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"question": {
"questionId": "2873",
"questionFrontendId": "2761",
"categoryTitle": "Algorithms",
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"title": "Prime Pairs With Target Sum",
"titleSlug": "prime-pairs-with-target-sum",
"content": "<p>You are given an integer <code>n</code>. We say that two integers <code>x</code> and <code>y</code> form a prime number pair if:</p>\n\n<ul>\n\t<li><code>1 &lt;= x &lt;= y &lt;= n</code></li>\n\t<li><code>x + y == n</code></li>\n\t<li><code>x</code> and <code>y</code> are prime numbers</li>\n</ul>\n\n<p>Return <em>the 2D sorted list of prime number pairs</em> <code>[x<sub>i</sub>, y<sub>i</sub>]</code>. The list should be sorted in <strong>increasing</strong> order of <code>x<sub>i</sub></code>. If there are no prime number pairs at all, return <em>an empty array</em>.</p>\n\n<p><strong>Note:</strong> A prime number is a natural number greater than <code>1</code> with only two factors, itself and <code>1</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 10\n<strong>Output:</strong> [[3,7],[5,5]]\n<strong>Explanation:</strong> In this example, there are two prime pairs that satisfy the criteria. \nThese pairs are [3,7] and [5,5], and we return them in the sorted order as described in the problem statement.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 2\n<strong>Output:</strong> []\n<strong>Explanation:</strong> We can show that there is no prime number pair that gives a sum of 2, so we return an empty array. \n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 10<sup>6</sup></code></li>\n</ul>\n",
"translatedTitle": "和等于目标值的质数对",
"translatedContent": "<p>给你一个整数 <code>n</code> 。如果两个整数 <code>x</code> 和 <code>y</code> 满足下述条件,则认为二者形成一个质数对:</p>\n\n<ul>\n\t<li><code>1 &lt;= x &lt;= y &lt;= n</code></li>\n\t<li><code>x + y == n</code></li>\n\t<li><code>x</code> 和 <code>y</code> 都是质数</li>\n</ul>\n\n<p>请你以二维有序列表的形式返回符合题目要求的所有 <code>[x<sub>i</sub>, y<sub>i</sub>]</code> ,列表需要按 <code>x<sub>i</sub></code> 的 <strong>非递减顺序</strong> 排序。如果不存在符合要求的质数对,则返回一个空数组。</p>\n\n<p><strong>注意:</strong>质数是大于 <code>1</code> 的自然数,并且只有两个因子,即它本身和 <code>1</code> 。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1</strong></p>\n\n<pre><strong>输入:</strong>n = 10\n<strong>输出:</strong>[[3,7],[5,5]]\n<strong>解释:</strong>在这个例子中,存在满足条件的两个质数对。 \n这两个质数对分别是 [3,7] 和 [5,5],按照题面描述中的方式排序后返回。\n</pre>\n\n<p><strong>示例 2</strong></p>\n\n<pre><strong>输入:</strong>n = 2\n<strong>输出:</strong>[]\n<strong>解释:</strong>可以证明不存在和为 2 的质数对,所以返回一个空数组。 \n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 10<sup>6</sup></code></li>\n</ul>\n",
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"Pre-compute all the prime numbers in the range [1, n] using a sieve, and store them in a data structure where they can be accessed in O(1) time.",
"For x in the range [2, n/2], we can use the pre-computed list of prime numbers to check if both x and n - x are primes. If they are, we add them to the result."
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