Comments by "Mikko Rantalainen" (@MikkoRantalainen) on "Numberphile" channel.

  1. It seems that Don thought that he had made a mistake but it turns out the only mistake was believing that there was a mistake :D
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  2.  @TheElCogno  For numbers in ballpark of 60000 factorizing p-1 is definitely doable with pen and paper. As MrElk wrote, the number is always divisible by 2 so you have a single number about the size of 30000 which in worst case is a product of two primes. As square root of 30000 is less than 200 the smaller of those prime numbers must be less than 200. And since you can rule out all even numbers, you have less than 100 numbers to test even if you didn't know any real shortcuts. And for most cases, like p = 60013 you get p-1 = 60012 which is clearly divisible by 2 and 3 (6+1+2 is divisible by 3) so you can immediately do 60012/6 = 10002 which is obviously divisible by 2. So you compute 10002/2 = 5001. But did Shanks know that since 5001 is divisor of 60012, then 10^5001 = 1 mod 60013?
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  3. That's true, if you already have proof for "All reciprocals are periodic". What Matt did here doesn't require that previous knowledge and this video could be extended to give proof for that, too.
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  4. It's also interesting how remakes nearly always show regression to the mean. You would think that remake that just fixes mistakes in the original movie or book should be better than the original. Similar to how newer version of a given software is slightly better than the previous version. However, in real world, the financing party wants to play it safe and prefers regression to the mean even if the end product actually ends up worse that way. With regression to the mean you get average books and movies. I think if you made remakes with first figuring out what makes this book or movie different from your average book or movie and only make that difference greater you should end up with a better product. Obviously you should also fix obvious mistakes such as poor lighting, continuity problems, errors in story logic etc.
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  5. I think the explicit lookup table also helps you understand how to do it with very big numbers.
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  6. I've learned to riffle the cards and then raise roughly third of the deck from the middle to top after each riffle (which is pretty simple to do simply by pinching from the sides of the deck and pulling the middle part away) before halving the deck again for the next riffle. I think that it improves the changes that the top and the bottom of the deck get mixed during the suffle, but I have no mathematical explanation if it really matters.
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  7. I think the description should say that this is a math magic trick – can you notice the trick?
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  8. It seems that there's really lot of work to correctly select the secret santa just to get one crappy present. I'd suggest getting a present for yourself instead. Or maybe you have a friend or significant other that can get you a non-crappy present?
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