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I came across this forum post for computing the sum of primes, but I’m not really sure how it works? Could anyone explain this to me because I don’t really understand this.

This was the post:

“The main idea is as follows: Let S(v,m) be the sum of integers in the range 2..v that remain after sieving with all primes smaller or equal than m. That is S(v,m) is the sum of integers up to v that are either prime or the product of primes larger than m.

S(v, p) is equal to S(v, p-1) if p is not prime or v is smaller than p*p. Otherwise (p prime, p*p<=v) S(v,p) can be computed from S(v,p-1) by finding the sum of integers that are removed while sieving with p. An integer is removed in this step if it is the product of p with another integer that has no divisor smaller than p. This can be expressed as


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