2^136,279,841-1. That number probably doesn’t tell you anything by itself, but it is an important number. And it is because it is the largest prime number in the world, and finding it is very difficult. So much so that it took us six years to do it: its predecessor was found in 2018.
GIMPS. The Great Internet Mersenne Prime Search (GIMPS) collaborative project is a distributed computing initiative that seeks to find Mersenne prime numbers (2^n-1 format). It does this by harnessing the combined power of thousands of “volunteer” computers around the world that are dedicated to doing intensive calculations to find those new primes. That is, numbers that can only be divided by themselves and by unity (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, …).
Eureka. The person responsible for the discovery, also known as M136279841, has been a very active user of the GIMPS project named Luke Durant, a former NVIDIA employee. He achieved this by combining the power of GPUs in the cloud that he was able to use for very little because he used them when those components were underutilized. What he ended up creating was a kind of “distributed supercomputer” with GPUs located in data centers in 17 different countries.
From CPU to GPU. Until a few years ago, the search for Mersenne prime numbers focused on the use of the main processor together with the Prime95 application. However, Mihai Preda, another member of the initiative, created a tool called GpuOwL that instead of using the CPU for these calculations used the GPU. The power of these components is much greater than that of general-purpose processors, which allows calculations to be speeded up significantly. The tool was later improved by George Woltman and Aaron Blosser fine-tuned its performance on servers. In the end the credit for finding the new largest cousin in the world has gone to the four of them.
We only have 52 cousins from Mersenne. One would imagine that by now the combined power of those computers and GPUs would have allowed us to find a lot of new primes, but in reality it has only allowed us to find 52 new Mersenne primes. These primes are so large that finding them is especially difficult and consumes a lot of computing resources. Of course: the GIMPS project has become the absolute protagonist in terms of searching for new cousins: this effort has been responsible for the discovery of the last 18.
You too can find a cousin of Mersenne. The GIMPS initiative remains fully open to new volunteers who give up computing capacity on their computers when they are not in use. Simply download and install a small program, which will run when it detects that our computer is inactive.
And reward (symbolic) if you do it. Those who find a new Mersenne prime number get a reward, although it is not very large. Specifically, $3,000. Of course: the prize will be bigger, $50,000, for whoever finds the first prime number with at least 100 million decimal digits.
Prime numbers have their that. The effort seems more like a curiosity than anything else, but as explained long ago in Ars Technica, these large prime numbers have practical applications. For example, they are part of RSA encryption: the person who wants to receive a message protected with this algorithm will publish the product of two large prime numbers as their “public key”, something that makes it very difficult to decrypt with brute force.
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