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What’s The Largest Known Prime Number | It’s 23 Million Digits Long

[Estimated read time: 3 minutes]
  • An Electrical Engineer found the largest known prime number in collaborative project. 
  • 277,232,917-1  is the new largest known prime number, which is 23 million digits long. 
  • The correctness of the number was verified by 4 distant programs running on 4 different hardware configurations.  

The Great Internet Mersenne Prime Search (GIMPS – a collaborative project of volunteers who use open source software to discover prime numbers) has found the largest prime number.

277,232,917-1  is the new largest known prime number, which is 23 million digits long (23,249,425 to be exact). It’s a Mersenne prime – a prime number that is one less than power of two. The number is also called M77232917 because it is obtained by multiplying two 77232917 times and then subtracting one.

It’s also the 50th known Mersenne prime, which is about 1 million digits larger than previous largest known prime number. And of course, the difficulty increases with the every next Mersenne prime number.

For more than 2,000 years, prime numbers have been one of the greatest interests of mathematicians. Before this, the largest known prime number was 274,207,618-1, which has 22,338,618 digits, discovered in 2016.

Who Discovered This Number?

A 51-year-old Electrical Engineer, Jonathan Pace made this discovery on 26th December, 2017. He is one of thousands of volunteers using free GIMPS program. He has been working on this for more than 14 years and finally his achievement made him eligible for the GIMPS research discovery award (worth $3000) and additional benefits.

Credit for this milestone not only goes to Pace for running the Prime95 program, but also to Woltman for developing the software, and Blosser and Kurowski for managing the server.

How Had He Done This?

It took him 6 days of continuously-running a special piece of computational software on an Intel i5-6600 processor. In order to prove the correctness of this number, it was verified by 4 distant programs running on 4 different hardware configurations.

  1. gpuOwL running on AMD RX Vega 64 GPU (took 34 hours).
  2. Prime95 running on Intel Xeon server (took 37 hours).
  3. CUDALucas running on Nvidia Titan Black GPU (took 73 hours)
  4. Mlucas running on Amazon AWS instance and 32-core Xeon server (took 65 and 82 hours respectively).

A logarithmic graph showing digits in largest known prime by year. Red line is the exponential of best fit | Wikimedia

About GIMPS

Founded in 1997 by George Woltman, GIMPS is registered as Mersenne Research Inc. Currently, it’s the largest distributed computing projects over the Internet for finding prime numbers.

As of January 2018, the project has discovered a total of 16 Mersenne primes, out of which 14 were the largest known prime number at the time they were discovered.

In order to check errors, the project uses Lucas-Lehmer primality test, which is an algorithm specialized in testing Mersenne primes, and much efficient on binary computer architectures. They use trial division phase to eliminate Mersenne numbers with small factors. Furthermore, to find large factors, they use Pollard’s p-1 algorithm.

How This is Useful?

Finding a prime number is not going to change any mathematics theorems, but it interests mathematicians. So far, these numbers seem to occur sporadically – they don’t follow any pattern.

Hunting for bigger prime numbers might seem frivolous, but they hold numerous practical applications as well, for instance, generating public key cryptography algorithms (like RSA encryption), hash tables, and it could be used in generating a random number.

Read: 16 Famous and Greatest Mathematicians

Moreover, this kind of works could help us understand more about mathematics, who knows, maybe one day we’ll discover a pattern.
As Carl Sagan hypothesized in “Contact”, sending streams of consecutive primes could be used as a method to say “hello” to an alien civilization.

The supermassive of primes is yet to be discovered – we are talking about 100 million-digits-long prime number. Electronic Frontier Foundation will award $150,000 to the first person who find this elusive number. Good Luck!

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