Numerology in Scripture us often debated, but the number three is significant. It is considered the number of divine perfection, represented in:
- The Trinity: Father, Son, and Holy Spirit
- The three-part nature of man - Body, Soul, Spirit
- Past, Present, Future
- Time, Space, Matter
- Depths, width, height
- Solid, liquid, gas
The number three is seen by some as significant all throughout creation and history. Others remain skeptical.
Specifically, the significance of three days applied to the death, burial, and resurrection is addressed at http://www.agapebiblestudy.com/documents/The%20Symbolic%20Significance%20of%20the%20third%20day.htm
In the symbolic language of the Bible, a three day period points to an
act of divine intervention which impacts Salvation History. Genesis
22:4 records that Abraham's journey to Mt. Moriah to offer his son in
sacrifice, as commanded by Yahweh, was a three day journey. In the
Matthew passage Jesus refers to three days, applying the significance
of the three day period to His resurrection and man's redemption. In
the Gospels Jesus often spoke of a three day period prophesying His
sacrifice and resurrection. (2)
Interestingly, in Judaism, the number three has this significance:
The number three symbolizes a harmony that includes and synthesizes
two opposites. The unity symbolized by the number three isn’t
accomplished by getting rid of number two, the entity that caused the
discord, and reverting to the unity symbolized by number one. Rather,
three merges the two to create a new entity, one that harmoniously
includes both opposites.
That can be taken many ways applied to Christ's death, burial, and resurrection. A new harmony between sinful man and righteous God made possible by Christ's atoning death, for example.
It seems likely (but not conclusive if you discount numerology) that there is a significance in the choice of three days.