Question Number 2148 by Yozzi last updated on 04/Nov/15
$${Is}\:\mathrm{3}^{\mathrm{2015}} −\mathrm{2}^{\mathrm{2015}} \:{prime}? \\ $$
Answered by sudhanshur last updated on 04/Nov/15
$$\left(\mathrm{3}^{\mathrm{5}} \right)^{\mathrm{403}} −\left(\mathrm{2}^{\mathrm{5}} \right)^{\mathrm{403}} \\ $$$$\mathrm{3}^{\mathrm{5}} −\mathrm{2}^{\mathrm{5}} \:\mathrm{is}\:\mathrm{a}\:\mathrm{factor}. \\ $$$$\therefore\:\mathrm{3}^{\mathrm{2015}} −\mathrm{2}^{\mathrm{2015}} \:\mathrm{is}\:\mathrm{not}\:\mathrm{a}\:\mathrm{prime}. \\ $$