The largest prime number and the largest perfect number were discovered

Prime numbers are unique in mathematics because they divide only by 1 and by itself. In other words, they can’t be broken down into smaller factors without remainders. Late last year, the international GIMPS initiative succeeded in finding the largest known prime number to date. It consists of more than 23 million digits, and its abbreviated name is M77232917. By the way, the largest perfect number known to date was also discovered.

The mathematical notation of the largest new prime number is 2,77232917 – 1 (two raised to the power of 77,232,917 minus 1). In total, it consists of 23 millionów 249 thousand 425 digits. Assuming that a standard A4 page holds almost 4 thousand charactersów, then to print the entire M77232917 it takes approx. 6 thousand pieces of paper! The new record holder has almost a million more digits than its predecessor.

Prime numbers fascinated the mathematicianóin as early as antiquity. Why are they so special? Because they divide only by 1 and by itself. Divided by any other number, they give a fractional result. Prime numbers include m.In.: 2, 3, 5, 7, 11, 13 or 17. During the centuryóIn many mathematicsóIn searched for larger and larger prime numbers.

One of the most prominent was the late 16th and early 17th century French monk Marine Mersenne. He studied the great prime numbers and discovered that someóre of them are in the form of powers of 2 minus 1. It is in his honor that today great prime numbers are classified as Mersenne numbers’a. M77232917 is the fiftieth number in this classification. Finding more causes more and more problems each timeów. It is predicted that 51. Mersenne number’and it will have more than 100 millionóin the digits.

The discovery of the largest known prime number today was made on December 26, 2017 by electronics engineer Jonathan Pace of Germantown, Tennessee (USA). The man has been involved in the search for large prime numbers for 14 years as part of the GIMPS program. The name of the project is skrót from Great Internet Mersenne Prime Search (with j. ang.: The Great Internet Search for Mersenne Prime Numbers’a).

The GIMPS project was launched in 1996. From https://www.mersenne.org/ anyone wishing to do so can download specialized software (big prime hunter) for searching for Mersenne prime numbers’a. Not an interferenceóIt ca work of the computer, because it only uses the computing power not used at the moment. With this solution, sixteen Mersenne prime numbers have been found in more than 20 years’a. What’s more, GIMPS is offering a reward of 3,000 to the lucky finder. dollarów. For finding the number Mersenne’a, whichórej the number of digits will be greater than 100 millionóa prize of 150 thousand is predicted in. USD.

The GIMPS project is overseen by Prof. Chris Caldwell, whoóry collects róalso stories of discoveriesów. It took an Intel I5-6600 CPU computer six days of non-stop operation to verify that M77232917 is indeed a prime number. However, in order to be certain of the discovery, the calculation needed to be confirmed on four róThey are used in computers and in four róof different programs. Each time, their work took from 37 to 82 hours.

In other words, each computer had to multiply by itself 77,222,917 dwóyek, subtract the number 1 from the resulting number and check that the resulting number actually divides only by 1 and by itself, giving no remainder.

Also associated with prime numbers are perfect numbers, whichóre are równe sum of its divisorsów. The smallest known perfect numbers are 6 and 28. The number 6 is divisible by 1, 2 and 3 (divisors). 1+2+3=6. According to the ancients, perfect numbers had magical properties. In the 18th century, mathematician Leonhard Euler proved the relationship between prime numbers Mersenne’a and the perfect numbers. Just take any prime Mersenne number’a (the nth power of 2 minus 1) and multiply it by 2 to the power of "n-1", a we get a perfect number. This means that with the discovery of the largest known prime number to date, we have also learned the largest known perfect number.