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I agree that this makes 37 somewhat interesting. Certainly more interesting than - say - 31. 31 is a prime number too, and therefore somewhat interesting. But
by mg 3y ago
I agree that this makes 37 somewhat interesting.
Certainly more interesting than - say - 31.
31 is a prime number too, and therefore somewhat interesting. But for sure not as interesting as 37, which as we just learned, is the median value for the second prime factor of an integer.
Any suggestions of integers which are even more interesting?
And while we are at it, is there an integer which qualifies to be the most interesting?
- falcor84 3y agohttps://en.wikipedia.org/wiki/Interesting_number_paradox https://en.wikipedia.org/wiki/Interesting_number_paradox
- mikepurvis 3y agoI know it's a joke, but I still feel like it would be more meaningful if it wasn't so generic that it could kind of apply to anything. Like, there's nothing specific to numbers about the idea that the least-"interesting" item in some set is itself interesting for possessing that property.
- mg 3y agoThen let's see who manages to write the least interesting comment in this thread.
- deleted 3y ago[deleted]
- falcor84 3y agoThe way I understood it, this formulation relies on induction on the natural numbers.
- SamBam 3y agoBecause it's numbers, which are sortable, you can ask which is the least member of a set. If a set of positive numbers doesn't have a least member, does the set exist? There's a similar paradox which asks what the smallest number that can't be defined in fewer than thirteen words. There must be some number, right? For instance, 7603201560, or "seven billion six hundred and three million two hundred and one thousand five hundred and sixty" seems to require 16 words. Maybe you can shorten it by removing the "ands," but I can come up with a longer number. But if there were such a number, then couldn't we describe it as "the smallest number that can't be defined in fewer than thirteen words?" And then it just got defined in fewer than thirteen words. So it can't really be a member of that set. So does the set have any members?
- mg 3y agoWell, that is about the question which is the most uninteresting number. And the paradox that - whichever number it is - this attribute makes it interesting. But since we are not looking for the most uninteresting number, but the most interesting one, we do not have to fight with issues of that calibre.
- function_seven 3y agoTrue, but you must still contend with your observational influence. Whatever number you crown as "most interesting" will become even more interesting for wearing that crown! So you must take this duty with extreme care and thoughtfulness, for when you anoint such a number, your action may crystalize it as such for all eternity. Other numbers will have to go further to supplant it.
- TeMPOraL 3y agoLike the Original Sin entered the Garden of Eden through the Serpent, mutable state breaks the time-invariant perfection of mathematics through the idea of interestingness, since it's clear the least interesting things only remain so until someone notices.
- deleted 3y ago[deleted]
- swayvil 3y agoI nominate 120 as "most interesting integer". For obvious reasons.
- AnimalMuppet 3y agoUm, it's not obvious to me. Could you specify?
- InfamousRece 3y agoThe smallest triply perfect number? https://oeis.org/A005820 https://oeis.org/A005820
- swayvil 3y agoSo many factors in such a small package, for one.
- goodmachine 3y ago120 - or twelfty to friends - is a delight. "The long hundred, also known as the great hundred or twelfty,[is the number 120 (in base-10 Hindu-Arabic numerals) that was referred to as hund, hund-teontig, hundrað, hundrath, or hundred in Germanic languages prior to the 15th century, and is now known as one hundred twenty, or six score." https://en.wikipedia.org/wiki/Long_hundred https://en.wikipedia.org/wiki/Long_hundred "120 is highly composite, superior highly composite, superabundant,[3] and colossally abundant. With sixteen divisors, 120 is the smallest number to have that many divisors..." https://en.wikipedia.org/wiki/120_(number) https://en.wikipedia.org/wiki/120_(number)
- jl6 3y agoMathematicians are locked in bitter struggle between the Zeroastrians who believe additive identity blesses 0 as truly the most foundational and therefore interesting integer, while the Unitarians favor multiplicative identity and thus champion 1. Uncountable souls have been lost to the conflict between these two groups.
- joenot443 3y agoUgh, must we relate every thread about integer fascination back to Zerry/Unny zealotry? It’s been going on for centuries now, nobody’s changing their opinion at this point.
- narinxas 3y agobecause numbers have a natural meaning. roughly speaking each integer has as many meanings as its value. so 0 and 1 are just the very beginning. zero's natural meaning is special, it's the void. sometimes the 'variable' stands in as having this meaning, sometimes the variable is zero. one is the easiest simplest to grasp. its meaning is "I", ego. two is duality in the broadest imaginable sense. wars are being fought right now over the precise meaning of 3
- ajhurliman 3y agoThis feels closer to a tarot reading than mathematics, and I’m here for it
- _0ffh 3y agoThe Tao Produced One; The One Produced Two; The Two Produced Three And The Three Produced All Things.
- Shorel 3y agoSounds very close to the firstness, secondness and thirdness categories from Charles Sanders Peirce. (Which I think are nothing but nonsense from a madman =)
- paulddraper 3y ago12 Smallest abundant number
- hyperliner 3y ago[dead]
- kmoser 3y ago12 is also the largest one-syllable number (at least in English).
- resource0x 3y agoPrime numbers are not especially interesting. E.g. all groups of prime size are cyclic. But each composite number has its own "character". The "interesting" number among primes is 2. Almost every theorem about prime numbers has to consider 2 as a special case.
