As 2020 drew to a close, it is time to welcome a brand new year with all hope and optimism and here's a small Mathematical note from my end
Some of these were already published in social media in recent days and so not necessarily unique for this post but it is amazing to see how many such patterns you could find when you look at 2021
a) 2021 is a difference of two perfect squares - 2025 and 4 (45 ^ 2 and 2 ^ 2) and hence applying a ^ 2 - b ^ 2 formulae, it ends up as a product of 2 prime numbers as well (47 and 43)
b) Prefix 1 to 2021 and you get a perfect palindrome 12021 which is a product of two prime numbers 4007 and 3!.
c) Suffix 1 to 2021 and you get 20211 which again a product of two prime numbers 3 and 6737
d) 20 + 21 is 41 which is again a prime and the subsequent two prime numbers when multiplied gives 2021! (43 and 47)
e) Sum up the digits of 2021 - 2 + 0 + 2 + 1 = 5 and it is a prime again!
f) 43 and 47 are the prime factors as we saw earlier. Now prefix 1 to both 43 and 47 and multiple the two - 143 * 147. The resultant number is 21021 which has a close resemblance to 2021 (1 inserted as the second digit)
g) Now add 2020, the year gone by with 2021 and you get 4041 which is again a product of two primes - 3 and 1347
These are other "prime" reasons why we should hope for the best in 2021 :)
Happy New Year again
