Answer by Victor Miller for Fastest algorithm to compute the sum of primes?
I'll put in a plug for my original paper with Lagarias and Odlyzko, as well as a recent paper by Bach, Klyve and Sorenson: http://www.ams.org/journals/mcom/2009-78-268/S0025-5718-09-02249-2/home.html...
View ArticleAnswer by Nathan McKenzie for Fastest algorithm to compute the sum of primes?
This has been great. Some nice answers here - I'll accept one shortly.I was looking for a lit review because I have implemented an approach that runs in $O(n^\frac{2}{3} \log n)$ time and...
View ArticleAnswer by Johan Andersson for Fastest algorithm to compute the sum of primes?
Edit Nov 22: Changed the condition of the test function $\Phi$ somewhat to simplify my argument (removed one sum in the identity below).Although I like Charles' answer and its application of the...
View ArticleAnswer by Charles for Fastest algorithm to compute the sum of primes?
Deléglise-Dusart-Roblot [1] give an algorithm which determines $\pi(x,k,l)$, the number of primes up to $x$ that are congruent to $l$ modulo $k,$ in time $O(x^{2/3}/\log^2x).$ Using this algorithm to...
View ArticleAnswer by Charles for Fastest algorithm to compute the sum of primes?
This is a difficult problem. I asked about it here on math.se and here on cstheory. In both cases my question was somewhat broader: allowing sums over different exponents rather than just 1. In the...
View ArticleFastest algorithm to compute the sum of primes?
Can anyone help me with references to the current fastest algorithms for counting the exact sum of primes less than some number n? I'm specifically curious about the best case running times, of course....
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