WEBVTT

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Hi, yesterday we introduced prime numbers as

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a low floor, high ceiling idea. Simple to begin,

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but endlessly deep. Today, let's take a little

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closer look at what prime numbers actually are.

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In one sense, they are the oddballs. If you take

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numbers and try to organize them, you can think

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of them as forming rectangles. Six, for example,

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can be arranged as two by three. 12, that's 3

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by 4, or 2 by 6. Most numbers are flexible like

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that. They fit into different rectangular patterns.

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But primes do not cooperate. Take 7. You can

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line up 7 objects in a row, but you cannot form

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a rectangle with more than one row. No matter

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how hard you try, it just does not work. They

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do not fit the pattern. They resist being broken

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down. So in that sense, prime numbers are the

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oddballs of the number world. They do not blend

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in. They don't factor nicely. They don't follow

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the same pattern as the others. But here's the

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irony. These numbers that don't fit end up being

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the building blocks for everything else. from

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prime numbers. 12, that is 2 times 2 times 3.

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30, that's 2 times 3 times 5. No matter how large

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the number, it can always be broken down into

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primes. And not just in any way, but in a unique

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way. It's like every number has its own prime

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fingerprint. So, The numbers that seem the most

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stubborn, the least cooperative, are actually

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the ones holding everything together. And to

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me, I find this a bit humorous. The misfits become

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the foundation. The ones that don't fit the pattern

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define the structure. Maybe there's an interesting

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idea lurking around. Sometimes what looks irregular,

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what looks out of place, is actually more important

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than we first realize. Prime numbers remind us

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that simplicity does not mean shallow. And being

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different does not mean not important. In fact,

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it might mean the opposite. So today, as we continue

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exploring this world of primes, notice how something

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so simple, numbers that do not fit into rectangles,

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can become the structure behind everything. And

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that leads us to a bigger question. Do these

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primes ever run out? Or do they go on forever?

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How can we even answer it? Can we test our way

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to the end? Or does math give us another way

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to know something is true? Give it some thought.