4 ms·
Is it of any particular relevance that such a number is a prime?
by ByThyGrace 8y ago
Is it of any particular relevance that such a number is a prime?
- letsgetphysITal 8y agoLarge prime numbers are crucial for public key cryptography to function.
- nicky0 8y agoA large prime is notable and hence is included in public databases.
- OscarCunningham 8y agoThat's not really true. There are loads of large primes (way more than you could store), so they're not all notable.
- paulgb 8y agoThere are infinite prime numbers. What's notable is the ones we have found.
- OscarCunningham 8y agoNo. Even then they're not notable. For example there are 10^97.6 primes with 100 digits, of which not all have been found (not enough storage space in the universe), but it's trivially easy to generate one at random.
- gowld 8y agoFound the Wikipedia Deletionist.
- OscarCunningham 8y agoI'm generally an inclusionist, but Wikipedia doesn't have enough server space to store pages on every known prime.
- paulgb 8y agoYou disagreed with the statement > A large prime is notable and hence is included in public databases. It is verifiably true that these public databases exist (bigprimes.net) I'm not sure what you're arguing here.
- OscarCunningham 8y agoI'm arguing that these numbers aren't notable just because they are large primes. They certainly aren't included in public databases just because they are large primes. The example site you gave bigprimes.net has one main database, that includes the first 1.4 billion primes. These are all much smaller than the illegal primes mentioned on the wikipedia page (they have at most 11 digits, whereas the ones mentioned on wikipedia have 1000s of digits). It also has a list of the Mersenne primes, which are the largest known primes. The largest has 23249425 digits. So primes with 11 digits or fewer are notable (because they are small), and primes with 23249425 digits or more are notable (because they are large), but primes with around 2000 digits are not notable.
- paulgb 8y agoOk, thanks for explaining that. It sounds like the condition for notability in this case is the combination of size and algorithm used? > Carmody created a 1905-digit prime, of the form k·256211 + 99, that was the tenth largest prime found using ECPP, a remarkable achievement by itself and worthy of being published on the lists of the highest prime numbers.
- OscarCunningham 8y agoOh, I didn't realize the page said that. I should have read it more carefully. You're right that it's a combination of size and method used. The Mersenne numbers are especially easy to prove prime, so it's also interesting to keep track of the largest primes proved by other methods. I think these days a 2000 digit prime wouldn't be notable in any case, but it sounds like it was back when Carmody was doing this, so this was in fact a good example of an illegal number that was independently interesting.
- nicky0 8y agoPerhaps I shouldn't have said "large" or "notable". The point is that when a prime number is discovered meeting certain criteria it is included in public databases. This makes the case of an "illegal" such prime interesting.