This resource presents a closed-form formula, referred to as “Mwanaute’s Closed-Form Formula,” for computing the RSA private exponent ddd given the public exponent eee and prime factors ppp and qqq. Unlike standard methods that require the Extended Euclidean Algorithm, this formula allows direct computation in constant time using basic arithmetic operations (addition, subtraction, multiplication, division) with floor/ceiling functions. Examples are included to illustrate its application.