Math in Christmas: The Present and the Future

For December 25, 2016, the day of the week is \(d_{\text{present}}\).

For December 25, 6102, the day of the week is \(d_{\text{future}}\).

If each type of days is denoted by the following:

  • \(2 = \text{Sunday}\)
  • \(3 = \text{Monday}\)
  • \(5 = \text{Tuesday}\)
  • \(7 = \text{Wednesday}\)
  • \(11 = \text{Thursday}\)
  • \(13 = \text{Friday}\)
  • \(17 = \text{Saturday}\)

What is \(\left|d_{\text{present}} - d_{\text{future}}\right|\)? Try not to use the calendar to work this problem out!

Note: The calendar is Gregorian.

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