If this sounds hopelessly arbitrary to you, Lindsay, rest assured that there actually was a historic basis for it -- check out the wikipedia article on "Dual Grammatical Number".

In various ancient languages, there were three categories of "grammatical number" for nouns:

Singular = Exactly one of something
Dual = Exactly two of something
Plural = More than two of something

In many modern languages, the "dual number" has mostly been absorbed into the plural -- so in English, "two dogs" and "five dogs" both take the plural verb form "(they) are barking"; there's not a special verb for when there are exactly TWO dogs.

However, even in English, there are a few remnants of the old "dual" category -- for example, our distinction between "neither of these two things" and "none of these three/fifty/thousand things"; or "between the two cities" and "among the three/fifty/thousand cities."

Historically, Slavic languages (including Russian) also had "dual numbers" for when there were exactly two of something. What happened in modern Russian (for some reason) is that when there were exactly three or four items, they got merged into the "dual" category, instead of being "plural" like the numbers five, six, seven, etc.

Again, this won't necessarily make it easier for you to remember, but at least you know there was some historic logic for it, and it's not totally random.