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Monday, March 12, 2018

23 million characters discovered the biggest Prime number

International collaboration GIMPS announced that on December 26, 2017, she managed to discover a new aquatic large Prime number. It consists of 23 249 425 characters, and represents two raised to the power of 77 232 917, minus 1.

Until the late eighteenth century all Prime numbers known to mankind, was no more than 6 characters, but later it became known about unimaginably huge numbers that no are divided only by themselves and one. Since the mid-twentieth century new records were set every few years and sometimes several times a year.

At first glance it may seem that the number of primes is limited, but there is a rather elegant proof that it is not. How many Prime numbers was not known to mankind, if you multiply them all together and add 1, the new number will also be simple – when divided by all known common denominators will remain a remainder of 1. This proof is attributed to the Greek mathematician Euclid and named in his honor.

However, new Prime numbers of modern mathematics, usually looking for not by multiplying the known. Most often they are searched for among the so-called Mersenne numbers obtained by raising two to the power of n, and subtracting from the result units. In the past, scientists have discovered that if n is a Prime number, then with high probability is simple and the corresponding Mersenne number. It is to this line include nine of the ten largest primes known to date. The only exception is a number, open 6 November 2016 – it is located in seventh place, is composed of 9.3 million digits and is 10 223×2^31 172 165 + 1. All the other major primes, including the new, were opened in the framework of the project GIMPS.

With the opening of the previous largest Prime number, consisting of 22 338 618 digits, it’s only been two years, and experts GIMPS noted that this record was broken surprisingly quickly.

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