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 \(m.\)