What’s the point to searching for the largest prime number?
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As we have already proven there are infinitely many prime numbers, there really isn’t much point. Some people will say cryptography, but that doesn’t require primes anywhere near as large as the largest primes we’ve found.
Basically, there’s two purposes to the search for large primes: a demonstration of new mathematical methods, and as a benchmark for computer systems. Finding prime numbers is a very simple, well-understood problem, so it’s a very effective test of computing power.
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