A new record for the largest known prime number was made late last year (but it has taken quite a long time to verify it). This prime number is nearly 25 million digits long or, to be more precise, to write it down you would have to type/write 24,862,048 digits. The new prime number is in a class called Mersenne primes, where the prime number is one less than another number to the power of two. Because of this definition, named after Marin Mersenne, a French Minim friar who studied such numbers in the early 17th century, we can write the number as M82589933 for short (rather than as 282,589,933-1).
Marin Mersenne lived from 1588 to 1648
Interestingly for computer enthusiasts, Great Internet Mersenne Prime Search (GIMPS) application user Patrick Laroche, from Florida, discovered M82589933 on his Intel i5-4590T 4C/4T (Haswell) powered PC. Laroche is one of thousands of GIMPS users who search for prime numbers using the software. It was his recent custom to use GIMPS to stress test home computer builds and Laroche is a relative newcomer as he first fired up this prime number crunching software just four months ago.
On this occasion Laroche decided to leave GIMPS running on his Intel i5-4590T to 'give back' to the GIMPS project. After about 12 weeks of running GIMPS on the fourth gen Core i5, he discovered M82589933. There are discovery rewards given out to lucky prospectors, of between $3,000 and $50,000. Furthermore, the finder of the first 100 million digit+ prime number will be awarded $150,000 by the EFF.
The GIMPS app appears to have been lucky in its strike rate. According to the organisation's blog it has been the source of 12 prime discoveries between 220000000-1 and 285000000-1, which is "triple the expected number of new primes." If the discovery trend continues it might be worth further investigation into the expected distribution of Mersenne primes. In contrast however, Jonathan Pace, the finder of the 50th Mersenne prime number a year ago, had been searching since the early days of GIMPS - for 14 years.
Verifying the new prime number took 12 solid days on the Intel i5-4590T system. Some more modern, but surprisingly modest, resources were used to third party verify M82589933 as being the largest prime number ever found (and disclosed):
- Andreas Höglund verified the prime using CUDALucas running on an Nvidia V100 GPU in 21 hours.
- Andreas Höglund also verified the prime using Mlucas running on 16 cores of an Amazon AWS instance in 72 hours.
- Aaron Blosser also verified it using Prime95 on an Intel Core i7-7700K processor in 6 days, 8 hours.
A list of the known Mersenne Primes (all 51 of them) is available here.
If you think it would be fun to "experience this new prime number viscerally by memorising it," then check out this Scientific American article.