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| 1 | +<h2><a href="https://leetcode.com/problems/complete-prime-number">4100. Complete Prime Number</a></h2><h3>Medium</h3><hr><p>You are given an integer <code>num</code>.</p> |
| 2 | + |
| 3 | +<p>A number <code>num</code> is called a <strong>Complete Prime Number</strong> if every <strong>prefix</strong> and every <strong>suffix</strong> of <code>num</code> is <strong>prime</strong>.</p> |
| 4 | + |
| 5 | +<p>Return <code>true</code> if <code>num</code> is a Complete Prime Number, otherwise return <code>false</code>.</p> |
| 6 | + |
| 7 | +<p><strong>Note</strong>:</p> |
| 8 | + |
| 9 | +<ul> |
| 10 | + <li>A <strong>prefix</strong> of a number is formed by the <strong>first</strong> <code>k</code> digits of the number.</li> |
| 11 | + <li>A <strong>suffix</strong> of a number is formed by the <strong>last</strong> <code>k</code> digits of the number.</li> |
| 12 | + <li>A <strong>prime</strong> number is a natural number greater than 1 with only two factors, 1 and itself.</li> |
| 13 | + <li>Single-digit numbers are considered Complete Prime Numbers only if they are <strong>prime</strong>.</li> |
| 14 | +</ul> |
| 15 | + |
| 16 | +<p> </p> |
| 17 | +<p><strong class="example">Example 1:</strong></p> |
| 18 | + |
| 19 | +<div class="example-block"> |
| 20 | +<p><strong>Input:</strong> <span class="example-io">num = 23</span></p> |
| 21 | + |
| 22 | +<p><strong>Output:</strong> <span class="example-io">true</span></p> |
| 23 | + |
| 24 | +<p><strong>Explanation:</strong></p> |
| 25 | + |
| 26 | +<ul> |
| 27 | + <li><strong></strong>Prefixes of <code>num = 23</code> are 2 and 23, both are prime.</li> |
| 28 | + <li>Suffixes of <code>num = 23</code> are 3 and 23, both are prime.</li> |
| 29 | + <li>All prefixes and suffixes are prime, so 23 is a Complete Prime Number and the answer is <code>true</code>.</li> |
| 30 | +</ul> |
| 31 | +</div> |
| 32 | + |
| 33 | +<p><strong class="example">Example 2:</strong></p> |
| 34 | + |
| 35 | +<div class="example-block"> |
| 36 | +<p><strong>Input:</strong> <span class="example-io">num = 39</span></p> |
| 37 | + |
| 38 | +<p><strong>Output:</strong> <span class="example-io">false</span></p> |
| 39 | + |
| 40 | +<p><strong>Explanation:</strong></p> |
| 41 | + |
| 42 | +<ul> |
| 43 | + <li>Prefixes of <code>num = 39</code> are 3 and 39. 3 is prime, but 39 is not prime.</li> |
| 44 | + <li>Suffixes of <code>num = 39</code> are 9 and 39. Both 9 and 39 are not prime.</li> |
| 45 | + <li>At least one prefix or suffix is not prime, so 39 is not a Complete Prime Number and the answer is <code>false</code>.</li> |
| 46 | +</ul> |
| 47 | +</div> |
| 48 | + |
| 49 | +<p><strong class="example">Example 3:</strong></p> |
| 50 | + |
| 51 | +<div class="example-block"> |
| 52 | +<p><strong>Input:</strong> <span class="example-io">num = 7</span></p> |
| 53 | + |
| 54 | +<p><strong>Output:</strong> <span class="example-io">true</span></p> |
| 55 | + |
| 56 | +<p><strong>Explanation:</strong></p> |
| 57 | + |
| 58 | +<ul> |
| 59 | + <li>7 is prime, so all its prefixes and suffixes are prime and the answer is <code>true</code>.</li> |
| 60 | +</ul> |
| 61 | +</div> |
| 62 | + |
| 63 | +<p> </p> |
| 64 | +<p><strong>Constraints:</strong></p> |
| 65 | + |
| 66 | +<ul> |
| 67 | + <li><code>1 <= num <= 10<sup>9</sup></code></li> |
| 68 | +</ul> |
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