# Number encyclopedia

March 16, 2023 8:49 PM Subscribe

*What's MetaNumbers.com ? MetaNumbers is a free math tool providing information about any positive integer (up to 9223372036854775807), such as its factorized form, its divisors, its classification, or its arithmetic properties (widely used in the field of number theory).*Example metanumbers entry: 198606

Doesn’t seem to recognize the most important property of 42. The internet is maturing.

posted by traveler_ at 9:04 PM on March 16 [4 favorites]

posted by traveler_ at 9:04 PM on March 16 [4 favorites]

Interesting resource. I wish each of the terms had a direct link to its definition, since I want to know what a polite number is.

posted by clawsoon at 9:11 PM on March 16 [1 favorite]

posted by clawsoon at 9:11 PM on March 16 [1 favorite]

Wikipedia on polite numbers doesn't say why they're called polite, just defines 'em.

posted by aniola at 9:15 PM on March 16

posted by aniola at 9:15 PM on March 16

Interesting that the significant numbers list doesn’t include 137, which is a Pythagorean prime (no great distinction there; about half of all primes are), and the reciprocal of which is the mysterious and elusive inamorata of generations of physicists.

posted by jamjam at 10:32 PM on March 16 [2 favorites]

posted by jamjam at 10:32 PM on March 16 [2 favorites]

Once you get a property name, you could search for it within the Online Encyclopedia of Integer Sequences: polite numbers (still doesn't explain the name tho).

(Practically all numbers are 'polite' = can be written as the sum of a sequence of positive integers; only logarithmically many aren't. Which ones aren't, and why that is, is a fun question.)

posted by away for regrooving at 10:48 PM on March 16

(Practically all numbers are 'polite' = can be written as the sum of a sequence of positive integers; only logarithmically many aren't. Which ones aren't, and why that is, is a fun question.)

posted by away for regrooving at 10:48 PM on March 16

As long as we're quibbling about it (...and it IS a cool resource, thanks!), it doesn't seem to mention the important feature of "1729", the Ramanujan-Hardy humber.

posted by AsYouKnow Bob at 11:05 PM on March 16 [4 favorites]

posted by AsYouKnow Bob at 11:05 PM on March 16 [4 favorites]

*There are 44 positive integers (less than 69) that are coprime with 69. And there are approximately 19 prime numbers less than or equal to 69.*

Nice.

posted by lock robster at 11:10 PM on March 16 [1 favorite]

*Wikipedia on polite numbers doesn't say why they're called polite*

To be fair, being explicit about that kind of thing is quite rude.

posted by flabdablet at 11:49 PM on March 16 [2 favorites]

*23,588 (twenty-three thousand five hundred eighty-eight) is an even five-digits composite number following 23587 and preceding 23589.*

Damn, now that’s insightful!

(23588 is my user number.)

posted by slogger at 3:49 AM on March 17

A cool recent finding is that all positive integers can be expressed as the sum of 3 palindromes. The 3 addends could be an additional characteristic in this listing (I didn't see it there.)

posted by JimDe at 3:56 AM on March 17 [1 favorite]

posted by JimDe at 3:56 AM on March 17 [1 favorite]

This would make for a great (albeit unweildy) series of baseball cards. ("Hey, check it out! A rookie 233467854!")

posted by PlusDistance at 4:14 AM on March 17 [1 favorite]

posted by PlusDistance at 4:14 AM on March 17 [1 favorite]

So (math teacher here) I went down a rabbit hole trying to find out just

However my conjecture is: they are numbers that are made up of "neighboring" numbers (1+2+3+4, etc.), and that none of the numbers can be negative. So, positive and neighborly equals polite?

posted by Ishbadiddle at 5:24 AM on March 17 [3 favorites]

*why*they're called "polite." Could not find a thing! Even the "talk" page on the Wikipedia article just says "that's what they're called, so that's what we're calling them, so stop complaining that this is just a fancy way of saying numbers that are not a power of 2."However my conjecture is: they are numbers that are made up of "neighboring" numbers (1+2+3+4, etc.), and that none of the numbers can be negative. So, positive and neighborly equals polite?

posted by Ishbadiddle at 5:24 AM on March 17 [3 favorites]

That seems like a reasonable conjecture for why they're called polite numbers. The OEIS entry says that:

posted by madcaptenor at 6:44 AM on March 17 [2 favorites]

in K-12 education, these are known as "staircase numbers." The "1" is often omitted.That seems like a better name to me, because you can draw a nice picture of a staircase made up of, say, 18 = 3+4+5+6 squares:

X XX XXX XXXX XXXX XXXXI guess a more "official" name for these would be "differences of triangular numbers" but if you're about to solve a problem involving them, who wants to say that over and over again? Alternatively, we could just call them Euler numbers, I'm sure he looked at them at some point.

posted by madcaptenor at 6:44 AM on March 17 [2 favorites]

