| Prime numbers are tricky things. They are one of the most fundamental parts of our numerical systems, but they're difficult to predict. You would kind of expect that something so elementary should be easily predictable, or follow a pattern. But while we've found some similarities (like the mersenne primes) there's still a kind of nagging feeling that there should be a more basic way to enumerate prime numbers than guess and check. We've learned some simple things about them, such as the existence of Mersenne primes, or ideas on the probability of any given number being prime being inversely proportional to its logarithm. But I think the biggest thing is that it's a puzzle. But a puzzle that bothers us because it seems like it should be easy to solve, but it's not. Finding larger prime numbers tells us more about them. It lets us see other parts of patterns. Patterns that might lead to some insight on how to predict if a number is a prime, or how to factor large numbers. This might have an impact on cryptography for instance. But finding this number doesn't solve a problem, it adds to a body of knowledge. It fills in a bit of the puzzle. In the end the hope is that we learn something about the puzzle, or at the least, learn why we can never learn something about the puzzle. |