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) = x2 + 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 x for which x2 + x + 41 is not prime?

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:

413 = 23 + 173 + 403 = 63 + 323 + 333 = 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…

• 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.
• You use the term surd, and you know how to calculate its value on a slide rule.

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