Brown Numbers - Numberphile

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There are only three pairs of Brown Numbers - and only five of the numbers themselves (because 5 is repeated)... At least we think that's all of them? No-one has proven it. This is called Brocard's Problem and has been entertained by great mathematicians such as Paul Erdos.

The Brown Numbers are (5,4) (11,5) and (71,7).

NUMBERPHILE

Videos by Brady Haran

[numberphile]

That's constructive & fair feedback.

My view is that our videos should leave some questions unanswered so people find out stuff themselves and have discussions here in the comments section.

I also think the videos should not have a formula... Should not answer the same questions each time.... Sometimes deal with nomenclature, sometimes don't... Sometimes do hard-core maths, sometimes skim the surface...

I don't want each one to feel like a Wikipedia entry... Rather an unexpected snapshot!

[TheElectra]

....And we weren't told why they are called "brown".

[drokles]

I really have come to love the way Brady asks these guys questions. He asks every question I want to ask before I know I want to!

[drepicpwn]

4 minutes and 5 seconds long... well played Brady, well played.

[Anonymous]

I noticed this: 5! and above, everything is the multiplication of 10, because 2 x 5 = 10. This means x! + 1 with x > 5 have "1" in the end. The only numbers that are squared and have 1 in the end must end with either 1 or 9, this narrows the possibility. Then, 10! and above, are the multiplication of 100. x! + 1 with x greater than 10 ends have "01" in the end. Well... what number squared has "01" in the end?

[SilverLining]

I love these guys! The way they find (well, present really) different special properties and relations between numbers is like my own math fun facts.To anyone that says math is boring or not fun, when you get into it, you will find certain surprises hitting you in the back of your head! It makes a really good hobby

[Anonymous]

Hey, a pair of *integer*, right? I don't see the word *"positive"* here. I have 3 more then.
1. (-5, 4) -> 4! + 1 = (-5)^2
2. (-11, 5) -> 5! + 1 = (-11)^2
3. (-71, 7) -> 7! + 1 = (-71)^2
Yay! I found 3 more brown numbers, didn't I?
1 of the reasons there're so few of them is because factorial numbers escalates very quickly and distance between 2 square numbers are getting wider the bigger the number (1 + 3 + 5 + 7 + ...).

[geocarey]

I have a conjecture. There is only 1 pair of Carey numbers. Carey numbers are pairs of numbers n, m such that n!+9=m^2

[FreethinkingSecularist]

I have seen this a handful of times already, and feel bad that I have only now finally gave it my thumbs up. Many times I am so excited to get onto another video I leave the current one using the side bar of options without giving my critique. Love you guys!

[ASilentS]

All values of n up to 10^9 have been tried, so I would suggest starting above that.

[numberphile]

What is the Mona Lisa used for? :)

But if one must justify everything in terms of what it is "used for"?

Say an eventual proof of this conjecture requires a conceptual leap which results in a new way to improve the performance of iPhones which results in a phone call between two doctors who discuss an innovative way to treat cancer which results in your uncle's sister's best-friend living 15 years longer than she otherwise would.

[johndoecro]

This might be one of the best and most interesting episodes of numberphile...

[ericsbuds]

Such nice handwriting, Mr. Copeland. I'm impressed!

[andregon]

Never heard of brown numbers.
I only heard of brown notes.

[bobsmith-ovkn]

I just wrote a simple ksh script and the limit it seems to be able to check up to is only n=30, that's where the factorial goes from 29 to 32 digits and so it starts to lose some of the digits and will give you false answers at n=30, 31 and 32

[mokopa]

Brady, if you keep on intriguing us with these "lesser" unsolved problems...well, just imagine: Numberphile, the first YouTube Channel to be nominated for an Ig Nobel Prize!

[neelesh]

Its a great video, watching it for the second time made me think, that if we can use integers, then why not use negative integers..
For example 2, -3.this satisfies it..

[davidcampos]

Why are they called "Brown"?

[binaryflawgic]

4:04 the duration of the video... Hmm... Like, no more video found... Like the brown numbers

[BritishBeachcomber]

The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth - by Paul Hoffman is a must-read for anyone who loves math.