Edit in JSFiddle

function addToList(num) {
    var li = document.createElement('li'),
        list = document.getElementById('primeList');
    li.innerText = num;
    list.appendChild(li);
}
function clearList() {
    var list = document.getElementById('primeList');
    list.innerHTML = '';
}
function primerize() {
    clearList();
    var numArray = [],
        primeArray = [],
        start = document.getElementById('primeStart').value !== null ? document.getElementById('primeStart').value : 0,
        end = document.getElementById('primeEnd').value != null ? document.getElementById('primeEnd').value : 20;
    for (var i = 0; i < end; i++) {
        var divisArray = [];
        numArray.push(i);
        [].forEach.call(numArray, function (num) {
            if (i % num === 0) {
                divisArray.push(num)
            }
        });
        if (i >= start && divisArray.length <= 2) {
            primeArray.push(i);
            addToList(i);
        }
    }
}
<input type="number" id="primeStart" placeholder="starting number">
<input type="number" id="primeEnd" placeholder="ending number" />
<button onclick="primerize();">get Primes</button>
<output id="result">
    <ul id="primeList"></ul>
</output>
input:focus, button:focus{
    outline: none;
    border: 1px solid #1EBE28;
}
input {
    padding: .618em;
    border: 1px solid #ccc;
    border-radius: 2px;
}
button {
    color: white;
    padding: .618em;
    border: 1px solid #1EBE28;
    border-radius: 3px; 
    background: rgb(30, 190, 40);
}
button:hover, button:focus{
    background: rgb(25, 158, 33);
}
li{
    color: #333;
    font-size: 1.2em;
    padding: 0;
    line-height: 1.618    
    
}