1080p is close to but not 2k and 4k is not 8 times the resolution of 2k.

  1080p = 1920 x 1080
  2K = 2048×1080 = 1.066 * 1080p
  4K = 4096×2160 = 4 times 2k = 4.266 x 1080p

http://en.wikipedia.org/wiki/File:Digital_cinema_formats.svg