Is it trite to say that prime numbers are unique? Probably. They are quintessentially unique. Pattern-seeking among prime numbers scattered here and there along the number line has ended many a time in a headache and a sleepless night. Why are they distributed so unevenly along the number line? And why, among the first 30 million numbers, are only 4 of the prime numbers *perfect* numbers?

Based on the work of Omar E. Pol, this stunning visualization by Jason Davies reveals the interplay of each number’s unique pattern, displayed as a periodic curve, superposed with the unique pattern of every other number. “For each natural number *n*, we draw a periodic curve starting from the origin, intersecting the x-axis at *n* and its multiples. The prime numbers are those that have been intersected by only two curves: the prime number itself and one.”

It begs the question: is it the superposition of these different patterns — these unique periodic curves — that causes the seeming irregularity of prime numbers? Something to ponder.

*“*This pattern cannot merely be a coincidence.* A mathematician who finds a pattern of this sort with instinctively ask, ‘Why? What is the *reason *behind this order?’ Not only will all mathematicians wonder *what *the reason is, but even more importantly, they will all implicitly believe that whether or not anyone ever finds the reason, there *must be *a reason for it. Nothing happens ‘by accident’ in the world of mathematics. The existence of a perfect pattern, a regularity that goes on forever, reveals — just as smoke reveals a fire — that something is going on behind the scenes. Mathematicians consider it a sacred goal to seek that thing, uncover it, and bring it out into the open.” — Douglas Hofstadter *(I Am A Strange Loop, p. 117)

DH, while ready to admit that it is certainly a pretty image, was quick to point out that it isn’t anything mathematically new. While true, there is a usefulness to this pretty image: it provides a way of determining the primality (even the perfection) of numbers as far out on the number line as you can imagine. An elegant improvement on prime number calculators, I think.

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