complete-prime-number

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Algorithms

You are given an integer <code>num</code>.

A number <code>num</code> is called a Complete Prime Number if every prefix and every suffix of <code>num</code> is prime.

Return <code>true</code> if <code>num</code> is a Complete Prime Number, otherwise return <code>false</code>.

Note:

<ul>
	<li>A prefix of a number is formed by the first <code>k</code> digits of the number.</li>
	<li>A suffix of a number is formed by the last <code>k</code> digits of the number.</li>
	<li>Single-digit numbers are considered Complete Prime Numbers only if they are prime.</li>
</ul>

&nbsp;
Example 1:

<div class="example-block">
Input: num = 23

Output: true

Explanation:

<ul>
	<li>​​​​​​​Prefixes of <code>num = 23</code> are 2 and 23, both are prime.</li>
	<li>Suffixes of <code>num = 23</code> are 3 and 23, both are prime.</li>
	<li>All prefixes and suffixes are prime, so 23 is a Complete Prime Number and the answer is <code>true</code>.</li>
</ul>
</div>

Example 2:

<div class="example-block">
Input: num = 39

Output: false

Explanation:

<ul>
	<li>Prefixes of <code>num = 39</code> are 3 and 39. 3 is prime, but 39 is not prime.</li>
	<li>Suffixes of <code>num = 39</code> are 9 and 39. Both 9 and 39 are not prime.</li>
	<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>
</ul>
</div>

Example 3:

<div class="example-block">
Input: num = 7

Output: true

Explanation:

<ul>
	<li>7 is prime, so all its prefixes and suffixes are prime and the answer is <code>true</code>.</li>
</ul>
</div>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= num &lt;= 109</code></li>
</ul>