Here's a short Mathematical note from yours truly on the occasion of New Year!
The number 2023 has lots to do with prime numbers and prime factors and exhibits some unique characteristics
a) To begin with, prime factors of 2023 are 17, 17, 7
b) Add 20 and 23 to get 43 which is prime and 4+3 is again a prime
c) Prefix 1 to 2023 and the resultant is 12023 which is a product of 11 and 1093 (two primes)
Suffix 1 to 2023 and we get 20231 which by itself a prime!
d) Now for some sheer prime magic around 2023!
Adding all the digits of 2023 gives 7
Adding squares of the digits gives 17 which is the other prime factor of 2023 apart from 7!
Adding cubes of the digits gives 43 which was sum of 20 and 23 as seen earlier!
Adding the digits to the power 4 results in 113 which is again a prime!
Adding the digits to the power 5 results in 307 which is still a prime!
The prime streak is "broken" when we add the digits to the power of 6 where the resulting number is 893 which is a product of two primes in any case! 19 and 47.
e)
Having seen a "Prime fest" all along, let's do a square of 2023 and the resulting number is 40,92, 529. This shows a nice pattern when you dissect the digits
20 + 20 = 40, 23 x 4 = 92, 23 x 23 = 529
If you add all the digits of 4092529 we get 31 which is a prime and if you add the digits 40 + 92 + 529, the answer is 661 which is a prime again!!
It has been raining Primes as far as 2023 is concerned and that's going to be one "Prime" reason for me to look at welcoming 2023 with lot of optimism and hope!
Wishing everyone a very Happy, Healthy and Prosperous 2023
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