Why Do Mathematicians Keep Looking for New, Bigger Prime Numbers?

Back in 2017, the Great Internet Mersenne Prime Search made an iconic discovery – it found the biggest prime number known to mankind, which is, by the way 23,249,425 digits long.

Yes, the largest prime number has 23 million digits!


Honestly, before writing this article, I didn’t know that the largest prime number was that large. After my initial shock response subsided, the very first question that came to my mind was rather, ummm… stupid?

However, when I inquired and asked around, I realized that the question wasn’t that stupid after all. That question, my dear reader, is the title of this article.

Let’s start from scratch.

What are prime numbers?

You may have studied prime numbers in high school, but let’s have a quick recap. A prime number is one that has only two factors, i.e., it can be perfectly divided by only two numbers – 1 and itself.

For instance, 17 is a prime number, because there are only two numbers – 1 and 17 – in the whole wide world that can perfectly divide 17. Here’s a list of the smallest prime numbers:

prime number chart

(Photo Credit : Blogspot)  The numbers in shaded boxes are prime numbers.

Determining whether a given number is prime or not is fairly simple for smaller numbers, but as the numbers become bigger and bigger, it becomes increasingly difficult to determine if it’s a prime number or not.

For really large numbers, they use special computers that run thousands of calculations per second to determine those numbers’ ‘prime’ status.

With all that in mind, have you ever wondered why mathematicians and math enthusiasts continue looking for new, bigger prime numbers? As in, what’s the point of doing it at all?

Finding new methods and techniques

The most useful aspect of finding new, larger prime numbers is the valuable learning experience that it provides. It goes without saying that writing programs and algorithms to discover new prime numbers is no cakewalk. It takes a very long time to discover the largest prime in the first place.


While toiling to find that largest prime, you are bound to learn many new things about prime numbers in general. And who knows, you might end up discovering something more than just the largest prime number!

A technical pursuit

Consider this: the largest prime number is 23 million digits long. Now, when you deal with numbers this long, you have to develop new algorithms that can manipulate and ‘play’ with such gigantic numbers efficiently. Once these novel programs and algorithms are developed, they can potentially be used in other areas of research.

Finding the biggest prime is not really considered a mathematical pursuit, but rather a scientific or technological pursuit by many. If you think about it, the biggest prime number itself doesn’t have much significance.


However, as mentioned earlier, finding that number is difficult… very difficult. So, if you develop a ‘tool’ that could do that, I’d bet that tool could accomplish many other amazing things, which may be a big help to the broader human race.

Generating interest

Such pursuits and breakthroughs invariably help generate interest in the common folk working in the field of math. There are people who engage in such pursuits on their own, and do dedicated research to discover the newest prime number. Such activities and practices give a boost to the general public interest in the field of math and prime numbers, which is a great thing that should not be underestimated.

Furthermore, just because something doesn’t have a tangible and immediate impact on our daily life doesn’t mean that it is of no use whatsoever. If that were the case, we would never know and understand so much of the world that we do today.


All in all, if you look at it from a number theorist’s perspective, there’s virtually no mathematical significance in finding new prime numbers; finding the largest prime isn’t really considered a major breakthrough by most mathematicians.

However, the things that may be of actual interest are the ways in which these new primes are discovered and how they can be applied. It could be a computer science, machine language, or even a hardware accomplishment that led to the discovery, and if that accomplishment can be applied in other areas of study and research, then everyone wins!


  1. University of Tennessee at Martin
  2. University of St Andrews
  3. The University Of Utah
  4. Minnesota State University Moorhead
  5. The University of Maryland
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About the Author:

Ashish is a Science graduate (Bachelor of Science) from Punjabi University (India). He spends a lot of time watching movies, and an awful lot more time discussing them. He likes Harry Potter and the Avengers, and obsesses over how thoroughly Science dictates every aspect of life… in this universe, at least.

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