I daresay that if such examples of “guided discovery” were a regular part of math education at the lower and middle grades, there probably wouldn’t be nearly as many people who hate math. It’s the sort of thing that will get you hooked on mathematics. Sure, it was already known, but replicating a significant scientific principle just by playing with small numbers is an immensely heady and joyful experience. For instance, a few years ago in our puzzle “ Are Genes Selfish or Cooperative?” I posed a simple arithmetic problem that led some readers to rediscover a fundamental law of genetics. Perhaps more surprisingly, playing with arithmetic can lead us to unexpected and profound discoveries that point toward deeper mathematics and sometimes even deeper science. You can also use simple arithmetic to confirm that a complex formula you derived does indeed work. Often this approach can reveal hidden insights. Me, personally, I'm satisfied with two and a half seconds.We solved our last Insights puzzle by performing some arithmetic on a simple version of a complex problem in order to discover its patterns.
Then I wrote a main() that notes the time before calling fillWithPrimes() with a quantity parameter of 1,000,000, and reports on the results:
Eventually I came up with this: static int fillWithPrimes(int quantity) while (coPrimeFlag & currPrime <= squareRoot) My first draft took even longer than yours. Maybe this is one of those cases where you should avoid the use of objects in favor of an array of primitives. Five, ten seconds, that I'd find acceptable. Still, a minute and a half, while it would have been considered miraculous by Mersenne, is too slow today. If you're building up a list, you might as well use it to check potential primes.īenchmarking Java's a little difficult because you're at the mercy of the runtime system. If n is not divisible by 7, it won't be divisible by 49 either. If number is divisible then skipping the number else adding it to the prime listĭoes "2 till the square root of the number" include numbers like 4, 6 and 9? The only potential factors that need to be checked are numbers that have already been proven prime. Trying to Divide the number starting from 2 till the square root of the number.On the other hand, this won't halve running time because odd numbers like 91 and and 2209 might require more effort to be ruled out as not prime. Your program should simply skip even numbers, because, aside from −2 and 2, they're all composite. Checking if the digit is 0, 2 or 4 or 6 or 8 then skipping the numberĮlse calculating the square root of the number.The last digit? In what base? Base 10? I think this might be your problem. Calculating the last digit of the number to be checked.You already knew, and working on this program would have helped confirm this. I am convinced that including it was an honest mistake.
Hard-coding 3 might save, at most, a millisecond. Adding 1 2 3 to the prime list initiallyĪctually, just 2 is sufficient.It should be fairly easy to take the same approach in Java. This program can be altered to generate prime numbers on-demand as well. Each time a new prime number is discovered, a filter is added to the stream so that the remainder of the stream gets filtered of any multiples of that prime number. N :: primes' (count' - 1) (filter s n) in Let rec primes' count' s = match count' with (* Get next prime, apply a new filter by that prime to the remainder of the stream *) (* Filter the given stream of any multiples of x *)
#List of prime numbers to 10000 excel trial
Here's an Ocaml program that implements the Trial division sieve (which is sort of the inverse of Eratosthenes as correctly pointed out by Will): (* Creates a function for streaming integers from x onward *)
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