On Oct. 12, the Great Internet Mersenne Prime Search (GIMPS) announced that Luke Durant from California discovered the new largest prime number.
This massive prime number is M136279841, or 2136279841-1, clocking in at over 41 million digits long. For comparison, the mass of the Earth in kilograms is only about 25 digits long. “It’s even crazier to me that we can even prove that numbers this big are prime,” stated junior Grant Cabay.
Part of a larger family of prime numbers, M136279841 is classified as a Mersenne prime, any prime number in the form 2n-1, where n is some integer. Despite its shocking size, this prime is only the 52nd Mersenne prime ever to be discovered.
Finding these enormous prime numbers is a computationally time-consuming task. The most basic method to prove a number is prime is to show it is only divisible by 1 and itself, but this requires a colossal amount of computations. Instead, mathematicians have developed algorithms that require far fewer computations but still guarantee a number is prime, such as the Lucas-Lehmer test for Mersenne primes.
Even with these algorithms, finding new prime numbers requires millions of calculations. In the past, GIMPS ran these processes on volunteer computers across the globe, but this method was neither efficient nor productive. To improve his odds of finding a prime, Durant devised a method to combine the computing power of hundreds of computers across the globe, which allowed him to find primes much more effectively.
Mathematical research such as discovering new primes may seem abstract but has many real-life applications. Prime numbers, although not ones quite as large as M136279841, lay the foundations for modern encryption.
RSA encryption, which is a common encryption technique, relies on the difficulty of factoring a large number. “[The algorithm] takes a sufficiently large prime, performs some operations on it and sends it to the receiver of the data,” stated math teacher and cybersecurity club advisor Jason Landa. Knowing the prime and the algorithm, the receiver can easily transcribe the message into words.
For a hacker, though, it is excessively difficult to factor a several hundred-digit number, essentially guaranteeing the security of the message. “It would cost someone more than what it is worth, and take more time than they would want to invest to decrypt the data,” Landa added.
However, with the advent of quantum computers, mathematical research is more critical than ever. Quantum computers use quantum properties of atoms rather than electricity to perform calculations, and because of this fundamental difference, they have the potential to break through RSA encryption, Landa explained. As this threatens the security of just about every file on the internet, mathematicians and computer scientists across the globe are working to find ways to make encryption “quantum safe.”
At the end of the day, mathematical discoveries like M136279841 hide the complex ways math applies to everyday life. In simple terms, “It’s cool that they discover new things in math!” Landa concluded.
