Here's another directly related phenomenon. Look at the function f(n) = n^2 + n + 41. Now start plugging in nonnegative integers. You get 41, 43, 47, 53, 61, 7

Here's another directly related phenomenon. Look at the function f(n) = n^2 + n + 41. Now start plugging in nonnegative integers. You get 41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, ..... All primes?! Well, not quite, plug in n = 41. But the fact that you get primes for so long is quite directly (but in a rather complicated way) explained by what ColinWright describes.