If you have been following Every integer is interesting and Part 2, you will see that we have come up with reasons for why the first 300 integers are interesting in their own way. Sometimes, the properties are not great, but we overlook that in the spirit of going further.

We have now taken a breather, so that people can nominate what is the most boring integer. This is how the process will work:

- Comment with what you think is the most boring number (that someone has not stated). Include the "interesting property" that was stated.
- If you agree with someone else, vote up on their comment.
- If you disagree that a number is boring, reply with an interesting factoid about it.

## Comments

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TopNewest298

– Brian Charlesworth · 1 year, 8 months agoLog in to reply

– Shobhit Singh · 1 year, 6 months ago

It is the only number for which if you search on wikipedia it redirects you to another number(i.e.290)Log in to reply

– Brian Charlesworth · 1 year, 6 months ago

Actually, this is the case for many numbers, including all numbers from 291 to 299.Log in to reply

– Shobhit Singh · 1 year, 6 months ago

I don't think so bcoz Year 298 (CCXCVIII) was a common year starting on Saturday of the Julian calendar.Log in to reply

– Michael Mendrin · 1 year, 8 months ago

I agree that, except for the fact you see this number all the time as a price, this is a particularly unremarkable number mathematically. However, in making the final decision which is the most boring, I think looks should matter--i.e., the plainest, most forgettable number should be the winner. So, for example, I think 178 or even 226 looks even more plainer than 298. But that's just a personal opinion.Log in to reply

P.S.. If you have a moment, could you check out this question. I have issues with the posted answer and I'd appreciate your input. Thanks. :) – Brian Charlesworth · 1 year, 8 months ago

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[122], [178], 226, [249], [284], 298

[...] indicates de-nominated numbers, see comments elsewhere.

Now, which one is the hardest to "make interesting" math-properties-wise?

Of the six, only 226 is a "small order figurate number". That basically leaves 298, as the winner of the most boring number. Dollar Store number, how boring is that? It is exactly twice another Dollar Store number, 149.

I have not been able to find any interesting math properties of 298 as of yet298 BC--"Ptolemy gives his stepdaughterTheoxena in marriage to Agathocles of Syracuse"

What I do notice is, which is kind of what's to be expected, is that the number of hits goes down as the number goes up. That is, the bigger the [random] number, the fewer special properties it has. For example, Wikipedia lists fewer and fewer numbers with four or more digits as having any notable properties at all. So, by that measure, 298 should be the hardest to "make interesting".

– Michael Mendrin · 1 year, 8 months agoLog in to reply

– Brian Charlesworth · 1 year, 8 months ago

I agree with all the de-nominations, and as mentioned elsewhere, \(226\) does have a couple of mildly interesting factoids associated with it. The "Dollar Store Number" doesn't even have that dubious honour going for it up north of the border; prices tend to end in a \(9\) here. Feeling sorry for \(298,\) I gave it another chance but came up empty, just as you did. Unless someone can come up with something soon, I think we may have a winner.Log in to reply

Anyway, I propose we vote 298 as the winner of the Most Boring Number Less Than 300, unless someone else can discover some special mathematical talent 298 has. – Michael Mendrin · 1 year, 8 months ago

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– Nihar Mahajan · 1 year, 8 months ago

I can't find nice property about \(298\) but I managed to create this: \(298=1 \times 298 = (1+2)^2+(9+8)^2\).Log in to reply

Here's an excellent approximation for \( \pi\)

\(\left( 2.98 \right) \left( 1+\sqrt { 3 } \right) -5=3.1415...\)

This is how one can make pi out of dog food. – Michael Mendrin · 1 year, 8 months ago

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– Nihar Mahajan · 1 year, 8 months ago

I can't find as such. I think this must be extended to 400.Or we can just declare \(298\) as the winner.Log in to reply

– Shobhit Singh · 1 year, 6 months ago

https://www.easycalculation.com/number-properties-of-298.htmlLog in to reply

– Michael Mendrin · 1 year, 6 months ago

Thank you for pointing out that 298 is an "unhappy, sad, deficient number that is not anything else of any interest"!Log in to reply

– Brian Charlesworth · 1 year, 8 months ago

I'll second your proposal. If no objections are raised by 8 a.m. GMT then we can make it official.Log in to reply

