Rough number

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A k-rough number, as defined by Finch in 2001 and 2003, is a positive integer whose prime factors are all greater than or equal to k. k-roughness has alternately been defined as requiring all prime factors to strictly exceed k.[1]

Examples (after Finch)[edit]

  1. Every odd positive integer is 3-rough.
  2. Every positive integer that is congruent to 1 or 5 mod 6 is 5-rough.
  3. Every positive integer is 2-rough, since all its prime factors, being prime numbers, exceed 1.

See also[edit]

Notes[edit]

  1. ^ p. 130, Naccache and Shparlinski 2009.

References[edit]