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# Largest Prime Number Discovered - Cryptography and Security Systems To Benefit

Curtis Cooper, a volunteer of Great Internet Mersenne Prime Search at the University of Central Missouri discovered the largest known prime number - 2 to power (74,207,281)-1. Also known as M74207281, this new numeral is calculated by multiplying together 74,207,281 twos and then subtracting one. Boasting of 22,338,618 digits, newest prime broke the previous record of the largest known prime: 2 to the power(57,885,161)-1, which had 5 million less digits than the current one. The previous ‘record breaking’ number was also discovered by the same team, headed by Curtis Cooper.

Our elementary mathematics classes at junior school, introduced us to the world of prime numbers. A prime number is simply any number which is divisible only by the number 1 and itself. A Mersenne prime, like the one discovered is a prime which is one less than a power of 2.

Prime numbers not only have immense applications in cryptography and security systems, but arguments regarding its distributions also have enormous significance in number theory and other fields of pure mathematics. Searching for the greatest prime eased the process of testing computer hardware design. The German computing community had uncovered a flaw in Intel's latest Skylake CPUs using GIMPS’ prime95 software, which is designed on the theory of Mersenne primes.

primes wheel

As of 2016, the 11 largest prime numbers are all Mersenne primes. The search for Mersenne primes gained greater importance in 20th century, with the introduction of the electronic digital computer. With this new discovery, Cooper added the 49th number in the Mersenne series.

The GIMPS press claimed that in order to attain an error free result, the prime was checked using different programs and different hardware. With the new addition, Cooper and his team have contributed 4 record largest primes at different times. Their first two record primes were discovered in 2005 and 2006, followed by the third in 2013 and the 4th in 2016.

The primality proof took a month of heavy computing on a PC with an Intel I7-4790 CPU and a free downloadable program developed by GIMPS. Astonishingly, the newest prime was reported to the software as early as on September 17, 2015. However, due to a bug the e-mail was unnoticed till the routine database maintenance took place months later. The latest discovery is eligible for a \$3,000 GIMPS research discovery award.

Watch Standupmaths interview with Curtis Cooper on his recent discovery:

Source: GIMPS