Local election day will soon be here in the UK – May 4th. My husband, Howard, is standing as a local councillor candidate and we have been incredibly busy with this. We have been knocking at people’s doors, asking them what they’d like to see more of / less of in the area, whether they plan to vote for Howard etc. We need to have an estimate of voters so that the party can target resources. I have found the experience generally quite enjoyable. I’ve met people in the ward who are completely new to me. I like walking around and chatting to people, even if they don’t plan to vote for Howard. One or two doors have been shut in my face and several people have come up with transparent excuses as to why they can’t speak to me but it’s nothing with which I can’t cope!

I think the most inspiring person I’ve met was a woman in her early twenties, working in a top position in engineering and who has just bought her own house. I was stunned! She lives just up the road and before last week I didn’t even know she existed. We met young people still at school who were 16 and 17 who would like to vote but can’t yet. Some have even registered so as to be ready when their time comes! Some people are putting up with an awful lot and, if Howard does succeed, he will be in a position to help.

Given all this it won’t surprise you to learn that my number for this post is 4 – as in the 4th of May. If you have read one of my posts before you will know that I choose a number that has occurred naturally in my everyday life and then find an interesting mathematical fact about it – preferably one with a familiar adjective. Today I’m going to write about brilliant numbers.

# Brilliant Numbers

A brilliant number is the product of two primes with the same number of digits.

The number 4 is a brilliant number because 2 x 2 = 4, 2 is prime and is repeated here so naturally has the same digits.

The first few brilliant numbers are:

4, 6, 9, 10, 14, 15, 21, 25, 35, 49 and so on.

Another example:

35 is a brilliant number as 5 x 7 = 35, 5 and 7 are both prime and single digits.

A larger example:

5,609 is a brilliant number as 71 x 79 = 5,609, both 71 and 79 are prime and also have two digits.

We have met many other properties of the number 4 before:

• 4 is a Harshad number (a bringer of joy) as it is a multiple of the sum of its digits – i.e., 4. See this post.
• 4 is impolite as it cannot be written as the sum of consecutive numbers. See this article.
• 4 is an odious number as the sum of the 1s in its binary representation is odd. See this article.

I am glad that I have found another positive-sounding property of 4. In China the number 4 is regarded as very unlucky as it sounds a lot like the word for death. Chinese people try to avoid living in addresses with 4s in them.