The largest number: candidates for this title

Formally, it is considered that the largest number does not exist. The number series can be continued indefinitely. But another question makes sense: what is the largest number necessary to calculate an application problem. Even if this task will be very highly specialized, such as the time of evaporation of the last black hole in the universe or the number of all elementary particles in it. In the applied aspect, there are several candidates for the role of the largest number.

As they say in the history of the development of one very popular search engine, its name was chosen similar to the name of the largest number. But which one is not always specified. In fact, googol (English googol) or 10 to the power of 100 is the largest number necessary for calculating applied tasks. It can be typed for calculations in any engineering calculator. The number of elementary particles in the universe is estimated at 10 to the power of 80, so why reinvent more numbers?
Perhaps, for the sake of scientific interest, the search for the largest prime number began (it should be divided only into itself and into 1). Later, simple numbers began to be used in cryptography, so the largest prime number should help in creating the most stable cipher (or its hacking). In the calculation of prime numbers, the most powerful supercomputers are occupied, and today a number equal to ... sorry, written down as (2 ^ 57 885 161) -1. In a linear record, its length would exceed 17 million characters, so continuing this article would not make sense.

The greatest number tried to find not only mathematicians, but also physicists. In science there are a number of the smallest numbers that have a physical meaning. The Planck length, the smallest measurable piece of space, is 1.6 * 10 to minus 35 degrees, and the volume of the universe should be at the present moment somewhere 8.5 * 10 to the power plus 185 Planck lengths. For what it is possible to apply this number, while it is not known. But there is an even smaller constant - Planck time ~ 10 ^ (- 45), on which one can also divide something and get another very large number.

But mathematicians still can not keep up with physics; in proving modern theorems on the existence of the largest number, one must operate with these largest numbers. Here it is worth mentioning the number of Graham, who was in his time in the Guinness Book of Records. It is generally impossible to write it with the help of usual mathematical notation. Officially, Graham's number is still the largest number in the world, but attempts to come up with something even bigger do not stop.

Finally, we mention another interesting number, which can be considered the largest in its field. German science fiction writer Kurd Lassvitz in his story "The Universal Library" tried to compare the dimensions The universe and the number of all information contained in it and structured in textual material. Today's Internet is accused of trying to take the form of such a library. But in it, according to the creator's plan, not only useful knowledge will be collected, but also erroneous, as well as entire volumes with punctuation marks and chaotic sets of numbers and letters. Nevertheless, the number was estimated as 10 to the power of 2 000 000, which is less, for example, the largest of the computed prime numbers. But if the library existed physically, in the universe it would not fit all. And the number of volumes is much less than googol.