Porter's constant

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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

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