IPv6 addresses - are there so many?

I think that each of us has heard at least once, and perhaps he himself told someone that the IP addresses of the sixth version should be enough to address every atom in the universe. Or, in another variation, every atom on planet Earth. Well, or at least on its surface, as Steve Leibson calculated .

Is it really? Under cat, we recall the school chemistry course and check the veracity of this legend.

So, for highly scientific calculations, we need:

• chemistry textbook, grade 8 (although Google also works)
• calculator - anyone will do, but here you can use the search line, it can count
• Yes, that's all.

To begin with, we’ll determine how many unique addresses we have in the IPv6 space.

As you know, the address length of this protocol is 128 bits. This means that there are ^2,128 possible values ​​(we will not throw out addresses reserved for different purposes, because the total number without any reservations is important to us), or 3.40282⋅10 ³⁸ , if we write this in a more familiar decimal form. For the future, let's call it N _IP .

The number, you see, is considerable. But is it so great as it is painted? We consider further.

Here we have to open the textbook and remember who the avocado Avogadro is. Or rather, not himself, but his number - a constant characterizing the amountstructural units in 1 mole of substance.


When the school chemistry textbook opened on Friday evening ...

For now, just write that N _A = 6.02,010 ²³ . And then we'll see what it gives us.

Now we have the total number of structural units (aka IP addresses) and there is the Avogadro number. We find out how many moles this number of units will contain - we will find the so-called amount of substance ν (if anything, this is “nude”, not “ve”). Everything is simple here:

ν = N _IP / N _A = 3.40282⋅10 ³⁸ / 6.02⋅10 ²³ = 565'253'101'197'572 moles.

To make it less difficult and more visual, let us consider not abstract horses in a vacuum, but dihydrogen monoxide, popularly called water. Namely, its molecules: H ₂ O.

To find out how much these moles will weigh, you have to look again at the textbook and find the concept of molar mass there.

Molar mass is the ratio of the mass of a substance to its quantity. Or simply - how many grams one mole of a substance will weigh (again this mole ... nothing, soon we will get rid of it).

For a water molecule, the molar mass is found as the sum of the molar masses of the constituent elements - oxygen and twice hydrogen (these values ​​are taken from the periodic table):
M (H ₂ 0) = 2⋅M (H) + M (O) = 2⋅ 1 + 16 = 18 g / mol.

And then, to find out the mass of our moles, obviously, we need to multiply them by the obtained molar mass of water:

m = ν ⋅ M = 565'253'101'197'572 ⋅ 18 = 1.01746⋅10 ¹⁶ g = 10'174 '555'821'556 kg

Ten million million kilograms. Impressive, right? Or not? Let's see ...

As we know, 1 kilogram of water is the same as 1 liter of it. Some also know that this is actually not the case, but for simplicity we will call it an error.

Ten trillion liters. We continue to simplify:
1 kg ≈ 1 l = 1 dm ³ .
1 m ³ = 10 ³ dm ³ .
1 km ³ = 10 ⁹ m ³ = 10¹² dm ³ .
V = m / 10 ¹² ≈ 10.18 km ³ .

A little over 10 cubic kilometers. The most attentive people have already guessed that this very small distance is far from the estimated volume of “the whole Earth” (unless it’s flat with a near-zero thickness) and even more so the “whole universe”.

And the truth is what is 10 km ³ ? I ask to love and favor - Kremenchug reservoir:



The second largest (after Kakhovsky) reservoir of the Dnieper cascade. Its volume is 13.5 km ³ . This volume is already enough for the addresses of the sixth version of Internet Protocol to end earlier than the water molecules in it. I note - molecules, each of which consists of 3 atoms.

For comparison, the volume of Lake Baikal is 23,615.39 km ³ - 23.6 thousand cubic kilometers. Almost two and a half thousand times more than the great and terrible IPv6 is ready to address.

Which of these can be concluded? Do not believe everything that you read somewhere on the Internet, even if it is "somewhere" - Habr. Including, do not believe me, and be sure to recount everything yourself - who knows, maybe I'm also trying to fool you!

And anticipating possible disputes on the topic “aaaaa, IPv6 addresses are so few, they will end, we will all die”: 3.4 :10 ³⁸there are still an incredibly large number of addresses, which even after deducting all special-purpose ranges, remains large enough to not be afraid of their exhaustion for a very long time. Yes, even if nanobots suddenly appear tomorrow and they all want independence, unique white addresses - that's enough for everyone!

PS : It’s probably worth telling Google that “thousand m ³ ”and“ km ³ ”are far from the same thing.

Source: https://habr.com/ru/post/undefined/