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Ana did her work first, and immediately looked at the chart she'd written up, the Sieve of Eratosthenes, and started looking for a pattern. When I realized what she was doing instead of finishing her work (finding prime factors of numbers) I quickly popped her bubble by pointing out that primes HAVE no pattern (or at least, none that's become obvious in literally centuries of study) and if there IS one, she won't discover it by looking at the list of primes under 100.
The next day, Eva did her work on primes. She was only looking at primes under 35. She had, with help, seen that of course she could eliminate multiples of 2 by crossing out every OTHER number, and multiples of 3 by crossing out every other-OTHER number (as she phrased it), though she seemed completely unable to generalize this to "cross out every fifth number" and whatnot. At any rate, once she was done, she also began looking for the pattern in the primes. "I see the pattern at the beginning, but it doesn't stay like that, so it can't be a real pattern!"
I burst her little bubble as well. They could easily spend all day on this. I wanted to go pick up the CSA.
At any rate, they're both really intrigued by the subject, especially when I told them that you can make a couple thou by finding new primes! (Which you won't do by hand, because they're all in the 25 digit range by now, but that's beside the point.) They guessed intuitively when asked that if the set of all numbers is infinite, the set of primes probably is infinite as well (we should walk through that proof), but what the heck else can we talk about or read about on the subject?
The next day, Eva did her work on primes. She was only looking at primes under 35. She had, with help, seen that of course she could eliminate multiples of 2 by crossing out every OTHER number, and multiples of 3 by crossing out every other-OTHER number (as she phrased it), though she seemed completely unable to generalize this to "cross out every fifth number" and whatnot. At any rate, once she was done, she also began looking for the pattern in the primes. "I see the pattern at the beginning, but it doesn't stay like that, so it can't be a real pattern!"
I burst her little bubble as well. They could easily spend all day on this. I wanted to go pick up the CSA.
At any rate, they're both really intrigued by the subject, especially when I told them that you can make a couple thou by finding new primes! (Which you won't do by hand, because they're all in the 25 digit range by now, but that's beside the point.) They guessed intuitively when asked that if the set of all numbers is infinite, the set of primes probably is infinite as well (we should walk through that proof), but what the heck else can we talk about or read about on the subject?
