Today we’re halfway through October, at the measured center of a month the ends with the thinning of the trusty veil holding back the dark from us. Or to take the other side of it, holding the chaos and discord of us back from the slower, comforting dark.
People have always been afraid of that dark, whatever they call it. The cold of it, the ancient, frozen constancy, holds no vivacity or animation. We may learn early in life that the stony, unchanging stare holds disapproval and disdain. At least we think that’s what we see, although ice is just water caught forever in stillness, and what is still water if not a mirror? But dissemble and rationalize as we might, we know what’s coming.
We know because we count; we incessantly count, and today the counting has reached 10 and 15. Those are numbers that resonate together, suggesting meaning. Maybe that’s because they represent a sequence of fives, and five is an auspicious number in any reckoning. It’s a number most of us encounter each time we use our hands, and lately — to use that term generously — it’s the basis of how we do a great deal of our other counting.
Five, as a number, has surprising depth. It’s a prime number, but more than that it’s a prince among primes. It’s a Fermat prime, in the first place. That means it’s one of the primes that can be expressed as 2^2^n + 1. Five is the first Fermat prime, so it has an ’n’ of one.
You may recognize the name “Fermat”, even if you’re not a devotee of mathematics, because he left behind a captivating mystery. In 1637 he made a note in the margin of a textbook that he had a proof of an elegant little formula, but it was too large to add in the limited space of the margin. As far as anyone could ever discover — and boy, did they searched, believe me — he never did write down the proof. But the formula was so small, and the notion of a proof was so captivating, that mathematicians tried for centuries to reproduce it.
One of the mathematicians who tried was Sophie Germain. In spite of being born in 1776, when women were not, as a rule, even welcome in schools, she became a physicist, philosopher, and, of course, mathematician. She didn’t solve Fermat’s Last Theorem, but her work was the foundation used for the next couple of centuries. In the process she managed to discover something new about prime numbers, and about five, and ever since the number five has not just been a Fermat prime, but a Sophie Germain prime as well.
A number — call it “p” — is a Sophie Germain prime if when you double it and add one, the result is also prime. If you do that to five, you get 11, another prime. The resulting prime is called a “safe prime”. But not only is five a Sophie Germain prime, it’s ALSO a safe prime, because two is also prime, and when you double it and add one, you get five. This seems like just a parlor game, but it’s more than that. Without Sophie Germain primes and safe primes, the cryptography that keeps things like web pages secure might not exist at all. I could prove it, but I don’t have the room for that right here…
The number five appears in a startling range of other functions and results significant enough to have names. Without going into the details, it’s a Catalan number (Eugene Catalan), a Wilson prime (John Wilson), and an Eisenstein prime (Gotthold Eisenstein). It appears in numerical sequences named after Fibonacci, Markov, Pell, and Sierpinski. There’s something unique about it in the Fibonacci series — it’s an infinite series, but five is the only Fibonacci number that equals its position in the sequence.
Many religions include five as an important or holy number in various ways. Even one fake religion, Discordianism (well it’s probably fake) reveres the “law of fives”, which states “All things happen in fives, or are divisible by or are multiples of five, or are somehow directly or indirectly appropriate to five.” Reportedly, Discordians find it important that “five” appears five times in that statement. They also explain that in Star Wars, Luke Skywalker’s X-wing fighter call sign is “Red Five.”
It doesn’t take advanced math to derive five from the fifteenth day of the tenth month of the year. The date is just a side effect of the calendar we happen to use. There have been countless different calendars across thousands of years and hundreds of civilizations. The one we’re using now is called the Gregorian Calendar, which isn’t all that significant (except possibly to Discordians), but it did begin to be adopted on October 15, 1582. That’s probably worth a high five.
