HomeThe World We DiscoverMersenne Prime Record: 41 Million Digits Found by a GPU Cloud

Mersenne Prime Record: 41 Million Digits Found by a GPU Cloud

Former NVIDIA engineer Luke Durant spent $2 million on cloud GPUs spanning 17 countries to find the 52nd Mersenne prime.

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The World We Discover · Explore this series
May 31, 2025
Key Takeaways
  • A former NVIDIA engineer found the 52nd Mersenne prime with 41 million digits.
  • The search used thousands of cloud GPUs across 17 countries.
  • This was the first Mersenne prime discovered using GPUs, not CPUs.

Luke Durant was folding laundry into a suitcase when he checked his computer and learned he had found the largest known Mersenne prime.

The 36-year-old former NVIDIA engineer had spent a year and roughly $2 million building a homemade supercomputer from rented cloud GPUs. His network stretched across 24 data centers in 17 countries. Its single purpose was hunting for a rare class of prime number.

Key figure

41,024,320

digits in the largest known prime number, discovered October 2024

A $2 Million Hunt for a Mersenne Prime

Mersenne primes take the form of 2 raised to a prime-valued exponent, minus one. Only 52 have ever been identified in all of mathematical history. Named after the 17th-century French monk Marin Mersenne, they sit at the boundary between number theory and computational endurance.

In 1876, the French mathematician Édouard Lucas verified a 39-digit Mersenne prime entirely by hand, a calculation so demanding the record stood for 75 years.

Today the process runs on thousands of processors simultaneously.

On October 11, 2024, an NVIDIA A100 GPU in Dublin flagged a candidate using a probable prime test. The following day, an H100 GPU in San Antonio confirmed it with the Lucas-Lehmer primality test.

What is the Lucas-Lehmer test?

The Lucas-Lehmer test is a procedure designed specifically for checking whether Mersenne numbers are prime. It runs a sequence of squaring operations that, for numbers of this form, is far more efficient than general-purpose primality tests.

The confirmed number, M136279841, stretches to 41,024,320 decimal digits.

Written out in decimal, it starts 8,816,943,275 and ends 486,871,551. Printed in a book, it would fill 20,000 pages.

Each Mersenne prime also generates a corresponding perfect number, a natural number whose divisors sum exactly to itself. This one spans more than 82 million digits.

GPUs Dethrone the Desktop

The discovery ended a 28-year streak.

Since George Woltman founded the Great Internet Mersenne Prime Search in 1996, every record Mersenne prime had been found on ordinary personal computers. Thousands of volunteers downloaded free GIMPS software, each hoping their home processor would strike first.

Durant, who set up an LLC to secure cloud GPU access from multiple providers, saw something others had missed. The same chips powering AI training could process Mersenne prime candidates far faster than any desktop CPU.

I wanted to push the boundaries of the known universe in whatever small way I was able.

Luke Durant, former NVIDIA engineer

Before his arrival, GIMPS received roughly 300 test results per day from all volunteers combined. Durant's GPU cloud pushed that average to 3,500.

Kevin Buzzard, a professor of pure mathematics at Imperial College London, noted that the record for largest known primes effectively tracks the progress of human computing power itself.

As of mid-2025, GIMPS had checked every exponent below 136,279,841 at least once. The project still welcomes anyone with a home computer and patience, though testing a single candidate typically takes weeks.

The 100-Million-Digit Milestone

Durant's Mersenne prime eclipses the previous record by 16 million digits, yet falls well short of the next target.

More On Prime Numbers

The Prime Number Proof That Borrowed From the Wrong Field

Ben Green and Mehtaab Sawhney proved infinitely many primes fit p² + 4q² by importing Gowers norms from combinatorics - a tool nobody expected would…

The Electronic Frontier Foundation has already awarded $50,000 for a million-digit prime in 1999 and $100,000 for a ten-million-digit prime in 2008. It now offers $150,000 for the first 100-million-digit prime. At 41 million digits, Durant's number is less than halfway there.

Practical applications for primes this large are essentially nonexistent. Cryptographic algorithms protecting online banking use primes of only a few hundred digits. George Woltman, the GIMPS founder, described the enterprise as "entertainment for math nerds."

Yet Euclid proved more than two thousand years ago that primes never run out. Whether the next record falls to a volunteer's laptop or another million-dollar GPU cloud, the mathematics guarantees a larger Mersenne prime is always waiting.


Sources

Fact Check: Claim-by-Claim Verification Verified

All major factual claims are accurate: the discovery date, GPU infrastructure details, digit count, Lucas-Lehmer test confirmation, and historical context about Édouard Lucas are correctly represented.

1 Verified
Luke Durant is correctly identified as a 36-year-old former NVIDIA engineer who spent approximately $2 million on cloud GPUs
2 Verified
The network infrastructure spanned 24 data centers in 17 countries, as stated
3 Verified
M136279841 has exactly 41,024,320 decimal digits
4 Verified
Discovery timeline is accurate: NVIDIA A100 GPU in Dublin flagged it as probably prime on October 11, 2024, with H100 GPU in San Antonio confirming via Lucas-Lehmer test on October 12
5 Verified
The 52nd Mersenne prime identification is correct
6 Verified
Édouard Lucas did verify a 39-digit Mersenne prime (M127) in 1876 by hand, as stated
7 Verified
Electronic Frontier Foundation prize of $150,000 for first 100-million-digit prime is accurate

Commentary

  • The article states the 28-year streak ended with Durant's discovery, which is slightly imprecise phrasing. More accurately, the previous record was discovered in December 2018 (M82589933), meaning desktop computers held the record for approximately 6 years from the last record holder before that (January 2013), not 28 years from GIMPS's founding in 1996. The "28-year streak" phrase could be interpreted as referring to GIMPS's entire history since 1996, during which every record before Durant's was found by GIMPS volunteers on personal computers—this reading aligns with the article's explanation and is acceptable for popular science.
  • The article accurately simplifies the Lucas-Lehmer test explanation for a general audience; this is appropriate for popular science writing
  • Marin Mersenne is correctly identified as a 17th-century French monk [2]

Sources used for verification

Academic/Peer-reviewed:

Other reliable sources:

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