Amateur mathematician discovers largest known prime number with 41 million digits

New prime is 16 million digits larger than previous one

An amateur mathematician from San Jose, US, has discovered the largest prime number yet with over 41 million digits.

Prime numbers, the building blocks of mathematics, are divisible only by themselves and 1.

The first prime numbers are 2, 3, 5, 7, 11. Finding the next ones in the sequence gets harder as the numbers get bigger.

Mathematicians typically used formulas to test whether a large number was prime or not, an approach which in later years began to be applied using special computer software.

Luke Durant, 36, a former Nvidia employee, used a free software called the Great Internet Mersenne Prime Search, or GIMPS, to test whether suspected large numbers were prime numbers using an algorithm.

Mr Durant’s attempt required the use of thousands of graphics processing units spread across 24 data centres in 17 countries.

The amateur mathematician found the new largest prime number dubbed “M136279841”, calculated by multiplying together 136,279,841 twos, and then subtracting 1.

The number, 2^136,279,841 – 1, is over 16 million digits larger than the previous one.

Among prime numbers, there is a class called Mersenne primes of the form 2^P-1, named after 16th Century French monk Marin Mersenne who discovered them.

For instance, 3, 7, 31, and 127 are Mersenne primes, corresponding to values of P being 2, 3, 5, and 7 respectively.

The latest discovery means 52 Mersenne primes are now known.

The latest prime “ends the 28-year reign of ordinary personal computers finding these huge prime numbers”, GIMPS said in a statement.

After nearly a year of testing, the number was confirmed to be prime.

A processor in Dublin, Ireland, flagged M136279841 as probably a prime number on 11 October and another processor in San Antonio, Texas, confirmed it was indeed so the following day.

The discovery method could be a shot in the arm for cryptographers.

The largest prime number: 2¹³⁶²⁷⁹⁸⁴¹-1 https://t.co/Bo6ThyWjSx pic.twitter.com/yNILZ6KYKz

— Prof B Buchanan OBE FRSE (@billatnapier) October 21, 2024

Large prime numbers play a key role in developing cryptography algorithms that ensure the security and confidentiality of digital communications.

These algorithms usually generate unbreakable codes by multiplying two large numbers to get a number that is hard to factorise.

They are used in online banking, private message services, and shopping algorithms to generate encryption keys to protect data.

The discovery also shows that graphics processing units, increasingly used in building artificial intelligence systems, are also well suited to fundamental math and science research.