4 ms·

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 exac

by lupire 2y ago

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 https://m.youtube.com/watch?v=jhObLT1Lrfo

deleted 2y ago
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ysofunny 2y ago
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
- kstrauser 2y ago
  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.
  - ysofunny 2y ago
    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.

by lupire 2y ago

deleted 2y ago

[deleted]

ysofunny 2y ago

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

kstrauser 2y ago
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.
- ysofunny 2y ago
  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.