# Re: Sum of Primes < 1000000

From:
Newsgroups:
comp.lang.java.programmer
Date:
5 Jan 2007 13:18:02 -0800
Message-ID:
Patricia Shanahan wrote:

Simon wrote:

Luc The Perverse schrieb:

I was messing around on a site where you answer questions for points. (No
prizes or anything)

Anyway, they say our programs *should* execute in less than 1 minute if well
formed.

Mine didn't - it was less than 10 minutes though and I got the right answer.

I was supposed to sum all primes less than 1 million.

Is there an algorithm out there, which I will be able to understand, which
works significantly faster than this one?

You may want to have a look at the Sieve of Eratosthenes (and its successors)
(see http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes). It finds all primes up
to n in time n log n. On my computer my implementation takes 150 milliseconds
for n=1000000.

As a matter of curiosity, did you use a boolean[] or BitSet?

I started with a boolean[], and mine was slower than yours, about 200
milliseconds. It dropped to under 100 milliseconds when I switched to
BitSet. I believe the improvement is due to more efficient caching.

Patricia

I personally got 66ms from:

public class SumPrimes {
public static void main(String...args) {
final int bounds = Integer.parseInt(args[0]) + 1;
final java.util.BitSet composits = new
java.util.BitSet(bounds);
long sum = 1;
for (int prime = 2; prime < bounds; prime =
composits.nextClearBit(prime +1)) {
sum += prime;
for (int composit = prime + prime; composit < bounds;
composit += prime) {
composits.set(composit);
}
}
System.out.println(sum);
}
}

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