Challenge Level

$3, 5, 7$ are a set of three consecutive odd numbers which are all prime.

$109, 111$ and $113$ are a set of three consecutive odd numbers which are not all prime $(111=37\times3)$.

**Can you find another set of three consecutive odd numbers which are all prime?**

If not, might it be impossible?

Mathematicians aren't usually satisfied with testing a few examples to convince themselves that something is always true, and look to proofs to provide rigorous and convincing arguments and justifications.

**Can you prove that there is only one set of three consecutive odd numbers which are all prime?**

Below is a proof that has been scrambled up.

Can you rearrange it into its original order?

If you can find a proof which is different to the one in our proof sorter, then please do let us know by submitting it as a solution.

**Extension:**

Take a look at Take Three from Five which requires similar reasoning to this problem.