<p>You are given 2 <strong>positive</strong> integers <code>l</code> and <code>r</code>. For any number <code>x</code>, all positive divisors of <code>x</code> <em>except</em> <code>x</code> are called the <strong>proper divisors</strong> of <code>x</code>.</p>

<p>A number is called <strong>special</strong> if it has exactly 2 <strong>proper divisors</strong>. For example:</p>

<ul>
	<li>The number 4 is <em>special</em> because it has proper divisors 1 and 2.</li>
	<li>The number 6 is <em>not special</em> because it has proper divisors 1, 2, and 3.</li>
</ul>

<p>Return the count of numbers in the range <code>[l, r]</code> that are <strong>not</strong> <strong>special</strong>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">l = 5, r = 7</span></p>

<p><strong>Output:</strong> <span class="example-io">3</span></p>

<p><strong>Explanation:</strong></p>

<p>There are no special numbers in the range <code>[5, 7]</code>.</p>
</div>

<p><strong class="example">Example 2:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">l = 4, r = 16</span></p>

<p><strong>Output:</strong> <span class="example-io">11</span></p>

<p><strong>Explanation:</strong></p>

<p>The special numbers in the range <code>[4, 16]</code> are 4 and 9.</p>
</div>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= l &lt;= r &lt;= 10<sup>9</sup></code></li>
</ul>

def generate_primes(limit):
    primes = []
    sieve = [True] * (limit + 1)
    sieve[0] = sieve[1] = False

    for num in range(2, limit + 1):
        if sieve[num]:
            primes.append(num*num)
            for multiple in range(num * num, limit + 1, num):
                sieve[multiple] = False

    return primes


class Solution:
    def nonSpecialCount(self, l: int, r: int) -> int:
        prime_numbers = generate_primes(100000)
        total = r-l+1
        # special_count = sum(1 for num in prime_numbers if l <= num <= r)
        special_count = 0
        limit = r*r
        for i in prime_numbers:
            if i >= l and i <= r:
                special_count += 1
            if i > limit:
                break
        return total-special_count
17600