Blog Post 141: Twin Primes - Part 2

In an earlier blog post (#137), I had documented about one of the properties of Twin Primes - If we multiple any Twin prime (except 3, 5) and add the digits of the resulting number, the answer is always 8

Here we look at another simple property of Twin Primes, which is very well documented by eminent Mathematicians but not very obvious to everyone

Again the Twin prime of (3, 5) is an outlier and doesn't directly satisfy this condition

Few examples for illustration

{11, 13} - If we add these two numbers then the resulting number is 24 which is a multiple of 6

{179, 181} - 360 is the resulting number and again a multiple of 6

{333029, 333031} - 666060 is the resulting number and a multiple of 6

Taking it a step further - Let's add two successive Twin Prime pairs {11, 13} and {17, 19}. The resulting answer is 60 which is the sum of {29, 31} which is the next Twin Prime pair in that sequence. {41, 43} is the next Twin prime pair which adds up to 84 and that is in turn the sum of {11, 13} and {29, 31}. Can we look at similar patterns as we go further?

Interestingly if we look at {3,5} which remains as the exception, their sum is 8 while their product is 15 and if we add the digits of 15, the resultant is 6! It is the complete opposite of what we observe with other twin primes

Drawing an analogy to the corporate world as I always do - Team members working together whether as part of a large or small group, produce consistent results as long as they have unique attributes and working towards a common goal.

#MathsIsFun #AnandMathemagic