1,877,527,745,437 (one trillion eight hundred seventy-seven billion five hundred twenty-seven million seven hundred forty-five thousand four hundred thirty-seven) is an odd thirteen-digits composite number following 1877527745436 and preceding 1877527745438. In scientific notation, it is written as 1.877527745437 × 1012. The sum of its digits is 67. It has a total of 2 prime factors and 4 positive divisors. There are 1,877,277,033,216 positive integers (up to 1877527745437) that are relatively prime to 1877527745437.

well it misses a subtle reference...

posted by sammyo at 6:45 AM on March 17

well it misses a subtle reference...

posted by sammyo at 6:45 AM on March 17

I'm just happy I won't be jamming up my search history with "factors of

posted by ob1quixote at 7:10 AM on March 17

*n*" to find math pages obviously meant for kids to help me solve the Matheler.posted by ob1quixote at 7:10 AM on March 17

I'm glad I'm not the only one who got immediately distracted by the quest to find the naming history. I came up empty as well; I was hoping there'd be some little note on an OEIS entry, but as noted above, no dice. I did however come across an OEIS entry for Politest Numbers which is a delightful consolation prize.

posted by cortex at 7:40 AM on March 17

posted by cortex at 7:40 AM on March 17

I remembered I have JSTOR access through my library and so went digging some more and found: nothing, so far. There's interesting cases of discussions of the idea without the name to be found, like a short 1979 article in

It might be possible to at least antedate "polite numbers" to some point prior to which no one is using those terms to narrow down the time of origin. Might dig a bit more after breakfast.

posted by cortex at 8:05 AM on March 17 [2 favorites]

*Mathematics Magazine*by Melfried Olson titled "Sequentially So", which talks through some observations on sums of consecutive numbers but doesn't call them polite. He does refer, however, to "'nice' sums", hrm!It might be possible to at least antedate "polite numbers" to some point prior to which no one is using those terms to narrow down the time of origin. Might dig a bit more after breakfast.

posted by cortex at 8:05 AM on March 17 [2 favorites]

Oldest hit I can find searching JSTOR for "polite numbers": there's a reference in a 1991 article by Terry S. Griggs, "Impolite Numbers", (The Mathematical Gazette, Vol. 75, No. 474 (Dec., 1991), p. 442) saying that

posted by cortex at 8:31 AM on March 17

"...in an edition of the Open University newspaper, Sesame (no. 124,Which antedates the usage to at least 1988; I can't find on a quick search an archive of that edition of Sesame but I may not be searching all that well.

December 1988), there appeared the following problem. A positive integer is

said to be polite if..."

posted by cortex at 8:31 AM on March 17

I've thrown up a math signal on mastodon, we'll see if anybody over there has a good lead. And in pasting the link this thread I finally saw what you did here:

posted by cortex at 8:36 AM on March 17 [1 favorite]

*Example metanumbers entry: 198606*posted by cortex at 8:36 AM on March 17 [1 favorite]

I once proposed an O(1) algorithm for determining if a number is prime. Just search for it on Google! This works remarkably well, particularly for setting, say, the size of a hash table (which you want to be prime so chaining is easy.) This website only makes it easier!

posted by Nelson at 9:05 AM on March 17 [1 favorite]

posted by Nelson at 9:05 AM on March 17 [1 favorite]

*He does refer, however, to "'nice' sums", hrm!*

When I was a Serious Mathematician I'd definitely use "nice" or "good" to mean something has the property I was trying to prove something about but that I didn't want to bother to come up with a better name for.

posted by madcaptenor at 9:17 AM on March 17

*I did however come across an OEIS entry for Politest Numbers which is a delightful consolation prize.*

Okay, but if you can go from "polite numbers" to "politest numbers" by a simple transformation then you can go from "politest numbers" to "politestest numbers" by the same transformation. Which means the politest numbers aren't actually the politest numbers.

posted by madcaptenor at 9:19 AM on March 17 [2 favorites]

The Penguin Dictionary of Curious and Interesting Numbers is very good. Makes for great bathroom reading.

posted by neuron at 9:42 AM on March 17

posted by neuron at 9:42 AM on March 17

On another note, I now know that Jenny's Number is prime! (Not to be confused with Jenny's Constant, per Munroe (2012).)

posted by Ishbadiddle at 10:09 AM on March 17

posted by Ishbadiddle at 10:09 AM on March 17

Very cool, as noted above just needs an “In Popular Culture” section.

posted by yarrow at 12:16 PM on March 17 [1 favorite]

posted by yarrow at 12:16 PM on March 17 [1 favorite]

I wondered why 9,223,372,036,854,775,807 was the highest number tracked.

This is not mentioned specifically on its page, but it is 2

posted by Phssthpok at 3:28 PM on March 17

This is not mentioned specifically on its page, but it is 2

^{63}- 1posted by Phssthpok at 3:28 PM on March 17

*This is not mentioned specifically on its page, but it is 2*

^{63 - 1}So you're saying they could've made twice as many pages if they'd used an unsigned long instead of a signed long?

posted by clawsoon at 11:24 AM on March 18

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posted by aniola at 8:58 PM on March 16