Photo: from open sources
There are a lot of prime numbers, but the largest of them has more than two tens of millions of digits.
Mathematicians have been studying prime numbers for more than 2 thousand years, since the time of the ancient Greek mathematician Euclid. There are a lot of prime numbers, but which one is the largest? Live Science writes about this.
Prime numbers are numbers that can be divided without a remainder only by one or by themselves, for example, 3 and 7. Every number that is greater than one is either a prime number or a multiple of a prime number.
According to Thomas Kecker of the University of Portsmouth, England, it has been known at least since the time of Euclid that there are an infinite number of prime numbers. Therefore, finding the largest prime numbers has become an important task for many mathematicians.
Currently, the largest known prime number is M82589933 or 2*82,589,933 – 1. To calculate this number, multiply 2 by itself 82,589,933 times and then subtract one. This number contains 24,862,048 digits.
M82589933 is a Mersenne number and is a type of number that takes its name from the French monk Marin Mersenne, who researched these numbers over 350 years ago. To calculate the Mersenne prime number, 2 is multiplied by itself several times and then one is subtracted.
Mathematicians use special software on computers to find the new largest prime numbers. The number M82589933 was discovered on December 7, 2018, after 12 days of continuous computer operation as part of the GIMPS project.
To date, this is the largest distributed computing project to search for Mersenne primes. In this project, groups of volunteers run software on their computers in the background to collectively solve problems, that is, find new prime numbers. This project was founded in 1996 and is the oldest continuously running distributed computing project. The GIMPS project currently runs on more than 2.6 million computers, which perform approximately 4 million billion calculations per second.
According to Kecker, for a large integer that has several thousand digits, checking whether the number is prime or not used to take a very long time. But over the years, mathematicians have developed faster methods for determining whether Mersenne numbers are prime. Until 2018, the GIMPS project discovered a new Mersenne prime approximately every two years. But since then, no new largest prime number has yet been discovered.
