3. Determine how many times the number $((2014)^{2^{2014}}-1)$ is larger than the number written in the following form: $\left.\left.\left((2014)^{2^{0}}+1\right) \cdot\left((2014)^{2^{1}}+1\right) \cdot\left((2014)^{2^{2}}+1\right) \cdot \ldots \quad \cdot\right)^{2^{2013}}+1\right)$.
Justify the solution.

Answer: 2013.