7.1. Given the number $N=2011 \cdot 2012 \cdot 2013 \cdot 2014+1$. Is this number prime or composite?
Answer. Composite. Solution. The last digit of the number $N$ is equal to the last digit of the number $1 \cdot 2 \cdot 3 \cdot 4+1$, i.e., it is equal to 5. Therefore, $N$ is divisible by 5. (For another, more general solution, see problem 8.2.)