To find the numerical equivalent of \( 81 \cdot 83 \), we can use the identity for the product of two numbers that are equidistant from a midpoint:
\[ a^2 - b^2 = (a - b)(a + b) \]
In this case, we can express it around the average of the two numbers:
Let \( a = 82 \) (the midpoint) and express the two numbers as:
\[ 81 = 82 - 1 \quad \text{and} \quad 83 = 82 + 1 \]
Using the identity:
\[ 81 \cdot 83 = (82-1)(82+1) = 82^2 - 1^2 \]
Calculating \( 82^2 \):
\[ 82^2 = 6724 \]
Now substituting back into the equation:
\[ 81 \cdot 83 = 6724 - 1 = 6723 \]
The value \( 6723 \) doesn't seem to be among the provided options, suggesting a different approach or identifying potential typographical errors.
However, looking through these responses doesn't yield a reconciliation with any logical transformations or breakdowns into factors that lead us to interpret them numerically to equal 81 * 83. Thus I would suggest recalculation in instances or a review for miscalculations throughout for further arrangements.
Final calculation:
\[ 81 \cdot 83 = 6723 \]
None of the options provided aligns with the calculated value from direct multiplication. Please check the values or representational formats for potential decimal shifts.