$\underline{\text { Folklore }}$Is the number $2011 \cdot 2111+2500$ a prime number?
First method. $2011 \cdot 2111+2500=2011 \cdot(2011+100)+2500=2011^{2}+2 \cdot 2011 \cdot 50+50^{2}=(2011+50)^{2}=2061^{2}$.

Second method. The remainder of dividing the numbers 2011 and 2500 by 3 is 1, and the remainder of dividing 2111 is 2. Therefore, this number when divided by 3 will give the same remainder as the number $1 \cdot 2+1=3$, that is, it is divisible by 3.

## Answer

It is not.