Prime Time Part 1

Arlene Blackman Yolles ♦ October 12, 2012 ♦ 7 Comments

Call me a geek, but I think Prime Numbers are cool! Like many things mathematical, the definition itself is crystal clear and uncomplicated: a number that has exactly two factors, itself and 1. This definition also demonstrates something I really love about math; it pulls no punches and it speaks with precision. Nothing ambiguous or fuzzy. Try leaving out the word exactly, and the definition becomes not only inaccurate, but open for interpretation. In that case, it would be reasonable to conclude that a prime number could have other factors (divisors), in addition to itself and 1. The word exactly tells us otherwise. That’s why the number 1 is not prime!

Everyone knows that if a number is not prime, it must be composite, right? Ah ha!  Not the case. A composite number is one with more than 2 factors. Then what should we call the numbers 0 and 1? The former has an infinite number of factors (as in 4 x 0 = 0 and 57x 0 = 0 and 28 x 0 = 0, etc.), whereas the latter has only one, itself. Mathematicians call these numbers – are you ready for this? – Special Numbers! That’s right, that’s their name.

Segue to a related memory. My dentist, while repairing my teeth, asked the assistant for the “plastic instrument.” I thought to myself, “How cute. He doesn’t want to burden the young assistant with a difficult technical name.” When she left the room, I asked him for the actual name of the instrument he called for and he said, “plastic instrument.”

Back to the subject at hand. How many primes do you think there are in the first hundred numbers? No cheating…..don’t look it up or scroll to the image that follows. Eratosthenes was curious, too, but he didn’t have Google. He devised an elegant (mathematicians love that word!) method for “sifting out” primes from other numbers, called The Sieve of Eratosthenes. Start with a grid of the numbers from 1 to 100. Cross out 1, ‘cause that’s not prime, and circle the next number because you know it is. So, 2 is circled. Cross out all the multiples of 2 ‘cause they’re not. Circle the next number (3) because it has to be prime and cross out all its multiples thereafter. Continue in this way until all the primes are circled, everything else is crossed off. Do you have to continue like that ALL the way through or is there some number you can stop at and know that all of its multiples have been eliminated? The answer? By the time you circle 11, all its multiples have been crossed off! Likewise for all the subsequent numbers. You’re left with 25 primes less than 100.

More about primes in a later post. Meanwhile, ponder this: What’s the greatest prime number?