In 2011, Google surprised everyone by submitting a $1,902,160,540 patent application. What would that mean?

Greetings, dear Readers! Today I want to tell a story that happened in 2011 during the auction for the sale of 6,000 patents and patent applications by Nortel, a Canadian manufacturer of telecommunications equipment. The winner of the auction was the RockStar patent consortium, which included such giants as Apple, Microsoft, RIM, EMC, Ericsson and Sony.

However, during the bidding, Google’s actions attracted the most. Already in one of the first rounds, they placed an order for $1,902,160,540. “Google was offering bids with numbers that weren’t ‘flat’ numbers. It wasn’t clear if they wanted to confuse competitors, intimidate them, or simply express the irreverence that is integral to its corporate image.” It turned out that this application exactly repeats the first 10 digits of Brun’s constant from number theory related to twin primes.

They are prime numbers that differ by 2. Mathematicians have not yet proven that there are an infinite number of them.

However, the Norwegian mathematician Viggo Brun showed back in 1919 that the sum of numbers reciprocals of twins still converges to the final value.

If there is a finite number of simple twins, then the Brun constant will be rational, otherwise it will be irrational.

In the zero years of the 21st century, mathematicians calculated this constant for numbers less than 10 ^ 14 (≈1.902160540), but a couple of years later, with the transition several orders of magnitude higher, the Brun constant began to be estimated somewhat differently.

At the moment, there is an opinion that the Brun number does not exceed ≈2.1754, however, this conclusion was made on the condition that the Riemann hypothesis, one of the 7 mathematical problems of the millennium, is true.

The hypothesis is related to the behavior of the roots of the so-called. zeta functions

Google’s claim repeating Brun’s constant was easily killed. However, the company went into a rage. One of the next claims was the Meisel-Mertens constant of $2614972128.

Defined as the limit of the difference between the harmonic series, summable over prime numbers only, and the natural logarithm of the natural logarithm. Equals approximately 0.2614972128

However, this request was cancelled. When the price hit $3 billion, Google moved on to the more well-known constant, bidding for $3.14159, but that was a beat. As a result, 6,000 patents went for $4.5 billion to the RockStar consortium. Google’s overall “cheerful” mood is already being explained by the fact that strategically the company won by forcing the winner to pay more than $4 billion for technology that was probably not worth it. One way or another, we will never know. Thank you for your attention!

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