2019 – Interesting Number

Starting the year with a short post about some interesting numbers facts about 2019. I have done a very similar post for 2018 last year and I thought I will start the year with the same vibe. I also discovered that 2018 and 2019 have some things in common and that was really interesting to discover.

2019 is an odd number and a composite one.  Very similar to 2018, this numbers gives me the feeling that it kind of wanted to be a prime number, but changed its mind in the last second. This is because it is the product of 2 prime numbers: 3×673. Due to this, 2019 has just 4 factors or divisors: 1 and 2019; 3 and 673. Some people, consider 1, 3 and 673 to be proper divisors. With this in mind, the sum of all factors is 2696. Also, the sum of all proper divisors is 677, which makes 2019 a deficient number. If you don’t know, a deficient number is a number whose sum of its proper divisors is less than the number itself. The different (or deficiency) is 2019 – 677 = 1342 – quite a big difference.

Still talking about factors, as you have seen above it has exactly 2 prime factors: 2 and 673. Generally speaking, a prime number is an integer, or whole number, that has only two factors — 1 and itself. 3 is the first odd prime number out there, but more interesting it is the first Fermat prime and the first Mersenne prime. Another fun aspect is that 3 is the only prime which is one less than a perfect square (4 = 2²). The sum of these prime factors is 676.

If you want to find out other interesting facts about the numbers 2019, I recommend you check Numbermatics – the number explorer. They offer this really beautiful representation for the number of divisors and prime factors. I have played with it a couple of times just to see these wonderful images.


Moving on, I discovered some other really interesting ways to write 2019 using different type of operations. First that really impressed me is that 2019 is the smallest number that can be written in 6 ways as the sum of the squares of 3 primes:

Next on the list is the fact that you can write 2019 as the sum of the fourth power for all numbers from 1 to 6. Maybe this is not a surprising fact for you, but it was a surprise for me:


If you want to find other similar facts, I totally recommend you check Inder J. Taneja’s blog post 2019 in Numbers – it is incredible. It has A LOT of representations of 2019 in different situations – 46 of them!!!! He describes them as “of crazy-type, running numbers, single digit, single letter, Triangular, Fibonacci, palindromic-type, prime numbers, embedded, repeated, magic squares, etc.”. This list is the inspiration for Matt Parker’s video on 2019:

Hope you liked this post and you find it useful. Have a great day. If you have ideas for future blog posts, let us know. Don’t forget to check our last post: “Taming the Infinite” by Ian Stewart | Book Review . You can find us on  FacebookTumblrGoogle+Twitter  and  Instagram. We will try to post there as often as possible. Enjoy the day!

Lots of love and don’t forget that maths is everywhere! Enjoy!

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