Prime numbers are the “atoms” of the mathematical realm. As they are only divisible by themselves and one, they represent the smallest whole units, the building blocks of other numbers. Mathematicians use them to discover the underlying structure of patterns and equations, so every new prime is a welcome addition. This month, a computer in Missouri has managed to discover the largest known prime yet – one with 22 million digits.

Deeply curious numbers, primes follow no discernable pattern in the long run. The only way another can be discovered is for a person or a computer to manually check for numbers that are only divisible by themselves and one – the prime divisibility rule.

The Riemann Hypothesis, perhaps the greatest puzzle in mathematics, is a function that may be able to predict where a prime occurs in any set of values. Unfortunately, it has yet to be solved, despite some dramatic claims to the contrary. So far, it can predict the position of prime numbers in a specific number sequence, but there is no way of predicting the position of primes further beyond this number sequence without manually going through and checking their divisibility.

So for now, it is left to computers to trawl through mind-bogglingly enormous numbers to find those that follow the prime divisibility rule. To this end, the Great Internet Mersenne Prime Search program – with the unfortunate acronym “GIMPS” – has been set up. This distributed computing project, which is now celebrating its 20th birthday, uses processing power from volunteers’ personal or work computers all around the world in order to search for larger and larger primes.

In 2013, GIMPS discovered what was then the largest known prime. With 17 million digits, it cannot be written out conventionally; in the case of extremely large numbers, power functions are sometimes used. For example, 2^{5} is the number two being multiplied by itself five times. 2013’s prime number discovery, then, can be depicted as (2^{57,885,161} – 1), which is the number two multiplied by itself 57,885,161 times, then subtracted by one.

^{Primes are often used in cryptography – or code-breaking. AndreasG/Shutterstock}

GIMPS actually searches for the Mersenne primes, named after the French monk Marin Mersenne who first investigated their characteristics 350 years ago. These primes all take the form of (2^{n }– 1), where “n” represents any whole number. As using this function provides numbers that the computer can “aim” for rather than just randomly searching through a number sequence, they are the easiest large primes to search for.

This month, a prime number with 22 million digits has been discovered by GIMPS: (2^{74,207,281 }– 1), a whole five million digits longer than 2013’s record-breaker. This prime was found using up to 1,000 of the University of Central Missouri’s university computers, overseen by Dr. Curtis Cooper, a professor of computer science. This is, in fact, the fourth prime number he has found using GIMPS.

Apart from being both a mathematical and computational challenge, finding primes has real-world uses: They are extensively used in cryptography to produce harder to break codes. Fortunately then, there’s no shortage of prims to be discovered, as is an infinite number of of them. It is a journey without an end.

[H/T: the Guardian]