31 students in a row were numbered 1,2,...,31 in order.
The teacher wrote down a number on the blackboard.
Student 1 said "the number is divisible by 1",
Student 2 said "the number is divisible by 2",
and so forth...until
Student 31 said "the number is divisible by 31".
The teacher remarked: "Very well class, but two of you gave a wrong statement, and those two sit beside each other".
Determine those two numbers.