Each different capital letter below represents a different digit. Each occurrence of the same capital letter represents the same digit.

ZWEI is a prime number.
DREI is a triangular number (that is, of the form n*(n+1)/2)
VIER is a perfect square.

What do DREI and VIER represent?

Added logic bonus:

If I told you there were no zeros anywhere, and I also told you that giving you the value of Z would allow you to figure out what ZWEI represented, what would you say the value of ZWEI is?