In mathematics, Porter's constant C arises in the study of the efficiency of the Euclidean algorithm.[1][2] It is named after J. W. Porter of University College, Cardiff.

Euclid's algorithm finds the greatest common divisor of two positive integers m and n. Hans Heilbronn proved that the average number of iterations of Euclid's algorithm, for fixed n and averaged over all choices of relatively prime integers m < n, is

Porter showed that the error term in this estimate is a constant, plus a polynomially-small correction, and Donald Knuth evaluated this constant to high accuracy. It is:

where

is the Euler–Mascheroni constant
is the Riemann zeta function
is the Glaisher–Kinkelin constant

(sequence A086237 in the OEIS)

See also

References

  1. Knuth, Donald E. (1976), "Evaluation of Porter's constant", Computers & Mathematics with Applications, 2 (2): 137–139, doi:10.1016/0898-1221(76)90025-0
  2. Porter, J. W. (1975), "On a theorem of Heilbronn", Mathematika, 22 (1): 20–28, doi:10.1112/S0025579300004459, MR 0498452.


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