The longest simple Mersenne number is found, consisting of 22 million digits

The large-scale project of voluntary calculations for the search for prime Mersenne numbers (GIMPS) marked its 20th anniversary with the discovery of the largest of the currently known prime numbers, 2 ^{74 207 281} - 1. Curtis Cooper, one of the many thousands of GIMPS volunteers, used one from the computers of his University of Central Missouri, to make this discovery.

A simple number, called M74207281, was calculated by multiplying 74 207 281 twos and subtracting one. The resulting number contains 22,338,618 digits, which is almost 5 million more than the number holding the previous record of the longest prime number.

Although the use of primes is very common, for example in cryptography, the longest prime number obtained is likely to be too large to be of practical significance. However, the search for the number itself has brought many practical benefits to scientists. Historically, the search for Mersenne prime numbers was used as a check on computer equipment. Earlier this month, thanks to the GIMPS prime95 software, members of the German computer community found some defect in the latest Intel Skylake processors, on the basis of which the group conducted the research. It is noteworthy that similar hardware problems were discovered in many other private personal computers that also participated in the calculations.

To prove that there were no errors in the main computational process, a simple number was analyzed by different programs on different computer equipment. Andreas Hoglund and David Stanfill analyzed using CUDALucas software for NVIDIA Titan GPUs. In addition, David Stanfill conducted a number analysis using ClLucas software for AMD Fury graphics chips. The last test was conducted by Serg Batalov, on MLucas software, running on an 18-core server.

For Dr. Cooper, a professor at the University of Central Missouri, the so long prime number found is the fourth. The first was calculated in 2005, after which in 2006 followed the opening of the second. The number of Cooper lost its record value in 2008, but the new number found in 2013 returned him the palm tree of the championship. Interestingly, the longest currently available prime number was discovered as early as September 17, 2015, but it took 127 days just to prove that the scientist was really worth something. The analysis was carried out with the help of a personal computer based on the Intel I7-4790 processor.

Despite the fact that the very number was discovered by Cooper's computer, the scientist notes that this discovery would be impossible without the other volunteers participating in the GIMPS project.

The new prime number refers to the Mersenne natural numbers, named after the French mathematician Maren Mersenne, who researched their properties in the 17th century. At the moment only 49 Mersenne numbers are known. Since the founding of GIMPS in 1996, only 15 of these numbers have been found.

The article is based on materials https://hi-news.ru/computers/najdeno-samoe-dlinnoe-prostoe-chislo-mersenna-sostoyashhee-iz-22-millionov-cifr.html.