How to sum the log of the first n primes?

asked 2023-05-22 14:10:52 +0100

toni
113 ●1 ●1 ●11

This is a very naive question, and it may not fit the etiquette of the forum.

How do you handle the fact that

log(7) prints out as log(7), and only after expressing it as log(7.0) do you get 1.94591014905531

I would try and generate the sum using the function primes_first_n(n). However, log(primes_first_n(n)) is not a valid expression, and I don't know if it is because of the point about the logarithmic function above, or it is because log cannot be applied to a vectorial expression.

answered 2023-05-22 16:17:26 +0100

Max Alekseyev

6540 ●9 ●47 ●154

For the exact value you can use:

sum(log(p) for p in primes_first_n(100))

or for an approximate numerical value:

sum(log(p).n() for p in primes_first_n(100))

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What is the most expedient way to get he actual decimal expansion of something like log(7)?

toni ( 2023-05-22 18:02:44 +0100 )edit

How could I include that in a function like y(x) = sum(log(p) for p in primes_first_n(x))

toni ( 2023-05-22 18:26:58 +0100 )edit

You can specify desired precision (in bits) as an argument to .n() method - like log(7).n(100). As for the function: y = lambda x: sum(log(p) for p in primes_first_n(x)) will do the job.

Max Alekseyev ( 2023-05-22 20:25:47 +0100 )edit

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