Tatami Mats Riddle

Four rectangular Tatami mats, depicted as four different colors as shown above, are arranged to form a big rectangle, where all mats have the side lengths as whole integers. Also, the blue mat is a square; the green mat is $2$ unit $^2$ larger than the blue one; the red mat $3$ unit $^2$ larger than the blue one.

If the white mat has side lengths of some odd prime numbers, what is the area of the white mat in unit $^2$ ?

Note : Figure not drawn to scale.

Inspired by Soldier Lines Riddle