December 2014 Bragging Thread

Morendil

Your job, should you choose to accept it, is to comment on this thread explaining the most awesome thing you've done this month. You may be as blatantly proud of yourself as you feel. You may unabashedly consider yourself the coolest freaking person ever because of that awesome thing you're dying to tell everyone about. This is the place to do just that.

Remember, however, that this isn't any kind of progress thread. Nor is it any kind of proposal thread. This thread is solely for people to talk about the awesome things they have done. Not "will do". Not "are working on". Have already done. This is to cultivate an environment of object level productivity rather than meta-productivity methods.

So, what's the coolest thing you've done this month?

Note that the memorability of the last few digits is a direct consequence of the way you constructed the number (yes, it's 12345^5). The last 4 digits of n^5 when n ends in 5 are always among {0625,1875,3125,4375,6875,8125,9375}. If the digit before the 5 is even you always get one of {0625,3125,5625,8125}. At the very least, the final 3 digits are always a multiple of 125 and you probably recognize all of those.

Still, even a completely random number typically has lots of little patterns in it to help this kind of memorizing. For instance, I just generated a random 20-digit number: 66474746605022249923. The first things that occur to me, looking through it in order:

66 4747 -- two pairs of repetitions
466 -- overlapping 46 (one less than the 47 we just had) and 66 (same as first two digits, and a pair)
050 -- symmetrical, all multiples of 5 (of which there aren't many among the digits :-))
222 --- threefold repetition
499 -- one less than 500
23 -- not a particularly interesting number but e.g. the number of chromosome pairs you have.

(I also noticed in passing that 60502 is reminiscent of 6502, the processor in the first few computers I used. Lovely instruction set. Having some overlap between the features one notices is useful because it makes it easier to remember what order things come in.)

I tried the obvious experiment: after writing the above, could I look away from it and reproduce my 20-digit number? Why yes, I could; and still could a couple of minutes later. I think I'd find things like reversing the digits quite painful, though.

Yes. Using x^y as a random number is bound to show patterns of this kind. I know enough number theory to recognize this. But it does alter the result only very slightly.

And yes. Your 'story' has the same basic structure as mine. I would have told it somewhat different but I think you got my approach. Note that it doesn't scale though. The major system beats it in that. But for small sequences of passwords it works nicely.