One core aspect of encryption is based on the idea that if you take a very large number (think 100 digits) it is very hard to figure out what numbers multiplied together get to that number (factoring). But it is super easy to take a bunch of numbers and multiply them to get a huge number. With prime numbers that process is unique. That is used a lot in encryption because you can share the giant number with anyone as an encryption key, but only the person that knows the original factors can prove it is the right key.
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