Finding prime numbers with the Sieve of Eratosthenes (Originally: Is there a better way to prepare this array?)

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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.

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