The primary purpose of using the <p> element in HTML is to define a paragraph of text.

The primary purpose of using the $<p>$ element in HTML is to define a paragraph of text.

The correct option is:

• To specify paragraphs of text

Here's why the other options are incorrect:

• To create a line break within text, the <br> element is used.
• To add headings to a web page, heading elements like $<h1>$, $<h2>$, etc., are used.
• To format text as bold, the <strong> or $<b>$ elements are typically used.

The final answer is $\boxed{\text{To specify paragraphs of text}}$.