A 22-million-digit prime number was just discovered and it’s the largest to date; so why should you care?

Image courtesy of Boris Drenec/Flickr

A new 22 million digit long prime number was discovered by a computer at the University of Central Missouri. This number, which is abbreviated as 2^74,207,281 – 1, is five million digits longer the previous largest prime number known to date.

For the readers joining us who are not STEM professionals or need a quick brush-up, prime number are numbers divisible by themselves and one: two, three, five, seven, thirteen, etc. Endeavoring to find the highest known prime number is long-held mathematical quest that dates back nearly 350 years ago to the 17^th century, when French monk Marin Mersenne began documenting his research. Today, prime numbers are becoming increasingly important as computers play increasingly dominant roles in our lives.

The most recent entry is the 49^th known Mersenne prime. It was found as a part of the Great Internet Mersenne Prime Search, the longest continuously running global computer network tasked with finding prime numbers. GIMPs—an ironic designation for such a capable project—discovered 15 of the largest prime numbers since it first began 20 years ago.

Although computers do the heavy lifting, a new prime number is said to be discovered when a human takes note of the results. In this case, Dr. Curtis Cooper of the University’s mathematics and computer science departments observed the number while performing routine maintenance on the computers running the GIMP software. It was found in September 2015, but sat unnoticed until now. This is the fourth Mersenne prime noted by Dr. Cooper, with the previous being in 2013.

So, why are prime numbers important these days? The most practical reason is cryptography, and by extension, cybersecurity reliant on public-key cryptography. Public-key cryptography is underscored by the complexity of integer factorization, or the time it takes to breakdown an integer into its prime factors. It’s called “public-key” because half of the key is the integer we’re trying to factor and it’s publically known and available, whereas the other half of the key is made up of the integer’s prime factors.

At face value it seems that deciphering the encryption is simply a matter of the time it takes to deconstruct the integer and brute force your way in. This is true, but completely unrealistic considering current Advanced Encryption Standard uses 256-bit keys, which would take a super-computer 3.31 x 10⁵⁶ years to crack.

Prime numbers also play a role in the Gödel numbering mathematical function, an inherent logic that allows any type of information to be encoded as a single integer. The logic works by assigning symbols to each number of a mathematical notation, allowing a sequence of natural numbers to be represented by a sequence of symbols. Next, these natural number symbols are represented by a single natural number.

Source: Guardian