<div id="vueapp">
  positive integer limit: <input v-model="intn" placeholder="Input positive integer">
  <p>{{ primes }}</p>
</div>

<script src="https://cdn.jsdelivr.net/npm/[email protected]/dist/vue.js"></script>

'use strict';

function SieveOfEratosthenes(n) {
      // Create a boolean array "prime[0..n]" and initialize
      // all entries it as true. A value in prime[i] will
      // finally be false if i is Not a prime, else true.
      var integers = [];
      for (var i = 2; i < n+1; i++) {
              integers[i] = true;
      }

      for (var p = 2; p*p <= n; p++) {
              // If integers[p] is not changed, then it is a prime
              if (integers[p] == true) {
                      // Update all multiples of p
                      for (var i = p * 2; i <= n; i += p) {
                              integers[i] = false;
                      }
              }
      }

      // return all prime numbers <= n
      var primes = [];
      for (var p = 2; p <= n; p++) {
              if (integers[p] == true) {
                      primes.push(p);
              }
      }

      return primes;
}

new Vue({
  el: '#vueapp',
  data: {
    intn: 5,
    primes: ""
  },
  watch: {
    intn: {
      immediate: true,
      handler(val, oldVal) {
        var n = parseInt(val);
        if (isNaN(n)) {
          this.primes = "please input integer";
          return;
        }

        this.primes = SieveOfEratosthenes(n);
      }
    }
  }
});