## Archive for March 19, 2012

### It’s Back to Prime Time

On Saturday, I turned 41 years old. I’ve been looking forward to this for a while. It’s a prime year, and its twin prime is two years away. In between, I’ll be a number of years that is “the answer to life, the universe, and everything.”

Forty-one is also cool because *f*(*x*) = *x*^{2} + *x* + 41 is a prime-generating function. That is, *f*(1) = 43, *f*(2) = 47, *f*(3) = 53, and so on.

What is the first value of

xfor whichx^{2}+x+ 41 isnotprime?

The following image might help you answer that question. The number 41 appears in the center, and consecutive positive integers then proceed in a spiral. Notice that all of the numbers highlighted in yellow are prime. A pattern of primes continues along the diagonal — at least for a little while.

It also turns out that 41 is the smallest number whose cube is the sum of three cube numbers in two different ways:

41

^{3}= 2^{3}+ 17^{3}+ 40^{3}= 6^{3 }+ 32^{3}+ 33^{3}= 68,921

And 41 is the sum of the first six prime numbers:

2 + 3 + 5 + 7 + 11 + 13 = 41

At 41, I still feel young. But you know you’re an old mathematician when…

- You report your age in hexadecimal. (I’m only 29!)
- You’re not dead, but you’ve lost most of your functions.
- The distance you walked to school as a kid is directly proportional to your age.
- Your age can be described as “countably infinite.”
- You regularly go off on tangents.
- The phrase “pulling an all nighter” means not getting up to pee.
- When asked your age, you reply, “I’m in the 99th percentile.”
- You use the term
*surd*, and you know how to calculate its value on a slide rule.