## A Dream of Number Theory

A curious “memory” popped up in a dream last night, an allusion to a proof that 69 is an even number. Half awake, I “remembered” reading this “proof” somewhere—a clever, elegant argument, although obviously quite specious. And entirely a product of my imagination, it turns out.

I always say that I have no imagination, and that is certainly true of my waking self. My sleeping brain, however, is prone to extravagant flights of fancy, and this was clearly one of them. As I woke up further, I dismissed this absurd concept but instead decided that I had read that 2 is not an even number, the rationale being that no even number is prime.

Waking still further, I became less confident even of that “fact,” but I do definitely recall reading somewhere recently—whether online or in hard copy I don’t recall—a discussion of prime numbers and their frequency in each increasing decade, and this discussion did definitely describe 0 and 1 and perhaps also 2 as special numbers that were outside the prime/not prime (and perhaps even the odd/even) dichotomy. Google research tells me that the word for “not prime” is composite and that indeed 0 and 1 are considered neither prime nor composite since they don’t have exactly two positive divisors (factors), which would make them prime, nor more than two, which would make them composite. Clearly 2 does meet the definition of prime, so my dream-induced “memory” completely falls apart.

I still wish I could remember where I read the article because its whole point was that there is a pattern to prime numbers. I did learn (from Wikipedia) that “The Riemann hypothesis implies results about the distribution of prime numbers.” A little more googling reveals that in 2010 a University of Texas professor, John Tate, received the Abel prize for his research on this subject. In March 2016, several publications reported mathematicians or “math experts” as “stunned” or “shocked” to discover a pattern in prime numbers.

Perhaps the best pattern of all, however, is the visual one revealed in this YouTube video. The Stephen Hawking voice is really annoying, but the video is intriguing.