– Michael Mendrin · 1 year, 8 months ago

By midnight here, PST, then.Log in to reply

@Calvin Lin Looks like we're done here. :) – Brian Charlesworth · 1 year, 7 months ago

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Check this out. :) – Nihar Mahajan · 1 year, 7 months ago

Brian Charlesworth Michael MendrinLog in to reply

– Michael Mendrin · 1 year, 8 months ago

I agree, Alex Li should explain his "correct answer" to that one. But I guess I'll have to discuss this only in the View Reports section, and not here.Log in to reply

– Brian Charlesworth · 1 year, 8 months ago

Great. Thanks for checking it out. Your report makes a pretty clear-cut case.Log in to reply

– Michael Mendrin · 1 year, 8 months ago

Okay, 248 de-nominated.Log in to reply

I have considered 49, for many non-mathematical people kind of forget that it's a prime number. – Timothy Wan · 1 year ago

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Next number I nominate is 226.

I think, visually for me, 226 is the most forgettable number there is less than 300. It looks like a classroom number at a school you'd rather forget about. – Michael Mendrin · 1 year, 8 months ago

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One curiosity about 226 is that the first three digits of \(\pi^{226}\) are \(226.\) This, along with the entry on record that 226 is the maximum number of permutation patterns that can occur within a 9-element permutation, should be enough to de-nominate 226, (at least in comparison to 298). – Brian Charlesworth · 1 year, 8 months ago

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Okay, I nominate 178. Except in connection with the number 196, it's hard to find anything interesting to be said about this one.

– Michael Mendrin · 1 year, 8 months agoLog in to reply

178 squared = 31684 196 squared = 38416

178 cubed = 5639752 196 cubed = 7529536

So, 178 should be "de-nominated" – Michael Mendrin · 1 year, 8 months ago

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– Brian Charlesworth · 1 year, 8 months ago

Agreed. For both the squares and the cubes to have this result is pretty cool. (4th powers are a no-go though, although both of them do end in the digits \(56.\))Log in to reply

Well, maybe we each can nominate more than one candidate. The first I will nominate myself would be 122, since I couldn't think of anything else except that Emperor Hadrian ordered that wall that today bears his name.

However, there are very few known examples of three relatively prime integers, of which different powers of two sum to yet another power of the third. Here is one.

\({ 3 }^{ 5 }+{ 11 }^{ 4 }={ 122 }^{ 2 }\)

so I withdraw 122 from nomination and look for another. – Michael Mendrin · 1 year, 8 months ago

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122 is a number \(n\) where the trailing digits of \((n_{10}+b_{10})\) in base \(b\) is \(n\) itself. – Garrett Clarke · 1 year, 8 months ago

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122 squared = 14884, while 221 square = 48841 – Michael Mendrin · 1 year, 8 months ago

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– Calvin Lin Staff · 1 year, 8 months ago

You can certainly nominate more than one candidate. Just make sure to start them off in a new comment.Log in to reply

249

– Garrett Clarke · 1 year, 8 months agoLog in to reply

– Garrett Clarke · 1 year, 8 months ago

The amazing about this note is that you can always find something interesting if you just look hard enough. 249 is the smallest 3-digit number such that \(249^{2n} = 1 \pmod{10^3}\). This means that 249 raised to any positive integer will either end in \(\underline{001}\) or \(\underline{249}\).Log in to reply

– Michael Mendrin · 1 year, 8 months ago

I propose that 249 be de-nominated.Log in to reply

– Calvin Lin Staff · 1 year, 8 months ago

That is part of the point :)Log in to reply

– Michael Mendrin · 1 year, 8 months ago

Any of us is free to find the most interesting things about any "boring" number that's been nominated, i.e., we're free to try shooting down the status of such numbers being boring. Then it's the last man...uh, number standing that wins--the one nobody can come up with anything truly special.Log in to reply

37 – Sachin Sharma · 2 months, 3 weeks ago

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– Calvin Lin Staff · 1 year, 8 months ago

284 has been nominated by Alex Li, so I'm deleting this comment.Log in to reply

284

– Alex Li · 1 year, 8 months agoLog in to reply

amicable pair. – Brian Charlesworth · 1 year, 8 months ago

\(284\) is a component of the smallestLog in to reply