2^(57885161) - 1 is now the largest known prime number.

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In summary, the largest known Mersenne prime as of January 25th, 2013 is $2^{57885161}-1$, which is 17,425,170 digits long. This is the first Mersenne prime discovered in about 4 years, with the last one being $2^{42643801}-1$ in April 2009. More information about Mersenne primes can be found here, including a text file with the latest prime's 17,425,170 digits available for download. Currently, the largest known Mersenne prime is ##2^{82,589,933} - 1##, which has 24,862,048 digits and was discovered on December 7,
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Chris L T521
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I noticed there was no mathematics news subforum, so this was the next best place to put this even though math related topics aren't really discussed in the chat room.

As of January 25th, 2013, $2^{57885161}-1$ is the largest known Mersenne prime and is an impressive 17,425,170 digits long. It's the first Mersenne prime discovered in about 4 years ($2^{42643801}-1$ was the last Mersenne prime discovered [April 2009]).

You can read more about the Mersenne primes here. They've even made available a text file containing all 17,425,170 digits of the latest Mersenne prime for downloading (but it's 22MB in size...I wonder why...).
 
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Currently, it is ##2^{82,589,933} - 1.## It has 24,862,048 digits and was found on December 7, 2018 and announced on December 21 of the same year.
 
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Related to 2^(57885161) - 1 is now the largest known prime number.

1. What is the significance of 2^(57885161) - 1 being the largest known prime number?

The discovery of 2^(57885161) - 1 as the largest known prime number is significant because it breaks the previous record of 2^(74207281) - 1, which was discovered in 2016. It also contributes to our understanding of prime numbers and their properties, which has implications in various fields such as cryptography and computer science.

2. How was 2^(57885161) - 1 calculated?

2^(57885161) - 1 was calculated using a specialized computer program designed to search for large prime numbers. This program uses the Lucas-Lehmer primality test, which is a fast and efficient way to determine if a number is prime.

3. How long did it take to find 2^(57885161) - 1?

The discovery of 2^(57885161) - 1 as the largest known prime number was a collaborative effort involving thousands of computers around the world. It took a total of 12 days to find and confirm the number as prime.

4. Is there a limit to how large a prime number can be?

As of now, there is no known limit to how large a prime number can be. However, as the numbers get larger, it becomes increasingly difficult and time-consuming to find and verify them as prime.

5. What applications does this discovery have?

The discovery of 2^(57885161) - 1 and other large prime numbers has practical applications in cryptography, as these numbers are used in encryption algorithms to secure sensitive information. It also has implications in mathematics and computer science, helping us further our understanding of prime numbers and their properties.

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