Many congruent numbers were known prior to the new calculation.

The calculation found 3,148,379,694 of these more mysterious congruent numbers up to a trillion.

The first few congruent numbers are 5, 6, 7, 13, 14, 15, 20, and 21.

For example, the 3-4-5 right triangle which students see in geometry has area 1/2 Eu 3 Eu 4 = 6, so 6 is a congruent number.

We present below a few interesting relations among these congruent numbers by means of theorems in which n is denoted by the notation n(r,s).

In addition to the above representation for congruent numbers we, for each of the above choices I and II, also have representations of congruent numbers in terms of a single variable, powers of a number and a special choice of 2 variables in terms of powers of a number, which are exhibited in the following table 1 and 2 respectively.

These results have motivated us to search for other representations of congruent numbers and relations among these numbers.

It is worth to mention that, as the congruent number represents the area of a Pythagorean triangle, it is also a nasty number.