Happy 2021 everyone!
As a way to start out the new year, what’s better than an article about the mathematical properties of the number 2021 to prepare for the next Mathematical Team Competitions?
To start out, 2021 is not a prime number, its factorization is:
Hence, be prepared for a lot of chinese remainder theorem modulo 43 and 47 this year, which is actually not that bad since last year we had to do modulo 4, 5 and 101.
It has 4 divisors and their sum is 2112.
The greatest prime not greater than 2021 is 2017 and the least prime greater than 2021 is 2027.
Also, the 2021th prime is 17579.
Its binary form is
Finally, its square is 4084441.