How to find prime numbers between 0 - 100?

Answer 1

Here's the fastest way to calculate primes in JavaScript, based on the previous prime value.

function nextPrime(value) {
    if (value > 2) {
        var i, q;
        do {
            i = 3;
            value += 2;
            q = Math.floor(Math.sqrt(value));
            while (i <= q && value % i) {
                i += 2;
            }
        } while (i <= q);
        return value;
    }
    return value === 2 ? 3 : 2;
}

Test

var value = 0, result = [];
for (var i = 0; i < 10; i++) {
    value = nextPrime(value);
    result.push(value);
}
console.log("Primes:", result);

Output

Primes: [ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 ]

It is faster than other alternatives published here, because:

• It aligns the loop limit to an integer, which works way faster;
• It uses a shorter iteration loop, skipping even numbers.

It can give you the first 100,000 primes in about 130ms, or the first 1m primes in about 4 seconds.

 function nextPrime(value) {
        if (value > 2) {
            var i, q;
            do {
                i = 3;
                value += 2;
                q = Math.floor(Math.sqrt(value));
                while (i <= q && value % i) {
                    i += 2;
                }
            } while (i <= q);
            return value;
        }
        return value === 2 ? 3 : 2;
    }

    var value, result = [];
    for (var i = 0; i < 10; i++) {
        value = nextPrime(value);
        result.push(value);
    }

    display("Primes: " + result.join(', '));

    function display(msg) {
        document.body.insertAdjacentHTML(
            "beforeend",
            "<p>" + msg + "</p>"
        );
    }

Answer 2

Here's my stab at it.

Change the initial i=0 from 0 to whatever you want, and the the second i<100 from 100 to whatever to get primes in a different range.

for(var i=0; i<100; i++){
    var devisableCount = 2;
        for(var x=0; x<=i/2; x++){
            if(i !== 1 && i !== 0 && i !== x){
                if(i%x === 0){
                   devisableCount++;
                 }
            }
        }
    if(devisableCount === 3){
        console.log(i);
    }
}

I tried it with 10000000 - it takes some time but appears to be accurate.

Answer 3

I have created a JSFiddle showing how it should work in a readable way,

idea is to have two functions isPrime and getPrimeNumbers to separate functionality, as well as using Math.pow and initial value of 2, as it should be always there, see the jsfiddle attached jsFiddle

window.onload = function() {
  (function() {
    var cont = document.getElementById('MainContainer');
    var curEl = document.createElement('span');
    var primeNumbers = [2];

    function fillContent() {
        var primeNumbersContent = document.createTextNode(JSON.stringify(primeNumbers));
        curEl.appendChild(primeNumbersContent);
        cont.appendChild(curEl);
    }

    function isPrime(n) {
        var divisor = 2;
        while (n > divisor) {
            if (Math.pow(divisor, 2) > n) {
                return true;
            }
            if (n % divisor == 0 || Math.sqrt(divisor) > n) {
                return false;
            } else {
                divisor++;
            }
        }
        return true;
    }

    function getPrimeNumbers(range) {
        for (var i = 3; i <= range; i+=2) {
            if (isPrime(i)) {
                primeNumbers.push(i);
            }
        }
        fillContent(primeNumbers);
    }
    getPrimeNumbers(11);
  })();
};

Answer 4

To find prime numbers between 0 to n. You just have to check if a number x is getting divisible by any number between 0 - (square root of x). If we pass n and to find all prime numbers between 0 and n, logic can be implemented as -

  function findPrimeNums(n)
    { 
       var x= 3,j,i=2,
       primeArr=[2],isPrime;
       for (;x<=n;x+=2){
           j = (int) Math.sqrt (x);
           isPrime = true;
           for (i = 2; i <= j; i++)
           {
                if (x % i == 0){
                    isPrime = false;
                    break;
                }
            }
            if(isPrime){
                primeArr.push(x);
            }

        }   

        return primeArr;
    }

Answer 5

First, change your inner code for another loop (for and while) so you can repeat the same code for different values.

More specific for your problem, if you want to know if a given n is prime, you need to divide it for all values between 2 and sqrt(n). If any of the modules is 0, it is not prime.

If you want to find all primes, you can speed it and check n only by dividing by the previously found primes. Another way of speeding the process is the fact that, apart from 2 and 3, all the primes are 6*k plus or less 1.

Answer 6

It would behoove you, if you're going to use any of the gazillion algorithms that you're going to be presented with in this thread, to learn to memoize some of them.

See Interview question : What is the fastest way to generate prime number recursively?