WEBVTT

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Hi, yesterday we saw that prime numbers are the

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oddballs. They do not fit into rectangles. And

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yet, that very feature is what allows them to

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become the building blocks of all numbers. And

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once you notice something like that, it is almost

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impossible not to ask a question. How many primes

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are there? How many of these strange, stubborn

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numbers actually exist? And what I find fascinating,

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is this is not just a mathematician's question.

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It is not tied to a certain time or place or

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culture. I think it's a human question. In fact,

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we've been noticing patterns in numbers for a

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very long time. There's an ancient artifact called

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the Ishango bone, over 20 ,000 years old, with

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markings that many believe reflect an awareness

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of prime numbers. Long before modern mathematics,

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long before formal proofs, humans were already

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noticing that some numbers behaved differently.

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The moment you start arranging rocks and realize

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that some numbers do not fit into rectangles,

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you can ask it. A child can ask it. How many

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are there? That is the low floor. But then comes

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the next step, trying to answer it. And suddenly

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you feel the ceiling because we're not counting

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objects on a table. We're talking about numbers

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and numbers do not stop. You can always go further.

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There's always a bigger number. So now the question

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becomes even more interesting. Inside this infinite

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world of numbers, does this special group, the

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primes, also go on forever? Or... Do they eventually

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run out? To me, it is not obvious. You might

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imagine that primes become more and more rare

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until eventually they disappear. But how would

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you ever know? You cannot check forever. You

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cannot reach the end of numbers. So how could

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you possibly answer a question like this? And

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this is what makes it such a beautiful question.

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Simple to ask, incredibly difficult to answer.

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A true low floor, high ceiling idea. So today,

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take some time to consider how would you approach

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it? If you had to decide, do primes go on forever

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or do they eventually stop? What would you do?

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What would you try? Tomorrow, we will look at

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a remarkable idea over 2 ,000 years old that

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indeed answers this question without ever needing

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to reach the end.