Largest known prime number discovered in Missouri



Largest known prime number discovered in Missouri

Prime numbers - such as two, three, five and seven - are divisible only by themselves and one, and play an important role in computer encryption.
The new prime is more than 22 million digits long, five million longer than the previous largest known prime.
Primes this large could prove useful to computing in the future.
Endless quest

The new prime number was found as part of the Great Internet Mersenne Prime Search (Gimps), a global quest to find a particular type of large prime numbers.
Mersenne primes are named after a French monk who studied them in the 17th Century.

They are hunted by multiplying two by itself a large number of times, then taking away one. It is a relatively manageable calculation for today’s computers, but not every result is a prime.
The discovered prime is written as 2^74,207,281-1, which denotes two, multiplied by itself 74,207,280 times, with one subtracted afterwards.

                                                                                                 The  Gimps project has calculated the 15 largest Mersenne primes in the 20  years it has been running and it is possible that there could be an  infinite number of them to discover.

What use are large primes?

Large prime numbers are important in computer encryption and help make sure that online banking, shopping and private messaging are secure, but current encryption typically uses prime numbers that are hundreds of digits long, not millions.
“This prime is too large to currently be of practical value,” the Gimps project admitted in a statement.

However, searching for large primes is intensive work for computer processors and can have unexpected benefits.
“One prime project discovered that there was a problem in some computer processors that only showed up in certain circumstances,” said Dr Steven Murdoch, cybersecurity expert at University College London.
The new large prime, the 49th known Mersenne prime, was discovered by Dr Curtis Cooper at the University of Central Missouri.

Love the headline – was the prime number found in a ditch by the road and just lucky to be found by a mathematician?
It would be interesting to see the new prime published as a book, possibly for insomniacs.


I thought it would be found in Texas.


No, that’s the largest prime beef steak dinner, not prime number.


There possibly could be an infinite number of prime numbers to discover? Seems to me that there is an infinite number to be discovered…unless there is a limited number of numbers out there in the first place.




This discovery may be of theoretical interest, but contrary to the article, it has no practical use in encryption.

The use of prime numbers in encryption is in the RSA public key algorithm, which allows you to establish a secure communication channel with, for instance, even though you and did not start out sharing any secret key information, as is necessary in ordinary encryption. It works by the fact that it is difficult to factor the product of two very large prime numbers. But that difficultly arises from the fact that there are so many prime numbers to try. If it were known that someone was using one of these very large Mersenne primes (not all primes are Mersenne primes) in their public key, it would be a simple matter to quickly run through all the known Mersenne primes and try them first before trying “ordinary” prime numbers. No, you would want to avoid Mersenne primes, or any other “special” kind of primes in your RSA encryption. By the way, very large prime numbers are “found” through a probabalistic test run many times. Each time you run the test you cut the probability of the number in question being non-prime in half. But the probability the number is prime never goes all the way to certainty. So all they can really say is that this new Mersenne prime number is prime with probability 99.999999999%.


You could print it out and hang it on a large wall to prove your geekiness to all your friends. When a larger prime number is discovered, it is time to redecorate.




Which is the runner-up, former largest prime number? I hope Steve Harvey isn’t the one who announced the discovery.


It was probably “discovered” on the McDonalds’ hamburgers served sign. :cool:




The prime number was always there. It didn’t suddenly become prime because it was confirmed. It’s like "Columbus discovering America’.

There is a lot of interesting math around prime numbers.

I would think there are infinitely many prime numbers.


That’s very funny! :rotfl:


Yes, it was proved by Euclid. A very simple proof. What is not known is whether there are infinitely many Mersenne primes - the kind they just discovered in Missouri.


At 22,000,000 digits it would take him a long time to announce it. Fact checking for the number of mistakes made during the announcement would become its own cottage industry. Hiring the people to do that might take a tenth of a point off our unemployment rate.


Which to me rather challenges the idea of “infinite”.
To take a simpler case there are an infinite number of integers, an infinity of odd numbers and an infinity of even numbers. Are all infinities equal? To my simple mind the answer has to be “no”.


Integers seem more numerous than even numbers only when you restrict your view to a finite subset of them both. But by any reasonable definition of comparing infinite sets, they are equal. The only reasonable definition of comparison I know of is the existence of a one-to-one correspondence. And by that definition they are equal. Can you propose a different way to compare infinities?


There’s a proof. I had to refresh my memory with Google.

There is no largest prime number.

Assume to the contrary that there is a largest prime number M. Take all prime numbers from 2 to M and multiply them together and add one (call it P). If you divide P by any prime number in {2,3,5,…M} you will get a remainder of 1. So P is either a prime number larger than M or it has a prime factor larger than M. Because our assumption led to a contradiction it has to be true that there is no largest prime number.

Please excuse any informality here, it’s been a long time since I proved anything mathematical. For example this relies on the fact that there is no largest integer but I’m too lazy to prove it.


No they aren’t. The cardinal number (i.e. “size”) of the set of positive integers is the same as the cardinal number of the even numbers. This can be proved by lining up all positive integers with the list of even integers.

1 2 3 4…
2 4 6 8…

Since there is a one to one correspondence (2n) both sets are equal. This is very informal as I don’t really remember isomorphisms.

The number of real numbers is not equal to the set of integers because there is no one to one correspondence between the two sets. What’s interesting about this is that it is actually the transcendental numbers that makes the set “larger” because it can be shown that the set of algebraic numbers is the same as the set of integers.

Next on the hierarchy is the set of curves in the plane. This is where I get completely and totally lost.



nah, I’m good. I’ll take your word for it.

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