new largest prime number discovered has 22 million digits

Why Is The Discovery Of New Largest Prime Number A Great News For Encryption?

Kofesto Technology: World’s ‘new’ largest prime number has been discovered by a computer at a university in Missouri in the United States. This prime number, 2^74,207,281 – 1, has over 22 million digits. It has broken the previous record by approximately 5 million digits. Large prime numbers are known for their importance in computer encryption. It helps to secure the online banking, private communications, shopping transactions and other important applications. 

The new largest ever prime number has been discovered by a computer in Missouri. The number, 2^74,207,281– 1, has about 22 million digits and it’s 5 million digits longer than the previous one discovered in January 2013.

Prime numbers are the numbers that are divisible by themselves and one, for example, 2,3,5,11 and 13. This new number was a result of the Great Internet Messene Prime Search (GIMPS) collaboration, which is an effort by the volunteers from all around the world to find a larger prime number. The team at the University of Central Missouri, that broke this record, also held the past record.

How are world’s largest prime numbers discovered?

The prime numbers written as one less than a power of two (2ⁿ – 1) are also called Mersenne primes. The GIMPS project running to discover these numbers has been running from past 20 years, linking thousands of computers around the world to search for prime numbers. The same GIMPS project was being run by Curtis Cooper on several computers of the university and it lead to this discovery.

This search for the biggest prime numbers is conducted using a software called prime95, which is developed by GIMPS team. In past 20 years, GIMPS project has found the 15 largest Mersenne primes.

Cooper and his team told the press that he was notified by an email sent by the software. This discovery was probably made in September last year, but the computer failed to notify Cooper due to a glitch. The current official discovery date is January 7th 2016.

GIMPS software discovered a flaw in Intel Skylake CPUs in this process

Interestingly, the same software also discovered a flaw in Intel’s Skylake CPUs. This bug caused a system to freeze when GIMPS prime95 software was performing the complex task to find Mersenne primes.

This affected both Linux and Windows-based systems. It was found that during the multiplications of extremely large sizes, a particular exponent size, 14,942,209, caused the system to crash.

Intel later identified the issue that affected the 6th generation Intel Core processors and fixed it by releasing a BIOS update.

Discovery Of New Largest Prime Number Is A Great News For Encryption

Large prime numbers are known for their importance in computer encryption. It helps to secure the online banking, private communications, shopping transactions and other important applications.

But, where does a prime number fit in this encryption story? Well, cryptography is all about number theory, and all numbers (except 0 and 1) are a result multiplication of primes. Narrowing down this explanation, some most important encryption algorithms like RSA depend on the fact that prime factorization of huge numbers takes a long period of time. Thus, it’s a source of a lot of Cryptographic algorithms.

In the early 1990’s, late Richard Crandall, Apple Distinguished Scientist, discovered the Fast Elliptic Encryption system, now owned by Apple Computer. This encryption system uses Mersenne primes to quickly encrypt and decrypt messages. The same algorithm was implemented in assembly language, that produced a prime-searching program used by GIMPS project.

However, the current encryption system uses prime numbers that are just hundreds of digits long. “This prime is too large to currently be of practical value,” GIMPS said in a statement. But, with the ever increasing new methods of encryption techniques, quantum computing and security measures, these super long prime numbers would surely find some important application.