Sunday, January 01, 2006

mathematical verification

My Dad, the Math Prof, sent me an email confirming my assertion that "2006 is not a prime number:"

You're right; hardly any even numbers are prime.

I looked for the most recent prime number year and also the next one. We can ignore numbers ending in 5 (except 5 itself) because they are divisible by 5, and we can add the digits of a number to see whether the number is divisible by 3 (the sum and the number itself will have the same status, since 9, 99, 999, ... all are divisible by 3 and when you add the digits you are simply ignoring 9, 99, 999, ...), and even numbers except 2 aren't prime.

This tosses out 2005 and 2004 immediately (2004 for two reasons -- even, and fails the 3 test), but 2003 needs checking. Out came the calculator and I tried dividing by 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, and 43 checking all the primes up through 43 and then I stopped. The quotient with 43 was 46.58139535 approximately and that's far enough because the next prime to test would be 47 which is past the square root of 2003. So 2003 is prime.

Then I looked in the other direction. 2007 fails the sum of digits divisible by 3 test (every third odd number will) and 2009 turns out to be divisible by 7 (every seventh odd number will be) -- that was quick! But 2011 isn't divisible by the primes 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, and 43 and when divided by 43 yields 46.76744186 approximately, so it's prime.
Interesting that 2010 will NOT be a prime number, nor will 2009, but 2011 will be a prime. In Vancouver we are all conscious of twenty-ten being the deadline for many magificent public works projects all geared to the Winter Olympics that will be held in our city. Maybe, my mathematical superstition suggests, this means that the leadup and year itself will be dodgy, but the aftermath positive??

All that said, I plan to enjoy 2006 even if it is not a prime number. Thanks Dad, for checking my math, and for the projections which are most helpful.

question: what's your favourite number?

mompoet - numbers are people too

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