Largest Known Prime Number Has Almost 25 Million Digits | Mathematics

Professional and amateur mathematicians from a worldwide research project called the Great Internet Mersenne Prime Search (GIMPS) have discovered the largest known prime number. The new number, expressed in shorthand as 282,589,933-1, contains 24,862,048 digits, more than one and a half million digits larger than the previous record prime number, discovered in 2017. It belongs to a special class of rare prime numbers called Mersenne primes and is only the 51st known Mersenne prime ever discovered, each increasingly more difficult to find.

The 51st known Mersenne prime has 24,862,048 digits. Image credit: Pete Linforth.

An integer greater than one is called a prime number (or a prime) if its only divisors are one and itself.

The first prime numbers are 2, 3, 5, 7, 11, etc. For example, the number 10 is not prime because it is divisible by 2 and 5.

The newly found prime number, dubbed M82589933, is calculated by multiplying together 82,589,933 twos, and then subtracting one.

A Mersenne prime is a prime number of the form 2P-1.

The first Mersenne primes are 3, 7, 31, and 127 corresponding to P = 2, 3, 5, and 7 respectively.

Mersenne primes have been central to number theory since they were first discussed by the Greek mathematician Euclid (born c. 300 BC) about 350 BC.

The man whose name they now bear, the French monk Marin Mersenne (1588-1648), made a famous conjecture on which values of P would yield a prime. It took 300 years and several important discoveries in mathematics to settle his conjecture.

Euclid proved that every Mersenne prime generates a perfect number.

A perfect number is one whose proper divisors add up to the number itself.

The smallest perfect number is 6 = 1 + 2 + 3 and the second perfect number is 28 = 1 + 2 + 4 + 7 + 14.

The Swiss mathematician Leonhard Euler (1707-1783) proved that all even perfect numbers come from Mersenne primes.

The newly discovered perfect number is 282,589,932 * (282,589,933-1).

This number is over 49 million digits long. It is still unknown if any odd perfect numbers exist.