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Comment by ysofunny | Hacker News Reader

I memorized all primes up to 127. and with a bit of effort I may come up with all the primes up to 307 (then 311,313, iirc) but I need pen and paper to double check.

the problem is that I don't know why do this.

nonetheless I can report that I've memorized 3 instances of two consecutive twin primes

11,13,17,19, then 101,103,107,109 (which just raises questions that I can only aspire to ask, nevermined answering, about the what, why, and how of decimal system),

and then 191,193,197,199. the next prime is 211. but the cool thing is how 210 = 2*3*5*7, which are all primes before the first double twin prime

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I know exactly why I do this. I use to deliver pizza. My store was on the edge of a medium-sized city, and a lot of our customers were quite the drive away. I'd get incredibly bored on these long drives. Somewhere along the way, I'd start calculating what percent of my shift I'd worked that minute, and I'd try to get it to 3 decimal places before the next minute came. Again, no reason whatsoever, just bored. And then at some point I thought it'd be more interesting to calculate (number of minutes worked) / (number of minutes remaining), which is fun because the ratio grows really slowly at first and then very quickly. I realized the first step in that was dividing out the common factors, so 248 minutes / 232 minutes was 31 / 29. (Yes, I'd been taught that in class, but it's one thing to have a teacher make you do something and another to realize why you'd ever want to do it voluntarily.)

Do that long enough and you find patterns, like 7 * 11 * 13 = 1001. If you ever end up calculating n / 11, it's approximately the same as n * 7 * 13 / 1000. E.g., 3 / 11 ~= .273. Or take 27 * 37 = 999. Now n / 37 ~= n * 27 and shuffle the decimals. 7 / 37 ~= 7 * 27 / 1000.

And that's how I ended up reasonably good at mental arithmetic, and memorizing a frankly unnecessary number of squares, and being able to factor lots of numbers at a glance (or recognize that they're prime). I was awfully bored for an awfully long time.

Boredom can be great.

Imagine being an ancient Babylonian or Greek with nothing to do but wait for your grapes to grow. No wonder they came up with lots of great stuff.

> Boredom can be great.

I agree, and I worry that the absence of boredom-time, especially for kids and adolescents, will turn out to be a bad thing.

I've never met a kid or adolescent who shares this concern. :)

191, 193, 197, 199 are also twin twin prime pairs

These primes have to be 11,13,17,19 + 30k, due to division by 3.

5 is half of 10, so we easily rule out exactly the number 10x+5.

49 = 7²,

77 is a multiple of 7, of course.

98 = 2 • 7²

In order to avoid a multiple of 11 interfering, we need the gap preceding 11•10

99 is (10+1)(10-1) = 10²-1 and 100 is 10²

, so that clears out space for primes after 100.

Also, You might enjoy "Paterson Primes" https://m.youtube.com/watch?v=jhObLT1Lrfo

I'm intersted in why (and how) you reason that thing about "multiple 11s interferring"

so I'll tell you how I memorized the primes between 2 and 127.

to begin: all primes less than ten: 2,3,5,7. I seem to have learned these by rote memorization. but then, the 'fun coincidences' begin.

because 5 is a multiple of "ten", all primes after 10 can only end in 1,3,7,9. this is a key somehow.

this gives the first fun coincidence: that 11 and 101 are both prime.

after 19 comes 23. similarly (and this is the part where every self-respecting numberphiliac waves their hands a little, in excitement I hope), 113 ("one one three") is the next prime after "one oh nine".

notice that 23,29,31,37 are as much prime as 30+{23,29,31,37} = 53,59,61,67

this covers almost all of them. but we're missing primes in the 40s, and the 70s. as well as primes in the 80s and 90s (only 3 primes: 83, 89, and 97. I have no tricks to remember these 3. only rote repetition)

the forties and seventies, are a very compact: both 1,3. but only 47, and only 79; because, well, what fun! seven squared and seven eleven are just so simple, like low-hanging fruit in the garden of prime-number coincidences

I confess that none of those patterns resonate with me at all. I’m not sure if I can even see that patterns in them that you see.

Conversely, to me, 9733 “looks prime”. I couldn’t explain that if I had to. It just does.

I like that there’s enough prime real estate for us all to see it differently.

I've realized that the way I explained the "patterns" is very different from what I was doing when I noticed them. which makes sense as I was not trying to explain that little "game". it's not a game it's just counting and writing primes in some base, and a dash instead for every composite. as the gaps get bigger I draw a triangle instead of 3 dashes; and then any glyph with as many strokes as dashes.

doing it in different bases helps to think about the numbers without their decimal representation. which I guess is the point, and might be helping me imagine patterns that may or may not be there. if I learned anything from doing this is that there is no pattern, it just seems as if there is one but it's never really there.

I like to think that the "patterns" expire, they have only so many uses in them. often just one use which breaks the point of being a 'pattern', but that's primes; is all am saying.

reading this just reminded me how i miss talking to my friends with scientific background

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