What’s so special about the Sieve of Eratothenes that it even gets a name? I can’t imagine that the first time someone has the concept of a prime number explained to them, that this sorting method isn’t basically the next thing that pops into their head. It seems so obvious; how could Eratosthenes’ve been the first guy to come up with it?
(On a side note, I propose a “Filter of Grady” as a way of figuring out which numbers are even: If they end in 0, 2, 4, 6, or 8, they’re even. There, I did it.)
The guy spent his time fucking with random math concepts at a time where most people would be making an honest living pressing olive oil, breeding sheep or forging spears. He finds a maybe tangentially useful thing for once in his gods’ forsaken life, you bet your ass everyone’s going to hear about it.
We don’t know for sure that he was. And mathematics is full of things that are named after someone other than the first guy to come up with them. (Here’s a PDF with some examples.)
And yeah, it’s pretty obvious, but not totally obvious: primes are defined in terms of factors or divisibility, and yet you’re finding them just by counting.
Okay, all these responses make sense. Maybe I should refine my question. It’s not so much that I’m wondering why it’s named after Eratothenes, but why it’s named at all. It seems like it’s just a restatement of what the definition (or, a definition) of what a prime number is: a number not evenly divisible by any smaller positive number except 1.
Well, yeah, but you need some sort of system for looking. That’s all the Sieve is - a systematic way of looking at numbers to see which ones are prime.
That’s not an algorithm. How do you tell “by looking”? How do you tell just by looking whether or not 491 is prime—let alone which ones, of all the numbers up to, say, 500, are prime?
I mean, using the Sieve seems like not so much a method as a concrete demonstration that one understands the concept of a prime number. If we define cats as small carnivorous mammals with retractable claws, and then are presented with a few cats mixed in with a bunch of alligators, used tires, rocks, and puddles of water, are we really using a method, an algorithm, when we go out into this conglomeration pointing, saying “cat, not a cat, not a cat, cat, not a cat, cat, cat, not a cat, not a cat”?
Circle 2, then cross out every 2nd number after 2.
Then look at the first non-crossed-out number, which is 3, and circle it, and then go through and cross out every 3rd number after that.
Then look at the first non-crossed-out number, which is 5, and circle it, and then go through and cross out every 5th number after that.
And so on: continue this process until all numbers on your list are either circled or crossed out. At no point do you have to look at a number and decide, just by looking at it, whether it’s a [del]cat[/del] prime.
What if you’re presented with a cat, mouse, dog, weasel, ferret, civet cat, otter, coati, meerkat, and red panda?
What may be obvious when you’re dealing with 1 and 2 digit numbers is not so apparent when dealing with 5 and 6 digits. You need a method that you or anyone else can follow and end up with the same results.
I’m pretty sure I get how the Sieve works, apparently I’m not up on exactly what constitutes an algorithm.
The cat/not a cat example was my attempt to eludicate how I thought one might go about applying a definition (maybe ‘applying a definition’, if that phrase makes any sense, simply means ‘using an algorithm’). Of course, when looking at the objects my mind quickly runs a little test: “Retractable claws? Yes. Mammal? Yes. Then, cat”, and I guess that constitutes an algorithm, just a much simpler one than the Sieve.
So since it’s probably the case that Eratosthenes didn’t discover this particular method for finding primes yet it’s named after him, and since the person who actually discovered the method for finding evens (“If ending in 0, 2, 4, 6, or 8, then even”) didn’t get to attach their name to it, I’m claiming “Grady’s Filter” for that particular test and its corollary (“If ending in 1, 3, 5, 7, or 9, then not even”).
There are a lot of folks in this thread missing the point, which is I think evidence of just how useful the Sieve is. The point of the Sieve of Eratosthenes isn’t to determine whether any particular number is prime; it’s to find all the primes, up to some number. If one were to do that by going through them one by one, asking “Is 2 prime? Is 3 prime? Is 4 prime? Is 5 prime?”, and so on, one would find oneself duplicating a lot of effort. By doing them all at once, you can get economies of scale. And it may be inefficient in some sense, but for the task it’s designed for, it’s still the best we’ve got.
It wasn’t once in his gods’ forsaken life. His greater accomplishment was his measurement of the size of the Earth.
I’m not sure he meant “by looking” in the sense of “just looking at it” but rather by, well, scanning to see if there are any integral divisors between 1 and, well, I guess the square root of the number. In this case, we hit the first divisor at 149, so we don’t have to go too far down.
ETA: And a numerical anagram of the 491 asked about, coincidentally.
And if he is using the Sieve of Eratosthenes to determine if 54,898,390,234,005,943,587,727,239,987,774,321,490,934,981 is prime then when he (eventually) has determined its primality he has also determined the primality of all numbers less than it. As Chronos said, the point of the Sieve is to generate all primes up to a given number.
I’m sure the sheep herders were thrilled and had a big parade about it, too
But come on, joke aside, read the first line of his Wiki entry, which goes :
and tell me that doesn’t sound like the kind of guy who, should you meet him at a party, is going to bore your ass off then hit you up for money for his next big Project. Or possibly became famous through his MySpace page.
