ps. Further down that twitter stream, there is a math problem presented by the UK mathematics trust. The problem is to find the smallest prime which divides (300^300)-1. Using the ideas in my post above we can see that (300^300)-1 is a very large number:
136891479058588375991326027382088315966463695625337436471480190078368997177499076593800206155688941388250484440597994042813512732765695774566000999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 For those that have learned the 3's trick, we can quickly verify that 3 does NOT divide this number because the sum of the digits here gives 6092 which is NOT divisible by 3. This is an example of considering the large number above to be a list of numbers. Next, applying the Pollard Rho method, I quickly found that 7 DOES divide this number. To verify, I use a method similar to the 3's trick (well really the same) and pop the last 9 off the list, multiply it by 2 and then subtract it from the remaining list. This gives another really large number, but iterating through the list eventually gives a much smaller number that can easily be verified to be divisible by 7. Therefore the whole number is divisible by 7. Now part of the beauty of the *div/mod* characterization I mentioned earlier is that we can then arithmetically define Kronecker deltas for numbers by defining functions that act on numbers as lists, which I do here <https://github.com/jonzingale/Haskell/blob/master/HaskellStudy/Lists/Listable.hs> . Techniques like this appear almost everywhere and deltas are a similar such thing. Consider the Dirac Delta in particular. There we have a generalized function that is tremendously useful for selecting values out of a time-series and yet really isn't a function at all. Jon
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