Sean has been entertaining himself all afternoon, writing little stories, drawing 3-dimensional shapes, imagined 4-D and other-D shapes; while Brian and I worked on some Singapore Math. Oh, he also watched Sound of Music alone. Eddie flew off to Athens for a meeting this morning, that's why I could get Brian to do some work on a weekend. Otherwise, we'd be vegetating in front of the tv watching dvds.
Right before bedtime, I found a piece of paper with the scribblings above. It's a mathematical term concocted by Sean called "Almost Prime Number".
Just to refresh, remember the definition of Prime Numbers? ie Numbers that have only 2 factors; 1 and itself.
Well, Almost Prime Numbers are numbers with only 3 factors, Sean says. He squares prime numbers, and discovers they only have 3 factors.
He goes on to explain:
"As you can see here, a prime number times itself equals an almost prime number. And there's also something special about it. Every almost prime number always has 3 factors. 1, itself, and its square root. The square root is the thing that makes the number not prime."
When I tucked him into bed just now, he asked this, "Mummy, are square roots of prime numbers always irrational numbers?"
Brian says, "Of course."
I said, "I'm not sure."
Brian goes, "Look Mummy, prime numbers only have two factors, 1 and itself, so obviously it cannot have any square roots that are rational numbers or that number would be be its factor."
I then wondered if all square roots of integers have to be either integers or irrational numbers. Brian says that is so and when I googled, Wikipedia says, "Square roots of integers that are not perfect squares are always irrational numbers."