Prime numbers are quite extraordinary. They're like "special snowflakes" - unique in the way that they don't have any other positive divisors other than the number 1 and the prime number itself.
Believe it or not, there are infinitely many prime numbers.
Because 1 is neither a prime nor a composite number, 2 is considered as the smallest prime number. Ironically, 2 is the only even prime, making it the "oddest" or the most unique prime number. Meanwhile, all sets of primes excluding 2 are odd primes.
If 2 is the smallest prime, is it possible to calculate for the largest prime number?
Yes, it is. A collaborative project dedicated to finding world record primes has been established since 1996. Now, in its 20th anniversary, this particular organization of prime number experts achieved another amazing feat in the field of Mathematics.
The Largest Prime Number
The Great Internet Mersenne Prime Search or GIMPS is a project with the sole mission of uncovering Mersenne primes, which are prime numbers that can be written in the form Mn = 2n - 1, where n is a number.
Named after 17th century French Minim friar Marin Mersenne, the formula for a Mersenne prime translates to a prime number that is one less than a power of two, where 2 multiplies itself and 1 is subtracted to the product.
As of today, there are exactly 49 known Mersenne prime numbers. Dr. Curtis Cooper, an expert at the University of Central Missouri, used one of the university computers to uncover the largest and the 49th Mersenne prime number ever found.
The prime number, which is newly-christened as M74207281, contains a number of digits twice the count of the population of Australia. This prime number is comprised of 22 million digits in total, with the shorthand version of 2^74,207,281-1. This means the number 2 multiplied by itself 74,207,281 times and then subtracted 1.
Experts say that if a person can speak two digits per second, it would take more than 100 days or about four months to speak or pronounce the largest prime number.
Dethroning Past Record Primes
M74207281 dethrones the 48th known Mersenne prime number by about five million digits. This 48th Mersenne prime number, which has the shorthand version of 2^57,885,161-1 and has 17,425,170 digits, was also discovered by Cooper in 2013.
So far, M74207281 is Cooper's fourth record prime. He and his team's first record prime was discovered in 2005, while their second record prime was found in 2006.
This second record prime was shattered by experts at the University of California, Los Angeles, but Cooper and his team's discovery of the 48th Mersenne prime made them re-claim the record.
"I think I still have the same excitement as when we were lucky enough to find the first one. The fourth time here is as exciting as the first time," said Cooper in an interview with mathematician Matt Parker.
Cooper and his team's discovery of the 49th Mersenne prime is eligible for a $3,000 GIMPS research discovery award.
While Cooper's computer detected the 49th record prime, the team of GIMPS volunteers sifted through the numerous non-prime candidates. David Stanfill and Andreas Hoglund each verified the prime through the CUDALucas software running on NVidia Titan GPUs in order to make sure there were no errors in the prime discovery process.
Interestingly, the GIMPS computer hardware used to calculate the 49th Mersenne prime was discovered through the Prime95 software on an Intel i7-4790 @ 3.60 GHz. The prime was actually reported to servers on Sept. 17, 2015, but a bug notification prevented the email notification from being sent.
Meanwhile, Mersenne primes have no practical use, but they are integral to the number theory which was first discussed by Euclid about 350 BC.
Other Fun Facts About Prime Numbers For The Numberphile
Aside from the largest prime and smallest prime, there are other things that experts have uncovered about these numbers.
For instance, no prime number greater than 5 ends in a 5. Any number greater than 5 that ends in a 5 is not a prime number because it can then be divided by 5.
There is no known pattern that dictates which numbers will be prime or how far apart these numbers are from each other.
The person who discovered the first prime number with more than a million digits was awarded with $50,000 in 1999.
Lastly, the largest known right-truncatable prime is 73939133. This means that even if you take away the last right digit, the number is still a prime number.
Watch Cooper's interview below.