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Given that we know that there are infinitely many primes, why are we interested in knowing ever larger ones? It's somewhat like asking, what is the largest kno
by auggierose 9y ago
Given that we know that there are infinitely many primes, why are we interested in knowing ever larger ones?
It's somewhat like asking, what is the largest known natural number?
- dev1n 9y agoNo one can predict the next prime. That's why people want to compute the next prime.
- jordigh 9y agoPrime numbers thin out. We have very good estimates of how they thin out. We also know that gaps between primes can get arbitrarily large. And we cannot predict when the next prime will happen without huge computations. And large primes have a use, e.g. cryptography (although, who knows when we'll have a use for such a large one). Having a list of primes is also very useful for empirical evidence for many conjectures in number theory. None of these things are true about natural numbers in general.
- auggierose 9y agoFor cryptography it isn't very useful to know the largest one. Think about it ... Your other answers amount to: it is difficult, that's why we do it. ?! Sure, just don't expect me to care about it.
- yenwel 9y agoBecause nobody knows a fast algorithm to factorize an integer into its prime factors. Yet, it is very easy to check if a set of prime factors multiply to a certain integer. https://stackoverflow.com/questions/439870/why-are-primes-important-in-cryptography https://stackoverflow.com/questions/439870/why-are-primes-im...
- p1mrx 9y agoIf nothing else, "what's the largest prime number you've found?" would be a fun question to ask another intelligent civilization, should we make contact with one.
- auggierose 9y agoAlright, that's a good one :)
- igravious 9y agoInnate curiosity isn't enough?