Blog Post #140: Welcoming 2023!

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

Blog Post #139: A tribute to the Man Who Knew Infinity

Here's a small tribute to Dr. Srinivasa Ramanujan, the Mathematics Genius on the occasion of his 135th Birth anniversary - 22-12-2022

Dr. Ramanujan was born on 22-12-1887 and many of us are familiar with his magic square which has 22, 12, 18, 87 as the topmost row that adds up to 139 and hence dedicating my 139th post to the eternal genius and one of the greatest mathematician the world has ever seen

Here are few patterns associated with his birthdate and magic numbers, which many mathematicians and number enthusiasts like me have always looked at in awe. Some of these are well documented but when we dig deeper, we get to unearth very interesting patterns and it is great fun to do that

a) 22121887 happens to be a Prime number! Yes - That happens to be his Birth date and the 8 digit number is a Prime!!!

b) 2212 + 1887 is 4099 which is again a prime!

c) The digits of 22-12-1887, when added in pairs, give 139 (22+12+18+87) which is a prime number. Go one step deeper - Take the first and third digit of 139 (19) and multiply that by its reverse (91) - We get 1729 which is Ramanujan number! 

d) When we add each digit of 22-12-1887 (2+2+1+2+1+8+8+7) we get 31 which is a prime and guess what - If we add each digit of 22-12-2022 (2+2+1+2+2+0+2+2) we get another prime - 13, which also happens to be the reverse of 31! The magic doesn't stop there though - 31 ^ 2 is 961 and 13 ^ 2 is 169 which are also mirror images of each other!

e) This is the 135th birth anniversary of Dr. Ramanujan and definitely the number 135 would show some interesting combinations and permutations given its association with the Man himself!

------->   1) For starters, the digits of 135 add up to a perfect square - 9

------->   2) The square of the digits add upto 35 which is a subset of 135

------->   3) The cube of the digits results in 153 which is the one of the 4 three digit Armstrong numbers (370, 371, 407 being the other three)

------->   4) 135 itself could be written as 61 + 74 and 61 and 74 combined would give us the famous Kaprekar constant - 6174!

f) Finally none of these blog posts around Ramanujan can be complete without writing about 1729

1729 = 12 ^ 3 + 1

9271 is one of the anagrams of 1729 

9271 = 21 ^ 3 + 10

21 is reverse of 12 and 10 is reverse of 01!

1729 + 9271 gives 10000 which is a perfect square (100 ^ 2)

#MathematicalGenius #srinivasaramanujan #TheManWhoKnewInfinity

 #NationalMathematicsDay