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Sorry i don't know if this thread should be or in the "Number theory" forum, in fact if you want to calculate the series over all primes:

[tex] \sum_{p} f(x) [/tex] this can be very confusing as you don't know the "density" of primes my question is if we can approximate such series by the integral:

[tex] \int_ {2}^{\infty}dx P(x)f(x) [/tex] where [tex] P(x)\sim 1/log(x) [/tex]. (since for x<2 there are no primes )

The definition for P(x) is the "probability" of a random integer to be a prime (obviously x>0 ), the integral above could be then considered as the "sum" of the series as an approximation..is this possible or coherent?.

[tex] \sum_{p} f(x) [/tex] this can be very confusing as you don't know the "density" of primes my question is if we can approximate such series by the integral:

[tex] \int_ {2}^{\infty}dx P(x)f(x) [/tex] where [tex] P(x)\sim 1/log(x) [/tex]. (since for x<2 there are no primes )

The definition for P(x) is the "probability" of a random integer to be a prime (obviously x>0 ), the integral above could be then considered as the "sum" of the series as an approximation..is this possible or coherent?.

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