Largest Prime Number M44 ?

If you seen the Rajinikanth Robort(2010) movie. Then you might remember a seen of the film where Dr. Vasikaran introduce his robot (Chitti) in front of journalist. Where one of the journalist asked about the Largest Prime Number according to robot and here robot answers the "M44 is the largest prime number" Although this movie is fictional and not based on any actual mathematical concept or theory related to prime numbers. But lets see how this M44 comes from and what is the largest known prime number?

Firstly, Let's understand something

Euclid's Theorem, which states that there are infinitely many prime numbers. The proof of Euclid's theorem is a classic proof by contradiction that assumes there is a largest prime number, and then shows that this assumption leads to a contradiction. Therefore, there can be no largest prime number.

So, If there is no largest prime number exists, then what is M44?

Actually, M44 is shorthand for a Mersenne number (NOT a Mersenne Prime!)

Mersenne numbers are numbers of the form

Mn=2n−1${\mathrm{<br>}}_{}$

Not all Mersenne numbers are primes, although some are.
So, M44 is 17592186044415, which by the way, is not a prime number.

If M44 is not the largest prime then what it is?

The largest known prime number as of my knowledge cutoff date (September 2021) is 2^82,589,933 − 1, which is a Mersenne prime discovered by the Great Internet Mersenne Prime Search (GIMPS) project in December 2018.

The number has 24,862,048 digits when written in base 10. However, it's important to note that new prime numbers are constantly being discovered as computational power and algorithms improve. So, while this was the largest known prime number as of my knowledge cutoff, it's possible that an even larger one has been discovered since then.

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