Sieve of Eratosthenes uses only the odd primes as base values, with both ranges of base values bounded to the square root of the range. When run for various ranges, it is immediately clear that while, of course, the resulting count of primes for a given range is identical between the two algorithms, the number of culling operations is much higher for the Sieve of Sundaram and also grows much more quickly with increasing range. From the above implementation, it is clear that the amount of work done is according to the following: or where: n is the range to be sieved and the range a to b is the odd numbers between 3 and the square root of n - the a to b range actually starts at the square of the odd base values, but this difference is negligible for large ranges. As the integral of the reciprocal of x is exactly , and as the lower value for a is relatively very small (close to one which has a log value of zero), this is about as follows: or or . Ignoring the constant factor of one eighth, the asymptotic complexity in Big O notation is clearly . See also Sieve of Eratosthenes Sieve of Atkin Sieve theory References A new "sieve" for primes, an excerpt from (translation of Russian book ) External links A C99 implementation of the Sieve of Sundaram using bitarrays Primality tests