 The first definition is the average time "T"("a") required to calculate the GCD of a given number "a" and a smaller natural number "b" chosen with equal probability from the integers 0 to "a" − 1

with the residual error being of order "a"−(1/6) + "ε", where "ε" is infinitesimal.The constant "C" ("Porter's Constant") in this formula equals

where "γ" is the Euler–Mascheroni constant and ζ' is the derivative of the Riemann zeta function.The leading coefficient (12/π2) ln 2 was determined by two independent methods.