Largest known prime number, spanning 41 million digits, discovered by amateur mathematician using free software

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The largest known prime number has been discovered, smashing the previous record by more than 16 million digits.

A draw housing six Sapphire Technology AMD graphics processing units (GPUs).
A draw housing six Sapphire Technology AMD graphics processing units (GPUs). (Image credit: Getty Images)

The largest known prime number has been discovered by an amateur researcher and former Nvidia employee.

The new number is 2136,279,841 – 1, which beats the previous title holder (282,589,933 – 1) by more than 16 million digits.

Prime numbers, described by mathematicians as the "atoms of integers," are numbers that are divisible only by themselves and 1. The smallest prime numbers are 2, 3, 5, 7 and 11. Technically, prime numbers run to infinity, but finding them becomes significantly harder the bigger they get.

To find the new prime, Luke Durant used a free program called the Great Internet Mersenne Prime Search, or GIMPS, to sift through the possibilities with an algorithm. His efforts required the harnessing of thousands of graphics processing units (GPUs) across 24 data centers in 17 countries — a feat that "ends the 28-year reign of ordinary personal computers finding these huge prime numbers," according to a statement released on the GIMPS website.

The newly confirmed prime number contains 41,024,320 decimal digits, according to the statement.

Related: Pi calculated to 105 trillion digits, smashing world record

The new prime number is also the 52nd known Mersenne prime — a series named after Marin Mersenne, a French monk and polymath who devised a formula for finding prime numbers by subtracting 1 from powers of 2. (The smallest Mersenne prime is 3 — or 2 to the power of 2, minus 1.) Though far from being the only way to discover primes, the method is slightly easier than others.

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As for the usefulness of the discovery, "At present there are few practical uses for these large Mersenne primes, prompting some to ask, 'Why search for these large primes?'" the GIMPS team wrote in the statement. "Those same doubts existed a few decades ago until important cryptography algorithms were developed based on prime numbers."

The discovery has netted Durant a $3,000 cash prize from GIMPS. Further prizes of $150,000 and $250,000 await those who discover the first hundred-million-digit prime and the first billion-digit prime, respectively.

Ben Turner
Ben Turner
Staff Writer

Ben Turner is a U.K. based staff writer at Live Science. He covers physics and astronomy, among other topics like tech and climate change. He graduated from University College London with a degree in particle physics before training as a journalist. When he's not writing, Ben enjoys reading literature, playing the guitar and embarrassing himself with chess.