Why Is 2025 A Special Year? Fair And Square!

Square One: Kicking Off 2025

Let’s start from square one! Wish you all a very happy 2025, and may it fulfill your wildest dreams and aspirations. And, I want to share with you some interesting facts that I have discovered, based on which I can look at you square in the eye, and tell you to dream higher and achieve even more in 2025!

Now that I have piqued your curiosity, let me tell you why 2025 is a very special year.

On A Square Note

Since we started off with squares, let us note that 2025 is a square too, being the square of 45 [45*45=2025]. And, the last time we welcomed a new year that was a square number was 89 years ago in 1936 [44^2], and the next time we will witness this phenomenon will be after 91 years in 2116 [46^2].

So, this in itself makes 2025 a very special year indeed, since most of us are likely to live through a “square year” just once in our lifetimes, unless you were around in 1936, or unless you live through until 2116!

However, there is more, within this square space itself that makes 2025 a very special year.

What will 2025 produce?

We do not know yet what 2025 will produce, but we know that it is a product of some special ingredients. Not only is 2025 a square number, but is the product of two squares. It can be expressed as the product of the squares of 5 and 9 [5^2 * 9^2 = 25*81 = 2025]. However, any square number, which is not a prime number will always exhibit this property.

Summing Up 2025

What actually makes 2025 remarkable is the fact that it is also the sum of two squares, being the sum of the squares of 27 and 36. [27^2 + 36^2 = 729 + 1296 = 2025]

This is far less common than you would think, and here are the results of some number crunching I did. The last time that we came across a year that could be expressed both as a sum of two squares and as a product of two squares was in the year 1600, i.e. 425 years ago!

And, the next time that we will witness a year with similar properties will be in the year 2500, that is 475 years away.

Squaring It Off

For the curious ones, while the product of squares can be easily computed for 1600 and 2500, the sum of the squares will need some work to figure out. I will give a partial answer here, and will provide more details as an endnote, just in case you want to take this up as a mental challenge.

2500 is the sum of squares of 30 and 40 [30^2 + 40^2 = 900 + 1600 = 2500]. Can you guess which two numbers’ squares add up to 1600? Also, 2500 can also be represented as the sum of squares of another set of two numbers. Can you figure out those numbers as well?

The answer is mentioned as an endnote, just in case you want to see some evidence.

After all, all claims need to be backed by evidence and driven by data.

What Does 2025 Add Up To?

We have crunched a lot of numbers, and things seem to be all squared up, but what does this all add up to? I will come to that shortly, and trust me, it will be worth the journey. The short spoiler alert is that the unique properties of 2025 hint at an incredible year ahead of us.

But, let us not get ahead of ourselves, yet. The mention of adding up reminds me of yet another incredible property of 2025.

It is the sum of cubes of all single digit numbers known to mankind!

In other words, if you add up 1^3 and 2^3 and 3^3 and so on, all the way to 9^3, you will get 2025! [1+8+27+64+125+216+343+512+729 = 2025]

In fact, 2024 was also the sum of cubes of 8 consecutive numbers from 2 to 9. The previous year was also a special year as it exhibited unique properties that do not repeat themselves over hundreds (or thousands of years). You can read about why 2024 was a year of the infinite force multiplier.

2025 – The Real RRR – Rare Recursive Residue

So far, we have seen properties of 2025 that will repeat themselves just once in our lifetime or in few hundred years. It is time to reap the richly deserved rewards for staying with me in this exploratory journey, as I unveil the property of 2025 that will not repeat itself until the year 9828, i.e. only after a gap of 7803 years.

Since we will most likely not have this conversation at that time, let us understand this unique phenomenon behind 2025, which is a real RRR number – leaving behind a Rare Recursive Residue.

What is a RRR (Rare Recursive Residue) number?

Do not search for this on Google, because I will tell you, of course! And, secondly because I just invented this term, and you will probably not find it elsewhere!

