# Longest Known Prime Number

• _Mayday_
In summary, the conversation discusses the topic of large prime numbers and their use in credit card security and encryption. The largest known prime number is m39 = 213,466,917-1, which requires 4,053,946 digits to be written fully. To find the next largest prime number, one would need a supercomputer and a sieve. There is a monetary reward for finding large prime numbers, but it is not for the primes themselves, but for the methods used to find them. Prime numbers are difficult to factorize, making them useful in sending secure messages and using credit cards online. The conversation also mentions the use of algorithms in calculating more digits of pi.

#### _Mayday_

Hey Everyone,

People keep on telling me that the biggest prime number known to man, is used for things like credit cards, how, I do not know, but I am hearing it more and more and need to know, because people think they are clever when they say it, but they have no further knowledge about it! Another question, what is that prime number? I have also heard that if you find the one after that one you get a hell of a lot of money. How would you go about finding it, because I want a lot of money.

Please don't move this maths forums, this isn't about the maths, but about the story around the maths.

_Mayday_

So far you don't use THAT huge primes for credit card security, I think around 512 bits is still enough (albeit you need two of them ).

_Mayday_ said:
I have also heard that if you find the one after that one you get a hell of a lot of money. How would you go about finding it, because I want a lot of money.

With a supercomputer and a sieve. Everyone has those lying around.

Super-computers are generally used to try to find these primes. There's tons of people out there even contributing to find these primes.

It's not easy to get unless you've found some miraculous algorithm to solve for a large number prime (up to at least what we have now) in record time. But that task itself isn't even easy.

_Mayday_ said:
I have also heard that if you find the one after that one you get a hell of a lot of money. How would you go about finding it, because I want a lot of money.
The money assigned to finding large prime numbers is not for the primes themselves, but for novel ways to investigate them. It is not just a matter of time to accomplish this, it is also a matter of cleverness/genius.

By the same token, people try to calculate more digits of pi, although we already have much much much more than what is necessary for practical purposes. Once again, it is a matter of algorithms.

The reason prime numbers are used to send secret (or secured) messages is that factorization is difficult. A prime number cannot be divided in the product of two other integers. Take two very large prime numbers (say 150 digits as indicated above) and multiply them together. Then give us the result of your multiplication. You can bet whatever you want that nobody will be able to find the prime numbers you started from within the next few weeks or even months, unless they huge massive supercalculators.

Consider the big product of two prime numbers as a padlock, easily unlocked if you know any of the two primes it is made of. Now somehow, you could send this padlock "open" to your friend, he locks his box with it and send it all back to you. You can unlock it. Nobody has been able to open the box containing the secret (or secured) data. And you can use your credit card on internet

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the details of how you lock/unlock or encrypt/decipher your data is mostly technical.

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## What is the "Longest Known Prime Number"?

The "Longest Known Prime Number" is the largest prime number that has been discovered and verified by mathematicians so far. It is a number that can only be divided by 1 and itself, with no other factors.

## How is the "Longest Known Prime Number" determined?

The "Longest Known Prime Number" is determined through a process called primality testing. This involves using various algorithms and methods to check if a number is prime or not. The current record holder for the "Longest Known Prime Number" was discovered using the Great Internet Mersenne Prime Search (GIMPS) project.

## What is the significance of the "Longest Known Prime Number"?

Prime numbers have been a topic of interest for mathematicians for centuries, and the search for the "Longest Known Prime Number" is a way of pushing the boundaries of our understanding of these numbers. The discovery of a new record-breaking prime number also helps to advance mathematics and computer science.

## How often is the "Longest Known Prime Number" updated?

The "Longest Known Prime Number" is updated whenever a new prime number is discovered and verified to be the new record holder. This can happen at any time, as there is no set schedule for discovering new prime numbers.

## Are there any practical applications for the "Longest Known Prime Number"?

While the "Longest Known Prime Number" may not have direct practical applications, the search for and discovery of prime numbers has led to advancements in cryptography, coding theory, and other fields. Additionally, the pursuit of the "Longest Known Prime Number" serves as a way to push the limits of our mathematical knowledge and understanding.