generatePrimeNumbersRange()

Step 1: Understanding Prime Numbers in the Context of Programming

Before we can begin writing our function, we need to understand what a prime number is. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In the context of programming, we can determine if a number is prime by checking if it has any divisors other than 1 and itself. If it does, it's not a prime number.

Step 2: Creating the Basic Structure of the Function

Let's start by creating the basic structure of our function. We're going to build a function named generatePrimeNumbersRange which will accept two integers as arguments: start and end. These arguments symbolize the range within which we want to find all prime numbers.

function generatePrimeNumbersRange(start, end) {
  // function body to be filled later
}

Step 3: Adding Prime Check Logic

We now need to create the logic that will check if a number is prime or not. We'll do this by creating a loop that starts from the number 2 and goes up to the square root of the number we're checking. Why the square root? It's because, after the square root, factors start repeating.

function generatePrimeNumbersRange(start, end) {
  for(let i = start; i <= end; i++) {
    let isPrime = true;

    for(let j = 2, sqrt = Math.sqrt(i); j <= sqrt; j++) {
      if(i % j === 0) {
        isPrime = false;
        break;
      }
    }
  }
}

Notice that we initialized isPrime as true for each number in the range, and it will only be set to false if a number other than 1 and the number itself is found which can divide the number.

Step 4: Recording and Returning all Prime Numbers

The last part of our function is to record all prime numbers we find and return that list. We add a condition within the first loop that if isPrime is true after the second loop has finished, it indicates that i is a prime number.

function generatePrimeNumbersRange(start, end) {
  const primes = [];

  for(let i = start; i <= end; i++) {
    let isPrime = true;

    for(let j = 2, sqrt = Math.sqrt(i); j <= sqrt; j++) {
      if(i % j === 0) {
        isPrime = false;
        break;
      }
    }

    if(isPrime && i > 1) primes.push(i);
  }

  return primes;
}

Step 5: Conclusion and Full Code

There you have it! You have built a function capable of generating all prime numbers in a given range. All that's left to do is to call this function with a specific range and see what it returns.

function generatePrimeNumbersRange(start, end) {
  const primes = [];

  for(let i = start; i <= end; i++) {
    let isPrime = true;

    for(let j = 2, sqrt = Math.sqrt(i); j <= sqrt; j++) {
      if(i % j === 0) {
        isPrime = false;
        break;
      }
    }

    if(isPrime && i > 1) primes.push(i);
  }

  return primes;
}

console.log(generatePrimeNumbersRange(10, 50)); // [ 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 ]

Therefore, you can see that between 10 and 50, the prime numbers are [ 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 ].