# Paradox for the existence of 4,5 and 7 using Brocard's problem

by dimension10
 P: 70 On the second page you get $\alpha\cdot sin(\alpha\pi)\Gamma(\alpha) + 1 = x^{2}$ and that is not correct since $sin(\alpha\pi)$ are canceling eachother. The correct result is $\alpha\Gamma(\alpha) + 1 = x^{2}$