I define a Rare Recursive Residue number as a number where repeated division by the sum of the digits (and its subsequent resulting set of numbers) results in the last 2 digits of the original number itself.

Let us apply this to the first 4 digit number which is a RRR number – 1215. When we divide the year 1215 by its sum of digits which is 9 [1+2+1+5], we get 135. When we divide 135 by 9 [1+3+5], we get 15, which are the last 2 digits of 1215.

Similarly, when 2025 is divided by its sum of digits, which is 9 [2+0+2+5], we get a residue of 225. Upon a repeated division of 225 by its sum of digits which also happens to be 9 [2+2+5], we get 25 which are the last 2 digits of 2025.

And, as promised, the next time we will encounter this attribute of a rare recursive residue will be in the year 9828 (9828/27 = 364 and 364/13 = 2, the last 2 digits of 9828).

In fact, there are only 4 four-digit numbers known to mankind where this attribute is on display. I have already shared three such numbers – 1215, 9828 and of course, our very own 2025.

A special mention awaits anyone who tells me which is the fourth (4-digit) number which displays this property!

2025 – A Special Year Awaits

But, more importantly, a special year awaits each one of us. We witnessed the year with the power of the infinite force multiplier in 2024, and it is now time for the opportunity of a lifetime, or should I say, an opportunity for the ages!

The fact that 2025 is bestowed with so many unique properties could be mere luck or co-incidence, or just random numbers at play. And, that could be your truth.

However, these patterns made themselves visible to me, and I think that there is an encoded message here.

Decoding Patterns Hiding In Plain Sight

To me, this signifies the triumph of a data-driven approach that can generate unique insights and decode patterns that were hidden in plain sight. And of course, it signals an opportunity to make the most of these unique circumstances.

I, for one, have set some of my goals for 2025 very clear.

I will continue decoding the hidden patterns that hide in plain sight, and generate unique insights and value from the same, in addition to my other endeavors.

Delivering Data-Driven Insights at StockPatri

These efforts have already taken shape in the form of the launch of StockPatri in 2024, with a mission to empower retail investors and traders with the power of data-driven insights that were hitherto available only to institutional players.

If we can uncode so many hidden properties of an innocuous number of the incoming year, imagine the value that can be unlocked by data-driven insights generated from the treasure trove of information that resides in the stock market.

At StockPatri, we have already launched the StockBal Index, which is a multi time-frame measure of relative strength of all NSE traded stocks updated on a daily basis, and probably the first of it’s kind!

Are You All Squared Up?

This is a fair and square account of how the numbers have added up for me, and why 2025 is a very special year indeed.

With so many unique things converging in 2025, it is time to go back to square one and take advantage of the opportunity that lies ahead of us. It is that kind of a special year, when we can attempt to square the circle, and achieve impossible dreams!

So, the question is not if, but rather, how will you make 2025 the most special year to remember for hundreds or thousands of years? Are you all squared up for the opportunity that will be remembered for ages to come?

Endnotes:

1. Sum of 2 squares – 1600 = 24^2 + 32^2 = 576+1024 (just as 2025 is the sum of squares of 27 and 36)
2. Sum of 2 square – 2500 = 14^2 + 48^2 = 196+2304 (2500 is also the sum of squares of 30 and 40)
3. Awaiting the answer to the 4th four digit number that reduces to its last 2 digits upon repeated division by the sum of its digits. The other 3 numbers are 1215, 9828 and of course, a very happy 2025 to all of you!

About The Author

Rajiv Maheshwari is a business and start-up advisor, and the co-founder of StockPatri.com and From The Experts Mouth. He is a management professional with over 25 years of experience, and worked as CEO for a decade, and in leadership roles with NYSE listed companies such as Accenture and WNS.

He is a Chartered Accountant and MBA (Director’s Merit List from IIM Bangalore) and an autodidact, who is on the path of self-directed life long learning and sharing. He is a thought leader, author and keynote speaker and has developed several frameworks to bridge the gap between academia and industry.