The domain of for which is prime is

MATHEMATICS · Numerical · AoPS · Mathematics · Special Functions · Special Functions

Problem

The domain of

f(x)=\frac{\left[x+\frac{1}{2}\right]}{\left[x-\frac{1}{2}\right]}

for which

f(x)

is prime is

[x_1,x_2)

, where

[\cdot]

denotes the greatest-integer function. Find

2(x_1^2+x_2^2)