What’s the point to searching for the largest prime number?
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Part of it is a deeper understanding of number theory. That is, calculating very large prime numbers can be very hard. The formulas used to calculate primes are like tools: once you have the tool, you can find other uses for it, and using that tool can give mathematicians insights about how numbers work in general.
Similarly, prime numbers that big aren’t calculated by hand anymore, it’s done by computers. Building the computers and programs to do it gives tools for computers that can help develop computer programs in general.
The most immediate application is for cryptography. Encrypting messages for things like sending data over the internet involves using big prime numbers as the “key”. Although computers don’t need to use the absurdly large primes people keep finding, the method to find those primes helps find smaller primes that *can* be used for cryptography. And, they can potentially help *break* cryptography.
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