Why isn’t the fundamental theorem of arithmetic obvious? (2011)

Re:Why isn’t the fundamental theorem of arithmetic obvious? ... by rahimnathwani on Wednesday June 22, 2016 @08:29AM (#11953328)

Although it was ~30 years ago, I recall doing some school homework when we had just learned about prime numbers and factorisation. I remember trying to divide by random primes until I came across a factorisation. It wasn't at all obvious to me (at ~10 years old) that prime factorisations were unique or that they could be found using a simple repetitive algorithm.

It seems obvious now, but only because I've never come across an integer with more than one factorisation. If there were an article on HN tomorrow with the headline 'Integer with more than one prime factorisation found' I wouldn't be able to resist clicking the link.

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Re:Why isn’t the fundamental theorem of arithmetic obvious? ... by AimHere on Wednesday June 22, 2016 @09:16AM (#11953616)

> If there were an article on HN tomorrow with the headline 'Integer with more than one prime factorisation found' I wouldn't be able to resist clicking the link.

Curiously, I've only just found out that

  48016416432886585186892071037001629018831524915070361  
  17449649760043615376581136847123881454516238486352419  
  62687300988949648670959062041377941995335910356581948  
  79838588416610716340382432762472099541373300228025778  
  94213135434471675634979394732216151334015571089605667  
  2861

has two distinct prime factorizations, thus providing a counterexample to Euclid's Fundamental Theorem of Arithmetic and showing that he made a mistake somewhere.

Unfortunately the truly marvellous lists of factors are too small to fit in a Hacker News comment, so you'll have to rediscover the details yourself.

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Re:Why isn’t the fundamental theorem of arithmetic obvious? ... by ColinWright on Wednesday June 22, 2016 @09:37AM (#11953768)

Please edit this to restore the formatting to something usable.

Edit: Thank you.

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Re:Why isn’t the fundamental theorem of arithmetic obvious? ... by CarolineW on Wednesday June 22, 2016 @10:07AM (#11953999)

I would rather trust the proof of the Fundamental Theorem of Arithmetic than trust the bald and unsupported assertion by someone I don't know and haven't heard of.

Sorry. :-(

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Re:Why isn’t the fundamental theorem of arithmetic obvious? ... by AimHere on Wednesday June 22, 2016 @10:14AM (#11954078)

Oh, that's fine.

I don't want anyone to trust me, I just wanted to get the OP to go to the trouble of checking up on me, since he or she is willing to go at least partways in that direction :)

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Re:Why isn’t the fundamental theorem of arithmetic obvious? ... by clux on Wednesday June 22, 2016 @12:20PM (#11955041)

Damn that Fermat margin.

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Re:Why isn’t the fundamental theorem of arithmetic obvious? ... by vinchuco on Wednesday June 22, 2016 @09:28AM (#11953698)

Your comment has destroyed the browsing experience on mobile :)

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Re:Why isn’t the fundamental theorem of arithmetic obvious? ... by AimHere on Wednesday June 22, 2016 @09:34AM (#11953741)

Hah. Apologies for that! I thought the downvotes were because it was a lame joke, not that I was destroying the site!

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Re:Why isn’t the fundamental theorem of arithmetic obvious? ... by umanwizard on Wednesday June 22, 2016 @10:48AM (#11954335)

FWIW, I downvoted you because it's a lame joke.

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Re:Why isn’t the fundamental theorem of arithmetic obvious? ... by wlesieutre on Wednesday June 22, 2016 @09:39AM (#11953778)

Also on desktop. Can we get some max-width and overflow:scroll in here?

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