Received an OTP as part of one of my regular online transactions and when i saw the number 347743, i told my wife that it is a palindrome. Ofcourse she gave me a surprised look and moved on with rest of the chores that she was focusing on!!
Given my penchant towards numbers, I started analyzing this in more detail and it was pretty refreshing to unearth some of the obvious and not so obvious properties.
347 and 743 are the two numbers in consideration and to draw a parallel to the corporate world, this is a great example of how complementary skillsets within the team can help galvanize everyone to come together to achieve a common goal
Let's start looking at some of the characteristics exhibited by the number
1. Both 347 and 743 are prime numbers to begin but 347743 has 11 as one of the factors given it was formed by 347 and its reverse!
2. Subtract 14 from 743 and it gives a perfect square (729). Now give whatever has been subtracted from 14 to 347 and the sum is again a perfect square! (361). Talk about balancing act!
3. 347, 349, 353, 359, 367 are successive primes and the difference between successive primes is 2, 4, 6, 8 (this is quoted in multiple mathematics articles). Now look at the reverse of these numbers - 743 is a prime as we already know, 943 is a product of two primes (23 and 41), 353 is a prime, 953 is a prime and 763 is again a product of two primes (7 and 109)!
4. From the original number 347743, let's do the following. Though some of these are pretty obvious in hindsight, it looks interesting on how it unfurls when we analyze deeper
a) Remove both 7s first and we get 3443 which is a multiple of 11 and 313 ( a palindrome).
b) Remove both 4s and we get resultant number as 3773 which is a multiple of 343 and 11. 343 is a palindrome as expected but it is also 7 ^ 3 and unique in its own ways (3 + 4) ^ 3 is 343!!
c) Remove both 3s and we get resultant as 4774 or since we are dealing with odd numbers let's go with 7447. 7447 is again a product of two primes - 11 and 677
5. Now let's add 347 and 743 and the outcome is 1090. To begin with, 1090 looks pretty much like any other even number but here is the fun part
a) It can be also written as Sum of two squares - 33 ^ 2 + 1 ^ 2.
b) What's more amazing is that it can be written as 32 ^ 2 + 66 and 34 ^ 2 - 66. 1090 exhibits such unique properties spread across 3 successive squares
6. Last but not the least when we multiply 347 and 743 the resultant is 257821. At first glance, there isn't much to look into except it is a 6 digit number and product of two primes. Dig a bit deeper - Take 821 and reverse it to get 128. 128 *2 + 1 is 257!
Numbers are fun as always and for me the trigger for this weekend post was a harmless OTP which turned out to be a very interesting palindrome showing lot of synergies just like we would all expect within a team in our corporate world!
