It could be you to discover the largest till date 50th Mersenne Prime

A FedEx employee, Jon Pace discovered the largest so far – 50th Mersenne Prime Number (largest known till date) on 26th December 2017 and you can be the one to find the next.

Prime numbers have made maths lovers always curious and it deserves the research time it has been given. The special thing about these Mersenne Prime Numbers is that these are so rare that their discovery rate is less than one per year. Yes, the 50th Mersenne Prime Number is the largest known prime number till date as well.

Hello Maths lovers!

For your love of Maths, I have the perfect thing for you and here it goes. Make a list of questions in your mind (you may already have one) and you’ll find all your answers below, as we at Kailasha Foundation – Fun & Learn Portal, love to clear confusions and make things simple.

Q: What is that number which this article is about?
A: 2^77,232,917 − 1. This number is 50th Mersenne Prime and is also the Largest known Prime number till date.
Q: What is a Mersenne Prime?
A: Mersenne Primes are the special prime numbers of the form $M n = 2 n - 1$ for some integer $n where n is also a prime number. Recently discovered all largest prime numbers are Mersenne Primes.$
Q: How large is this number?
A: Big enough to fill an entire shelf of books totalling 9,000 pages! It is a number of 23,249,425 digits.
Q: Will you please describe more? Who works on these prime numbers? How are these found? What’s the use?
A: Euclid proved that there is no largest prime number, and many mathematicians and hobbyists continue to search for large prime numbers. Many of the largest known primes are Mersenne primes. As of January 2018, the seven largest known primes are Mersenne primes.
They are named after Marin Mersenne, a French Monk, who studied them in the early 17th century.The exponents $n$ which give Mersenne primes are 2, 3, 5, 7, 13, 17, 19, 31, … (sequence A000043 in the OEIS) and the resulting Mersenne primes are 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, … (sequence A000668 in the OEIS).

The formula for finding the Mersenne Primes isn’t a sure-shot method to find Prime numbers. The formula only takes us to a more likely place to find them.

Prime numbers are useful in cryptography; however, the largest discovered prime is too large to be used even in cryptography in near future.
Q: Is there any chart or list of the Mersenne Primes?
A: Yes. It is available on Wikipedia. The 46th, 47th, 48th, 49th and 50th Mersenne Primes are not sure of their respective ranks. There can be more Mersenne Primes in between 45th and 50th.
Q: What method is used to find all these 50 prime numbers? What is OEIS?
A: The first four Mersenne Primes: 3, 7, 31 and 127 were found by Ancient Greek Mathematicians. Thereafter trial division was employed. The 8th Mersenne Prime, 2147483647 was found by Leonhard Euler using Enhanced Trial Division.Thereafter Lucas Sequences were used until 1952 when Raphael M. Robinson found 5 Mersenne Primes in a single year using LLT (Lucas-Lehmer Test) on a SWAC computer.Further developments have two important names: Donald B. Gillies and David Slowinski.

From 35th through 50th (the latest one), all Mersenne Primes are found using GIMPS.

All the Mersenne Primes are found using one or more computers, and LLT was the employed method in all of these.

OEIS is the On-Line Encyclopedia of Integer Sequences (OEIS), also cited simply as Sloane’s, an online database of integer sequences. It was created and maintained by Neil Sloane while a researcher at AT&T Labs. Foreseeing his retirement from AT&T Labs in 2012 and the need for an independent foundation, Sloane agreed to transfer the intellectual property and hosting of the OEIS to the OEIS Foundation in October 2009. Sloane continues to be involved in the OEIS in his role as President of the OEIS Foundation.
Q: What is GIMPS?
A: The Great Internet Mersenne Prime Search (GIMPS) is a collaborative project of volunteers who use freely available software to search for Mersenne prime numbers.
Q: How can I be the next person to discover the next prime number?
A: If you want to join the hunt for the 51st Mersenne prime, you can download the software here, and find instructions here. However, Your competition is with Jon Pace too. 🙂