<h2><a href="https://leetcode.com/problems/prime-subtraction-operation/">2601. Prime Subtraction Operation</a></h2><h3>Medium</h3><hr><div><p>You are given a <strong>0-indexed</strong> integer array <code>nums</code> of length <code>n</code>.</p>

<p>You can perform the following operation as many times as you want:</p>

<ul>

<li>Pick an index <code>i</code> that you haven’t picked before, and pick a prime <code>p</code> <strong>strictly less than</strong> <code>nums[i]</code>, then subtract <code>p</code> from <code>nums[i]</code>.</li>

</ul>

<p>Return <em>true if you can make <code>nums</code> a strictly increasing array using the above operation and false otherwise.</em></p>

<p>A <strong>strictly increasing array</strong> is an array whose each element is strictly greater than its preceding element.</p>

<p>&nbsp;</p>

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

<pre><strong>Input:</strong> nums = [4,9,6,10]

<strong>Output:</strong> true

<strong>Explanation:</strong> In the first operation: Pick i = 0 and p = 3, and then subtract 3 from nums[0], so that nums becomes [1,9,6,10].

In the second operation: i = 1, p = 7, subtract 7 from nums[1], so nums becomes equal to [1,2,6,10].

After the second operation, nums is sorted in strictly increasing order, so the answer is true.</pre>

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

<pre><strong>Input:</strong> nums = [6,8,11,12]

<strong>Output:</strong> true

<strong>Explanation: </strong>Initially nums is sorted in strictly increasing order, so we don't need to make any operations.</pre>

<p><strong class="example">Example 3:</strong></p>

<pre><strong>Input:</strong> nums = [5,8,3]

<strong>Output:</strong> false

<strong>Explanation:</strong> It can be proven that there is no way to perform operations to make nums sorted in strictly increasing order, so the answer is false.</pre>

<p>&nbsp;</p>

<p><strong>Constraints:</strong></p>

<ul>

<li><code>1 &lt;= nums.length &lt;= 1000</code></li>

<li><code>1 &lt;= nums[i] &lt;= 1000</code></li>

<li><code><font face="monospace">nums.length == n</font></code></li>

</ul>

</div>