Tuesday, January 01, 2008
Prime Time with Barnacle Boy
The boys and I are in Vermont, house and cat sitting for friends. Yesterday we went skiing (the ski boot acts just like a cast, no lateral motion...whee, I can ski!) and as I got on the lift with Barnacle Boy he checked out our chair number, promptly mused about it's significance (25, a perfect square); the total number of chairs on the lift (113, prime); and then dove into the topic at the top of his mind: "There are more composite than prime numbers. Have we talked about this already?" "Uh, no." At least not precisely this topic - last year it was evens and odds! I think his statement isn't correct, that the same proof that applies to evens and odds (there are the same number) applies to this question, but my real analysis is too far in the past. Where's Cantor (or Math Man) when you need him?
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I think he may be correct - if from 1-100 there are fewer prime numbers than composite, and even fewer from 101 - 200, and so on, would it go to say that overall there are fewer prime numbers?
ReplyDeleteI don't pretend to be a math expert, but in my mind, I would think there are fewer prime than composite.
High here today - 41 - for us weather wimps near Florida border, that's mighty cold 'round here.
I agree with Cathy on the primes.. but like her I have nothing but my gut feeling... living with uncertainty.
ReplyDeletesome cold days agaed for us in SE PA then a major warm up.
enjoy the skiing... from what I hear there is plenty of snow and more happening now or soon up that way.
I have no idea about the math stuff but I'm glad you're having good mom and son time. Goign to do that myself now with High School Musical.
ReplyDeleteHe is right. There is a famous theorem about primes, called (unsurprisingly) the Prime Number Theorem. One way of phrasing it is that the number of primes <=n is approximately equal to n/ln(n).
ReplyDeleteSo the fraction of numbers <=n that are prime is
(# primes)/n ~ (n/ln(n))/n = 1/ln(n).
So yes - most numbers are not prime, since as n gets arbitrarily big the fraction of numbers that are prime gets arbitrarily small.
(The Wikipedia entry on the Prime Number Theorem is pretty good.)
-Sue (Stasa's partner)
Michelle, that's awesome; I'm so glad you got to ski! (Sue - thanks!) - Stasa
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