## DEV Community # Sieve of Eratosthenes, What is it?

## What is it?

Sieve of Eratosthenes is an algorithm devised by the Eratosthenes of Cyrene. It does the job of finding all the prime numbers within a given upper limit. This ancient algorithm is efficient and smart till the upper limit is a few billions. So we'll discuss the process and JavaScript code for the same, below.

## How it works?

The algorithm starts with generating a list of all numbers starting from 2 to n (where n is the upper limit), with the assumption of all the numbers in the list are prime. It starts from 2 and removes all the multiples of 2 in the list by traversing the list in the interval of 2.

So, now we consider n as 10

``````let sample_array = [2, 3, 4, 5, 6, 7, 8, 9, 10];
``````

Starting from 2, it removes the multiples of 2 by traversing the above list in a step count of 2.

Note: '*' below means removed from list.

``````let sample_array = [2, 3, 4*, 5, 6*, 7, 8*, 9, 10*];
``````

After removing all the multiples of 2, we move to the next non-removed number (that is 3), now from 3, we traverse the list with the step count of 3 and remove its multiples.

``````let sample_array = [2, 3, 4*, 5, 6*, 7, 8*, 9*, 10*];
``````

We then proceed to the next non-removed number, which is 5. But here's the thing, the multiples of 5 are already removed from the list. We just make sure when to end this cycle of traversal and removal by calculating the square of 5, that is 5*5 = 25, which is obviously greater than n that is 10. So we stop the process and get the remaining elements, which are prime.

Here's the final list we get,

``````let sample_array = [2, 3, 5, 7];
``````

Hurray!, we've done with the theory part, let's get our hands dirty with some JS to actually code it. ## Execution in JS 💻

Let's start by creating an empty array called `Boolarray`, why naming 'Bool', because we are going for a Boolean array. We also initialize the value of n as 20.

``````let Boolarray = [];
let n = 20;
``````

Remember, we first made an assumption that all the numbers in the list (here array) are prime. So we use `true` for `is prime` and `false` for `not a prime`, with this in mind we first fill the empty array with boolean values of all `True` (based on our assumption). We use a `for` loop with iterator `i` to iterate from 1 to n and fill the array with `True`.

``````let Boolarray = [];
let n = 20;
for (var i = 0; i < n; i++) {
Boolarray.push(true);
}
``````

Now, we have an array of length 20 with `true` on all indexes. We now follow the procedure of Sieve of Eratosthenes by starting the `for` with iterator `j` from 2 to j*j<=n (j*j<=n checks when to end the looping). If the current element in the array is `true`, we then loop over its multiples with iterator `k`and a step count, (according to the current element) and mark them `false`.

``````let Boolarray = [];
let n = 20;
for (var i = 0; i < n; i++) {
Boolarray.push(true);
}
for (let j = 2; j * j <= n; j++) {
if (Boolarray[j] == true) {
for (let k = 2 * j; k <= n; k += j) {
Boolarray[k] = false;
}
}
}
``````

After this execution, we are left with a Boolean array, which contains `true` in places of prime (remember `true` → is prime) and `false` in places of non-prime numbers in the array.

### Now it's all logging it onto the console 🎉

We use another `for` loop to iterate on `Boolarray` with iterator `num`, starting from 2 to num<=n. We console log only the `num`'s which contains `true` in the `Boolarray`.

`````` for (let num = 2; num <= n; num++) {
if (Boolarray[num] == true) {
console.log(num);
}
}
``````

So, we end with this final code,

You can also use the JSFiddle, to change the hard-coded input `n` to your wish.