Why is it in news?

Recently, a very big number — over 23 million digits long — became the “largest known prime number.

Details

• The number, 277,232,917-1, was discovered using a software called GIMPS, which allows volunteers to search for Mersenne prime numbers (more on that below). Jonathan Pace, a volunteer from Tennessee, made the discovery on December 26, and it was further confirmed using four different programs on four different pieces of hardware.
• A prime number is a number that can only be divided by itself and by 1. For example: 2, 3, 5, 7, 11, and so on.
• One of the oldest theorems in mathematics (the Euclid theorem) says that there are infinitely many primes. So there is a possibility that we are going to find larger and larger primes.

Why is the new prime number called a Mersenne prime number?

• Mersenne prime is a prime number of the form 2n-1. For example, 7 = 23-1 and is a prime, so it is a Mersenne prime.
• One the other hand 11 is a prime, but it is not of the form 2n-1. So it is not a Mersenne prime. Not all numbers of the form 2n-1 are primes either. For example, 24-1 = 15 is not a prime.
• The GIMPS project looks at such numbers to figure out which of them are going to be primes.   

Applications of prime numbers

• One of the major applications of primality testing (testing whether a number is prime) is in cryptography. (Cryptography, which is derived from the Greek word for the study of secret messaging, involves sharing information via secret codes)
• Our credit cards, cell phones, all depend on cryptography.

Source

The Hindu