It may be seen only as a mathematical curiosity to most of us, but did you know that very large prime numbers are indispensable in maintaining effective cyber security?
By: Ringo Bones
Previously seen as a mere mathematical curiosity – and it still is by most of the population – but prime numbers – such as two, three, five and seven – numbers that are divisible only by themselves and one, play a vital role in computer data encryption. The latest prime number discovered so far back in January 20, 2016 is more than 22-million digits long – 22,338,618 digits long to be exact - five million digits longer than the previously discovered largest known prime number. Prime numbers this large could prove useful to computing in the future – which is sooner than you might think given the current rapidity of advances in hardware and software.
The new prime number was found as part of the “endless mathematical quest” called the Great Internet Mersenne Prime Search or GIMPS, a global quest to find a particular type of large prime numbers. Mersenne Primes are named after a French monk, Marin Mersenne, who studied them in the 17th Century during his spare time. Given that modern programmable digital computers processes data in binary code, they can be configured to hunt for Mersenne Prime Numbers by multiplying two by itself a large number of times, then taking away one. It is a relatively manageable calculation for today’s computers, but not every result is a prime number. This year’s newly discovered prime number is written as 2^74,207,281-1, which denotes the number two, multiplied by itself 74,207,280 times with one subtracted afterwards. Since it began 29 years ago, the GIMPS project has calculated the 15 largest Mersenne Prime Numbers and it is possible that there could still be an infinite number of them to discover.
Very large prime numbers are important in computer encryption and help make sure that online banking, shopping and private messaging services are secure, but current encryption typically use prime numbers that are only hundreds of digits long – not millions. But given our increasing reliance on computers for online commerce and private messaging, the search for very large prime numbers can be very important to maintain encryption with ever increasing processing power – although mathematicians involved in the GIMPS project admitted in a statement that this year’s newly discovered prime number is “too large to currently be of practical value”.
However, searching for large prime numbers is intensive work for computer processors and can have unexpected benefits. “One prime project discovered that there was a problem in some computer processors that only showed up in certain circumstances.” said Dr. Steven Murdoch, cybersecurity expert at University College London. This year’s new large prime number – the 49th known Mersenne Prime Number, was discovered by Dr. Curtis Cooper at the University of Central Missouri. Although computers do most of the hard work, very large prime numbers are said to be discovered only after when a human operator takes note of the result.