Here the sequence of primes is presented graphically in terms of a step function or counting
function which is traditionally denoted π(x). (Note: this has nothing to do with the value
π = 3.14159...) The height π(x) of the graph at horizontal position x indicates the number of primes less than or equal to x. Hence at each prime value of x we see a vertical jump of one unit. Note that the positions of primes constitute just about the most fundamental, inarguable, nontrivial information available to our consciousness. This transcends history, culture, and opinion. It would appear to exist "outside" space and time and yet to be accessible to any consciousness with some sense of repetition, rhythm, or counting. The explanation in the previous page involving piles of stones can be used to communicate the concept of prime numbers without the use of spoken language, or to a young child. |