The difference of fractions $\frac{2024}{2023} - \frac{2023}{2024}$ was represented as an irreducible fraction $\frac{p}{q}$. Find the value of $p$.
1. Start with the given expression:
   \[
   \frac{2024}{2023} - \frac{2023}{2024}
   \]

2. Find a common denominator for the fractions:
   \[
   \frac{2024 \cdot 2024 - 2023 \cdot 2023}{2023 \cdot 2024}
   \]

3. Simplify the numerator using the difference of squares formula \(a^2 - b^2 = (a - b)(a + b)\):
   \[
   2024^2 - 2023^2 = (2024 - 2023)(2024 + 2023)
   \]

4. Calculate the values:
   \[
   2024 - 2023 = 1
   \]
   \[
   2024 + 2023 = 4047
   \]

5. Substitute these values back into the expression:
   \[
   \frac{2024^2 - 2023^2}{2023 \cdot 2024} = \frac{(2024 - 2023)(2024 + 2023)}{2023 \cdot 2024} = \frac{1 \cdot 4047}{2023 \cdot 2024}
   \]

6. Simplify the fraction:
   \[
   \frac{4047}{2023 \cdot 2024}
   \]

7. Since 4047 is not divisible by either 2023 or 2024, the fraction is already in its irreducible form.

8. Therefore, the numerator \(p\) of the irreducible fraction is:
   \[
   p = 4047
   \]

The final answer is \(\boxed{4047}\)