Who is wrong?

A teacher wrote a number on the board and asked the students to tell about the divisors of the number one by one.

• The $1^\text{st}$ student said, "The number is divisible by 2."
• The $2^\text{nd}$ student said, "The number is divisible by 3."
• The $3^\text{rd}$ student said, "The number is divisible by 4."
• $\quad \quad \vdots$
• The $30^\text{th}$ student said, "The number is divisible by 31."

The teacher then said that exactly two consecutive students were incorrect.

Which two students were incorrect?

If the $m^\text{th}$ and $(m+1)^\text{th}$ students spoke wrongly, then enter $m.$