## Happy 2019!

Happy 2019, the first 4 digit number to appear 6 times in the decimal expansion of Pi.

By the way:

2019 = 14 + 24 + 34 + 54 + 64.

Also, 2019 is the product of two primes 3 and 673. The sum of these two prime factors is a square.

This is not all that is interesting about factors of 2019. Every concatenation of these two prime factors is prime. Even more unusual, 2019 is the largest known composite number such that every concatenation of its prime factors is prime. [Oops, the last statement is wrong, Jan 3,2019]

Happy Happy-go-Lucky year, as 2019 is a Happy-go-Lucky number: the number that is both Happy and Lucky.

In case you are wondering, here is the definition of Happy numbers: One can take the sum of the squares of the digits of a number. Those numbers are Happy for which iterating this operation eventually leads to 1.

In case you are wondering, to build the Lucky number sequence, start with natural numbers. Delete every second number, leaving 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, …. The second number remaining is 3, so delete every third number, leaving 1, 3, 7, 9, 13, 15, 19, 21, …. The next number remaining is 7, so delete every 7th number, leaving 1, 3, 7, 9, 13, 15, 21, …. The next number remaining is 9, so delete every ninth number, etc.

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1. #### Angelo Scordo:

The number 2019 can be represented as the sum of three squares in 7 different ways as follows:
1^2+13^2+43^2 = 2019
5^2+25^2+37^2 = 2019
7^2+11^2+43^2 = 2019
7^2+17^2+41^2 = 2019
11^2+23^2+37^2 = 2019
13^2+25^2+35^2 = 2019
17^2+19^2+37^2 = 2019

2. #### Angelo Scordo:

If you are curious about the complete list of the 2019 number attributes have a look to this site:
http://www.numbersaplenty.com/
This site is owned by an Italian computer scientist Giovanni Resta.
You can use the site for every number you are curious about up to 15 digits.

3. #### Giovanni Resta:

“2019 is the largest known composite number such that every concatenation of its prime factors is prime.” does not seem to be right. Just take 2047 = 23 * 89 or 2059 = 29 * 71, and so on.

4. #### tanyakh:

Giovanni, thanks. I added a note.