[HN Gopher] Untouchable number ___________________________________________________________________ Untouchable number Author : optimalsolver Score : 71 points Date : 2023-08-25 14:37 UTC (8 hours ago) (HTM) web link (en.wikipedia.org) (TXT) w3m dump (en.wikipedia.org) | cj wrote: | Other than being theoretically or intellectually interesting, | what value do things like "untouchable numbers" have in the real | world (or in any practical application)? | svat wrote: | You could ask the same "Other than <its value>, what value does | <it> have?" question about anything. | | (The answer is: none. For that matter, how would you answer | questions like: what value does the concept of even-and-odd | numbers have? Or, say, Fibonacci numbers: sure the Fibonacci | sequence itself might have some applications, but what value | does _knowing whether or not a certain number is a Fibonacci | number_ have?) | permo-w wrote: | you could ask that, and you would be right to | | untouchable numbers have what seems like a pretty arbitrary | definition and yet the article mentions the numbers being | studied a thousand years ago, which begs the question: why? | why not numbers that can only be produced by adding 3 primes | together? why not only numbers that can be produced by | multiplying squares greater than 1? there are infinite unique | infinite sets of integers. why is this one _more interesting_ | than the other infinity to the degree that it 's been studied | for a thousand years? | | if it's given that the Fibonacci sequence has uses, then | knowing the numbers in that sequence is also obviously going | to be useful | gizmo686 wrote: | > why not numbers that can only be produced by adding 3 | primes together? | | Goldbach's weak conjecture: Every odd number greater than 5 | can be expressed as the sum of three primes. | | First proposed in 1742, and proven in 2013 [0]. The | original proposal considered even numbers as well, nowadays | those are covered by Goldbach's strong conjecture, with a | tighter bound of 2 primes. | | > why not only numbers that can be produced by multiplying | squares greater than 1? | | You mean squares containing at least 2 distinct prime | factors? Fully classifying this set of integers would fit | well on an undergrad intro to proofs exam. | | [0] https://arxiv.org/pdf/1501.05438.pdf | permo-w wrote: | the actual examples I give are just that, examples. why | not numbers that can only be produced as the sum of 17 | primes? or 459? or numbers that have the same number of | factors as their digits added together does? there are | infinite of these constraints that can be invented. why | is this one particularly interesting | contravariant wrote: | Viewing it as sets lacking a certain property may help explain | why it's useful to know and why simply using a countable model | is not preferable. | | Uncountability means that real numbers lack certain properties. | If you accept the claim of physicists that the world is best | described using real numbers then this has some applications. | | Among the things that are impossible are things like | constructing a function to pick a number for each set of real | numbers. Or making an algorithm to decide two numbers are | equal. | | Even more concretely the fact that it is incredibly hard to | determine whether something is non-zero (or even nonnegative) | is the bane of various numerical algorithms. Obviously you can | work around these issues, but uncountability is the first sign | of trouble. | dhosek wrote: | None at this time, but until the advent of modern cryptography, | the same was true of primality. Then again, other mathematical | curiosities retain their lack of application (and some of us | prefer that). | JadeNB wrote: | > None at this time, but until the advent of modern | cryptography, the same was true of primality. | | I'm not sure that this is true, at least if you are flexible | about what counts as an 'application'. The concept of | divisibility, and then of primality, surely developed from | considerations of how a certain number of objects could, or | could not, be broken into groups, say for storage or | transport. To know that there are several ways to group 24 | objects, but only two (trivial) ways to group 23 objects, is | an application, even if it's not especially sophisticated. | tantalor wrote: | If you ever see Paul Erdos mentioned on a math article, it's | just for funsies, not real world. | deepspace wrote: | What does that even mean? | effie wrote: | Paul Erdos is known for work in hobby mathematics which has | little or no use "in real world". | LordShredda wrote: | Well if you click on the link you can see that 5 is the only | odd untouchable, much like how 2 is the only even prime. Maybe | there's a connection that ties them to cryptography? | dhosek wrote: | To be more accurate, 5 i the only _known_ odd untouchable. | It's believed it's the only odd untouchable, but, like the | Goldbach conjecture, it remains likely but unproven. | bmacho wrote: | They help us to develop tools that will allow us faster | computation. | lubujackson wrote: | Reminds me of the number my son invented when he was 4. A | killion. It's a number "so big, ya die." | kccqzy wrote: | A great opportunity to begin teaching your son some set theory | until he understands inaccessible cardinals! | Lichtso wrote: | Not as a number, but as a unit it actually exists. It is called | a "mort" (from mortality). In that sense one mort is "so much, | you'll die". | | Though, the commonly used scale is a mort * 10 ^ -6. | https://en.wikipedia.org/wiki/Micromort | ndsipa_pomu wrote: | [flagged] ___________________________________________________________________ (page generated 2023-08-25 23:00 UTC)