- 8bitsrule 3y agoExcept that it's interesting that prime numbers have led inordinate numbers of individuals to devote uncountable but significants chunks of their lives investigating them. It's not their fault that they're leftovers when an artificial grid is created by crossing-out every multiple of 2, 3, 5, or other prime numbers. Yet for some reason this seems to give them a fascinating aura for many. Maybe naming them 'prime' instead of 'leftover' is to blame.
- joe_the_user 3y agoMuch as I appreciate the reference, I think the fact this limit exists at all and is an integer is more interesting than what the integer is. A lot of paradoxes and confused ideas begin with "choose an integer at random" - what is the average value of number chosen between 0 and infinity, for example.
- addaon 3y ago> and is an integer How could a median prime factor not be an integer?
- nextaccountic 3y agoThe median value of [1, 2, 3, 4] is 2.5
- addaon 3y agoSure, but 2 is the only even prime, so this is super constrained.
- andrewflnr 3y agoThat's the mean.
- CrazyStat 3y agoBut the median of [1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 4] is 2. As the individuals observed values collect more and more repetitions—as they do when making a list of the second prime factor, for example—it becomes increasingly unlikely that the median will be between two values, not equal to one of the values. It would be surprising if the median second prime factor was not a prime.
- layer8 3y ago> is there an integer which qualifies to be the most interesting? I’d say that 664571016291591957042161991109590159107314773607 and 590488317782859198927092718316232684864014739572 qualify, which are the big- and little-endian versions of ASCII “the most interesting”, respectively.
- aquafox 3y agoHistorically, I'd say 60, because relative to it's size, it has many divisors (12), and among them a lot of useful ones (2, 3, 4, 5, 10), which is why our time system and trigonometry are probably based on it (360 = 6*60; 360 has 24 divisors).
- deleted 3y ago[deleted]
- hurryer 3y ago17 is well known as the most random number between 1 and 20.
- User3456335 3y agoOne other special property prime numbers can have is being irregular. And guess what the first irregular prime number is? 37. Interesting that it appears so late because irregular prime numbers do make up around 41% of all primes. See: https://encyclopediaofmath.org/wiki/Irregular_prime_number#:~:text=An%20odd%20prime%20number%20p,prime%20numbers%20are%20called%20regular https://encyclopediaofmath.org/wiki/Irregular_prime_number#:.... So the most interesting prime number really depends on what you consider more interesting. If you prefer the median second prime factor, then 37 is the best, but if you prefer the first irregular prime number then 37 is also the best. So it all depends on your perspective. Another reason to like 37 is that it ends in a 7 so that it "sounds random" when someone asks for a number and it is better than 27 because it is prime. 7 is too low and 17 has connotations with bad luck. Although 37 is quite scary too: it's not just prime, which is pretty irregular, but it's also an irregular prime.
- DevX101 3y agoI nominate 60. Babylonian mathematics was sexagesimal (base 60) which is a superior mathematical system to base 10. The number 60, a superior highly composite number, has twelve factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, of which 2, 3, and 5 are prime numbers. With so many factors, many common mathematical operations are much simpler than in base 10. Base 10 has no special mathematical properties apart from as an accident of evolution, we primates ended up with 10 fingers. We still have some vestiges of the babylonian system however, 60 minutes in an hour. 360 (6 sixties) degrees in a circle.
- mikewarot 3y agoSince small prime factor are so useful, why not use 2 3 times and 3 2 times along with 5 2*2*2 * 3*3 * 5 = 360 360 is a very handy number, it has a high degree of usefulness, when you're circumferential in your calculations.
- emmelaich 3y agoYou're perilously close to being a eikositriophile. We try not to talk about such things openly fnord. https://en.wikipedia.org/wiki/23_enigma https://en.wikipedia.org/wiki/23_enigma
- gowld 3y agoHow is that related?
- emmelaich 3y agoI was being mostly frivolous but there's a larger point. 23 is used in also sorts of numerological explanations and connections. And of course, there is no actual connection 99% of the time. The "explanations" get very inventive by also considering 2 and 3 invidually, 2+3, etc. Doesn't take long to get something to pull the gullible in.
- jkhdigital 3y ago
- jvalencia 3y agoI love the number 27 3^3 2+7 = 3+3+3
- joseluis 3y agoVery pretty. And to relate it somewhat to the topic: 1/27 = 0.037 repeating 037 and 1/37 = 0.027 repeating 027 :)
- layer8 3y ago37 is also the smallest base (or second int argument) not supported by itoa(). Surely not a coincidence. ;)
- rbonvall 3y agoIt's because the characters in the result can be one of 10 digits or one of 26 letters.
- mort96 3y agoThe most interesting integer out there must certainly be the least interesting integer!
- deleted 3y ago[deleted]
- joewferrara 3y agoEvery prime is odd and 2 is the oddest of them all!
- klyrs 3y agoTwo is the oddest prime.
- doubloon 3y agowhat is interesting to me is that we call imaginary integer numbers "Gaussian Integers", but we call the quaternion integer numbers "Hurwitz Quaternions" instead of "Hurwitz Integers".
- bandrami 3y agoI love that there could never be a least interesting natural number, because that fact would be interesting. In fact there can be no uninteresting natural numbers, because then you could list them, and the lowest one would be interesting for that fact.