Here is a solution to unbounded prime sieving in C#, which can be implemented using the Sieve of Eratosthenes (SoE) or the Sieve of Atkin (SoA) algorithms; however, I maintain that it is hardly worth the extreme complexity of an optimized SoA solution given than the true SoE gives about the same performance without as … Read more
UPD: This is a compiler optimization issue, obviously. While MinGW used only one div instruction in loop body, both GCC on Linux and MSVC failed to reuse the quotient from previous iteration. I think the best we could do is explicitly define quo and rem and calculate them in the same basic instruction block, to … Read more
int a, b; Console.WriteLine(“Please enter your integer: “); a = int.Parse(Console.ReadLine()); for (b = 2; a > 1; b++) if (a % b == 0) { int x = 0; while (a % b == 0) { a /= b; x++; } Console.WriteLine($”{b} is a prime factor {x} times!”); } Console.WriteLine(“Th-Th-Th-Th-Th-… That’s all, folks!”);
Your method of finding primes, by comparing every single element of the array with every possible factor is hideously inefficient. You can improve it immensely by doing a Sieve of Eratosthenes over the entire array at once. Besides doing far fewer comparisons, it also uses addition rather than division. Division is way slower.
I stumbled across a comment that sheds some light on what DJB is up to: /* * DJBX33A (Daniel J. Bernstein, Times 33 with Addition) * * This is Daniel J. Bernstein’s popular `times 33′ hash function as * posted by him years ago on comp.lang.c. It basically uses a function * like “hash(i) = … Read more
The implementation you’ve borrowed is able to start at 3 because it replaces sieving out the multiples of 2 by just skipping all even numbers; that’s what the 2*… that appear multiple times in the code are about. The fact that 3 is the next prime is also hardcoded in all over the place, but … Read more
Your method for finding if your number is prime is the correct method. To make it so that it does not consistently print out whether or not the number is prime, you could have an external variable, which represents whether or not the number is prime. Such as boolean prime = true; for (int p … Read more
This can be done with Memory complexity O(Sqrt(N)) and CPU complexity O(N * Log(Log(N))) with an optimized windowed Sieve of Eratosthenes, as implemented in the code example below. As no language was specified and as I do not know Python, I have implemented it in VB.net, however I can convert it to C# if you … Read more
Here’s another approach that celebrates Clojure’s Java interop. This takes 374ms on a 2.4 Ghz Core 2 Duo (running single-threaded). I let the efficient Miller-Rabin implementation in Java’s BigInteger#isProbablePrime deal with the primality check. (def certainty 5) (defn prime? [n] (.isProbablePrime (BigInteger/valueOf n) certainty)) (concat [2] (take 10001 (filter prime? (take-nth 2 (range 1 Integer/MAX_VALUE))))) … Read more
About a year ago I was working this area for libc++ while implementing the unordered (hash) containers for C++11. I thought I would share my experiences here. This experience supports marcog’s accepted answer for a reasonable definition of “brute force”. That means that even a simple brute force will be fast enough in most circumstances, … Read more