Searching for the largest prime number is the most common hobby among amateur and professional mathematicians globally. There are two projects that the seekers of the solution usually become a part of in their pursuit. One is the Prime Grid, which uses the Berkeley Open Infrastructure for Network Computing(BOINC) and is in operation since 2005, while the other and the more popular, Great Internet Mersenne Prime Search(GIMPS), started in 1996 and focuses primarily on Mersenne primes.
The new biggest prime number is 24,862,048 digits long and was discovered with the aid of GIMPS.
The mammoth number can be written in its Mersenne form as 282,589,933-1, meaning that the prime number can be found by multiplying 2 to itself a total of 82,589,932 and subtracting 1 from it.
It was discovered by a Florida based IT professional, a 35-year old Patrick Laroche. GIMPS said that while people give thousands of attempts, searching for decades without any success, Laroche who was using GIMPS’ tools as a stress test for his system, discovered the huge prime number in only his 4th attempt.
A natural number is called prime when it is only divisible by itself and 1. For eg. numbers like 2, 3, 5, 7 are prime, while 20 is not, as it is divisible by 2, 4, 5, 10 beside 1 and 20.
Mersenne prime is a special category of prime numbers which can be broken into a form of 2n – 1. For eg. numbers like 3(22-1), 7(23-1), 31(25-1), 127(27-1),…, are Mersenne primes.
Like the last sixteen times, a Mersenne prime was once again the highest prime number.
One more advantage of finding a Mersenne prime is that you get an even perfect number for free out of it. A perfect number is one whose proper divisors on addition results in the number itself.
For eg. 28 = 1+2+4+7+14
According to the Euler-Euclid Theorem:
Every even perfect number has the form 2n-1 * (2n − 1), where 2n − 1 is prime.
Hence, we get a perfect number 282,589,932 * (282,589,933-1).
The largest prime number can be downloaded from the official website of GIMPS(mersenne.org) and is 24 MB(unzipped) large.