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 > Intrinsic Nature of Primes
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 Other Bases   Number Line

## Intrinsic Nature of Primes

As I explained in a footnote to another essay, when I started learning products, I soon realized I had no associative hooks for the larger primes. That wasn't the only disappointment, though … I also realized that the hooks I did have had almost nothing to do with the intrinsic nature of the primes, and everything to do with base 10, and with accidents of culture. I had pretty solid ideas of two-ness, three-ness, and five-ness, but even the idea of seven-ness was already pretty tenuous, and beyond that, it was hopeless … I couldn't even begin to distinguish eleven-ness from thirteen-ness.

Since then, I've been thinking a little bit about different ways of understanding the intrinsic nature of the primes. I haven't come up with anything amazing, but I think I have enough that it's worth writing down.

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