisor <= sqrtNum) {
        if (x.remainder(divisor).compareTo(BigInteger.ZERO) == 0) {
            return false
        }
        divisor = divisor.add(BigInteger.ONE)
    }
    return true
}