According to Wikipedia, the most significant known prime number at this moment in time is 282589933−1. This is a nice illustration of two phenomena:
The profound unpredictability of the growth of knowledge. If we can predict the next prime, then we should know what it is, but we don’t.
It tells us something profound about the reality of (Platonic) abstractions. We know that a more significant prime number must exist (there are infinitely many primes), but we just haven’t found it yet. But we know it’s out there in reality.
For instance if I’ve to prove a math theorem on some particular number, I may not actually need to know the number (in the sense of directly writing it out on paper), I just need to know some useful properties of the number which I can use for the proof. I can just assume it is N, and say N has some properties and move on.
Don’t forget to prove that some such number exists! I can’t remember the details[1], but IIRC there was an entire branch of math based around a class of objects that, it turns out, doesn’t actually exist[2].
(Edit: it appears to be apocryphal. See my reply to acylhalide below.
According to Wikipedia, the most significant known prime number at this moment in time is 282589933−1. This is a nice illustration of two phenomena:
The profound unpredictability of the growth of knowledge. If we can predict the next prime, then we should know what it is, but we don’t.
It tells us something profound about the reality of (Platonic) abstractions. We know that a more significant prime number must exist (there are infinitely many primes), but we just haven’t found it yet. But we know it’s out there in reality.
Don’t forget to prove that some such number exists!
I can’t remember the details[1], but IIRC there was an entire branch of math based around a class of objects that, it turns out, doesn’t actually exist[2].(Edit: it appears to be apocryphal. See my reply to acylhalide below.
And it may be an apocryphal story
As in, a vacuous / empty set.
I looked it up, and it appears to be apocryphal.
There are specific instances of it occurring to a single person, but nothing as widespread as a branch of math.