## Saturday, September 18, 2010

### Happy Birthday to Me!

Today is my birthday!  I am 35, which is the product of two odd prime numbers (5 and 7).  I haven't been the product of two odd primes since a decade ago (25), and won't be again for 14 more years (49) 4 more years (39).* which is the product of twin prime numbers (5 and 7).  I was last the product of twin primes two decades ago (3 and 5), and I will never again be the product of twin primes unless I live to be 143 (11 and 13).

The next time my age will be the product of two prime numbers that are adjacent in the sequence of primes is when I am 77.

Just as something cool to think about, 5 and 7 are one less than and one more than 6, respectively.  Remember in algebra the product of x-1 and x+1?  It's x2-1.  Plugging in six for x, we have an alternate way of computing 5 times 7. Six squared is 36, and 36-1=35.  Cool, huh?

This formula is actually more handy for computing the squares of numbers without resorting to a calculator or long hand calculations, in my experience.  For example, what is 21 squared?  It's 20 times 22 plus 1: 440+1 = 441.  You can change the 1 to any integer a, and get a formula (x-a)(x+a) = x2-a2.  So what is 43 squared?  It's 40 times 46 plus 9: 1840+9 = 1849.

* Math is hard.  Also, I need a vacation.

Scott said...

Are you planning to skip age 39?

Rebecca said...

Yes.

Amy K said...

And age 33 wasn't worth remembering? :-)

Rebecca said...

I realized that after I made the other correction. I think I am just going to have to rewrite this whole thing.

Amy K said...

Sorry... This reminds me of the problem with grading. With grading I'm always finding myself circling the mistakes in red. That's how I was taught to do it in grad school-- you start with the perfect score, then you take off points for mistakes. There's no need to comment on the triumphs.

So I'm writing now to do this over. I love your blog! I love your stories about Vinny, and running, and math. And I love the difference of squares trick-- my favorite teacher ever taught me that in high school algebra class, and I hadn't thought about it lately, so thank you for reminding me!

Rebecca said...

Amy K, I was not offended, just more embarrassed that I didn't check my work :)

Glad you like the blog and thanks for the encouraging words. I've been so busy lately that I haven't had much time to write any good quality entries, especially not about math. Hopefully there is some relief in sight and I'll be able to write some interesting stuff.

GMP said...

Happy belated birthday! I am always very happy when I turn a prime number (like now, I am 37) or a square of an integer (was last year). And I often try to factorize random numbers I see on licence plates, or receipts, etc. So your post really cheered me up!

Rebecca said...

Thanks, GMP! It is nice to know that there are other like-minded people out there isn't it? :)