In an alphametic, each letter is represented by a different base ten digit from 0 to 9 inclusively. No number can contain any leading zero.

Solve this alphametic, knowing that:

SEIS is a triangular number, and:
SIETE is a prime number, and:
DIEZ is a triangular number.

*** In Spanish, the first ten counting numbers are: uno, dos, tres, cuatro,cinco,seis, siete, ocho, nueve and diez.

*** Adapted from a puzzle appearing in Missouri State University Problem Corner.