Today being the 11th of December, let me point out that 11 is what mathematicians call a *número primo/prime number*. The primes are one of three categories into which the positive whole numbers are divided. Most common are the composites, each member of which can be represented by a rectangular array of dots with the same number of dots in each row. For instance, we can represent the composite number 12 as three rows of four dots each:

• • • •

• • • •

• • • •

In contrast, a prime number cannot be represented as a rectangular array. We may try with the prime number 11, but we have one dot too few to fill up a second row

• • • • • •

• • • • •

or we have a surplus dot that spills over into a third row

• • • • •

• • • • •

•

(That last dot can also serve as the period at the end of the previous sentence.) No, the only possible arrangement for 11 is

• • • • • • • • • • •

In other words, all the dots end up in the *first*—and only—row. That’s one way of explaining why such a number is called *primo/prime*, from the Latin word for ‘first,’ *primus*. Historically, the ancient Greeks had the notion that the primes are first in importance, the fundamental type of whole number. The composites were secondary because they can always be expressed as products of primes (which amounts to saying that we can make rectangular arrays of dots to represent them).

Ironically, as fortunate readers may remember having been taught during their years *en la primaria/in primary school*, the Greeks placed the very first positive whole number, 1, which was of prime importance to them, in a category of its own. The ancients accorded the number 1 that distinction for being the first [positive whole] number, the generator (by addition) of every other number.

All of this tempts me to proclaim the *primacía/primacy* of mathematics over everything else, but I would never do such a thing in a column about etymology, where words are our prime consideration.

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For more about the English word *eleven* and its not-at-all-obvious connection to something in Spanish, see last year’s post “The hidden one in *once* and *eleven*.”

© 2015 Steven Schwartzman

Jim in IA

Dec 11, 2015@ 08:33:36Is the population of prime numbers infinite? I figure some mathematicians have that figured out.

Steve Schwartzman

Dec 11, 2015@ 08:42:43You’re reading my mind. I’d thought of mentioning that more than two thousand years ago the Greek mathematician Euclid offered a proof that there are infinitely many prime numbers. The primes do, however “thin out” as you look at larger and larger numbers.

Steve Schwartzman

Dec 11, 2015@ 15:00:03Here’s that brief proof:

http://www.math.utah.edu/~pa/math/q2.html

shoreacres

Dec 11, 2015@ 09:02:34It used to be that, whenever Math entered the room, I’d utter a primal scream. People would roll their eyes and say, “Even a primate could solve

that.Stop being such a prima donna.”In the end, it turned out I’d only been given the wrong primer: a decent primer being a prime requisite for learning. I still prefer the forest primeval (those murmuring pines! those hemlocks!) to prime numbers, but at least now I can enjoy both.

* * * * *

Steve Schwartzman

Dec 11, 2015@ 09:16:34Now that you’ve given prime examples of related words (primal, primate, prima donna,…), I wish you could get in a time machine and go back to primary school for a second shot at a first impression of prime numbers.