# 5

Five

5

Five is the number that comes after 4, a number that is just large enough that it can be a little tricky to recognize at once. For example, try to count the e's in:

deeeeerp

You can’t really tell that there are 5 e’s without counting. How about:

ooooo

A bit easier since the o’s are isolated, but you still might need to count them. How about:

o o

o o o

Since the o’s are arranged in a better and clearer way here, now you can instantly identify five o’s. This tells us that five is still usually within our primary number sense’s capabilities, but it often needs to be seen as two and three instead of just five - fiveness is beginning to be a concept that is a bit shaky in our mind, but I still consider five a naturally palpable number.

Just for a few of five's many many properties, it is:

- a Fibnoacci number (next is 8)

- the number of Platonic solids (the tetrahedron, cube, octahedron, dodecahedron, icosahedron) - those were known since ancient times, and they were given somewhat mystical significance.

- the third prime number

- part of the only twin prime triplet (3, 5, 7)

- the lowest degree of polynomials that cannot be solved with radicals

- the second Fermat prime (preceded by 3 and followed by 17)

- the number of tetrominoes

- the smallest automorphic number (52 = 25)

- the smallest number of points that can make a star (as opposed to a polygon)

- many many more

For more on some of these properties, see primes at 19, groups of equally spaced primes at 47, polyominoes at 12 and 35, Fibonacci numbers at 89, Fermat numbers at 257, and automorphic numbers at 76.

Five is significant to humanity because there it is half of our normal base, or 10. For example, tally marks are grouped in five and top 5 lists are common. 5's significance as half our base is because humans have ten fingers. Five fingers on each human hand (and toes on each foot) instantly proves that five is still very common in nature - there are five of similar things in most mammals, like paws of cats and dogs. If we had, say, six fingers per hand, our number system would definitely be based on twelve instead of ten. Some early numbering systems were actually five-based instead of ten-based, and many had five as a sub-base.

Also, since 5 is half of our numerical base, testing for divisibility by 5 is super-easy in base 10 - the last digit has to be 0 or 5. It's the single easiest prime to test divisibility in base 10, followed by 2, 3, and 11.

There are several things that come in 5's, such as the five weekdays (Monday through Friday), the five senses, five fingers on a human hand, 5 points of a star, and so on. This is partially because of 5's symmetrical feel (see 3 for more) and partly because 5 is half of our base.

The main prefixes for five are quint- (Latin, such as quintillion, quintuplets, quintet, quintessential) and penta- (Greek, such as pentagon, pentagram, pentatonic). Both are commonly used.