examday

/TMUA

A student attempts to answer the following question.

What is the largest number of consecutive odd integers that are all prime?

The student's attempt is as follows:

• I. There are two consecutive odd integers that are prime (for example: 17, 19).
• II. Any three consecutive odd integers can be written in the form $n-2$, $n$, $n+2$ for some $n$.
• III. If $n$ is one more than a multiple of 3, then $n+2$ is a multiple of 3.
• IV. If $n$ is two more than a multiple of 3, then $n-2$ is a multiple of 3.
• V. The only other possibility is that $n$ is a multiple of 3.
• VI. In each case, one of the integers is a multiple of 3, so not prime.
• VII. Therefore the largest number of consecutive odd integers that are all prime is two.

Which of the following best describes this attempt?