Amateur Discovers The Largest Known Prime Number, And it’s Gigantic

Breaking a Six-Year Drought in Prime Discoveries

A recent participant in the Great Internet Mersenne Prime Search (GIMPS) has broken a six-year stretch without new discoveries in the quest for large prime numbers, among the usual composites.

This new prime number has an impressive 41,024,320 decimal digits—it would take months to write out in full. To simplify, it’s 1 less than 2 raised to the power of 136,279,841. Officially named M136279841, it’s the latest milestone in mathematics.

Luke Durant, a former NVIDIA employee, only began contributing to the search last October, but had more than beginner’s luck on his side. He used thousands of graphics processing unit servers spread across 24 datacenter regions in 17 countries to run the software that helped in the discovery.

Confirmed as a Prime Giant

On October 11 of this year, a server in Dublin identified M136279841 as a possible prime. The next day, another server in Texas confirmed its authenticity, sealing its legendary status.

Prime numbers are integers greater than 1 that are not products of two smaller numbers. Although they seem simple at first, like 2, 3, and 5, indivisible numbers become rarer as we count higher, raising the question of whether they eventually run out. To the relief of mathematicians, the answer is no: primes are infinite, though hard to find.

Although technology has evolved, the search for massive prime numbers hasn’t changed much since the 17th-century French friar Marin Mersenne popularized a method for finding primes of a specific type that bears his name.

What Are Mersenne Primes?

“Mersenne primes” follow the formula 2ⁿ – 1. However, not all numbers in this form are prime—an example is 2 raised to the 4th power minus 1, which results in 15, a composite number (divisible by 3 and 5). Likewise, not all primes are of Mersenne type.

But this approach is particularly effective, and GIMPS, founded in 1996, adopted it to identify 18 of these giants so far, bringing the known total to 52.

The previous record, discovered in 2018 by Patrick Laroche from Ocala, Florida, had almost 25 million digits. He used his own equipment for the search, while Durant relied on a GPU network, marking a new era in the hunt for Mersenne primes.

The Appeal of Massive Primes

Why search for such large numbers? Beyond prestige, cash prizes, and the admiration of fellow enthusiasts, there aren’t many practical reasons. George Woltman, co-founder of GIMPS, explained that it’s essentially entertainment for math fans.

Prime numbers are useful for certain types of encryption, though quantum computing may soon limit this application. Even so, primes are the “atoms” of all positive integers and possess a unique beauty.

Soon, a new Mersenne prime may appear within the expanding global network of technology. And it will be number 53 on the list. A prime number.

Read the original article on: Science Alert

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