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It was a bit difficult to grasp at first, but it clicked after realizing it's all primes up to 37, not just 37. Kind of a neat fact, and I enjoyed reading this.
by zelda-mazzy 3y ago
It was a bit difficult to grasp at first, but it clicked after realizing it's all primes up to 37, not just 37. Kind of a neat fact, and I enjoyed reading this. Thanks for posting!
- kstrauser 3y agoI don't think that's right. My reading of it was that 37 is the median prime among all primes.
- gattilorenz 3y agoI think you’re both expressing the same concept :) 37 is the median factor, it doesn’t mean that 37 is the actual second prime of 50% of numbers. The OP probably missed “median”, I know I did
- twelvechairs 3y agoOriginal comment said "all primes up to 37" which isn't correct there's no point where 37 is being used as an upper limit
- gattilorenz 3y agoI think that was an intuitive and imprecise way of expressing “median value”, so that 50% of primes are “up to 37”
- zelda-mazzy 3y agoIm going off what the article originally said: "We see that 37 is the prime where roughly half of all numbers have something less than or equal to 37 as their first prime! So we’ve proven that 37 is the median second prime!"
- NooneAtAll3 3y agodid the title change or smth?
- Dylan16807 3y ago> it's all primes up to 37 Can you elaborate on "it" in this sentence? What is "all primes up to 37", when you phrase things in an easier to understand way? I can't tell if you're suggesting the word median is being used in a misleading way? But it's basically the definition of "median 37" that half your numbers are "up to 37".
- zelda-mazzy 3y agoI admit I read it wrong at first, but it made sense to me at the end of the article. So I don't believe median was misleading. My initial thought was, as numbers get larger and larger, the chance that the second most common prime factor is 37 so 50%, which didn't make sense because of how common 3 and 5 are. By the end I realized the function is taking into account the range of prime factors as an aggregate. Now I understand that with enough composite numbers, the chance that their second prime factor is 37 OR BELOW converges to 50%, which is pretty neat.