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.

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## Comments

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TopNewestWell, 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.

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\(122_{10}+3_{10} = 11122_3\)

122 is a number \(n\) where the trailing digits of \((n_{10}+b_{10})\) in base \(b\) is \(n\) itself.

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Yet another interesting property of 122:

122 squared = 14884, while 221 square = 48841

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

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298

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

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

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

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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.

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I guess that it's all in the eye of the beholder. I like the look of \(178\) since \(1 + 7 = 8.\) \(226\) is pretty plain, but at least it looks like it did a mirror-check before heading out the door. \(298\) looks like it forgot to shave and decided to wear a checked shirt with a striped tie, (which might actually be hipster fashion, making it that much more distasteful). And as for all the shade being thrown at \(284,\) at least it doesn't look boring, (as you've noted), and its amicability seems to me like a significant feature.

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. :)

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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".

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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.

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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.

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@Calvin Lin Looks like we're done here. :)

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Check this out. :)

Brian Charlesworth Michael MendrinLog in to reply

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10 is the most boring number up to 300. Multiplication/Division by 10 is easier than any other number(except 0 & 1).

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I have considered 49, for many non-mathematical people kind of forget that it's a prime number.

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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.

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Hahaha That's exactly what that number reminds me of too, and I sure can't remember the course I took in that classroom, either. :)

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).

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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.

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178 does have this interesting property "with 196"

178 squared = 31684 196 squared = 38416

178 cubed = 5639752 196 cubed = 7529536

So, 178 should be "de-nominated"

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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 \(56.\))

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249

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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 \(\underline{249}\).

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I propose that 249 be de-nominated.

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That is part of the point :)

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37

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Comment deleted Jul 31, 2015

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

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284

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\(284\) is a component of the smallest amicable pair.

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