37 lines
942 B
Text
37 lines
942 B
Text
;Task:
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Calculate Meissel–Mertens constant up to a precision your language can handle.
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;Motivation:
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Analogous to Euler's constant, which is important in determining the sum of reciprocal natural numbers, Meissel-Mertens' constant is important in calculating the sum of reciprocal primes.
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;Example:
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We consider the finite sum of reciprocal natural numbers:
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''1 + 1/2 + 1/3 + 1/4 + 1/5 ... 1/n''
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this sum can be well approximated with:
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''log(n) + E''
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where ''E'' denotes Euler's constant: 0.57721...
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''log(n)'' denotes the natural logarithm of ''n''.
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Now consider the finite sum of reciprocal primes:
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''1/2 + 1/3 + 1/5 + 1/7 + 1/11 ... 1/p''
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this sum can be well approximated with:
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''log( log(p) ) + M''
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where ''M'' denotes Meissel-Mertens constant: 0.26149...
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;See:
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:* Details in the Wikipedia article: [https://en.wikipedia.org/wiki/Meissel%E2%80%93Mertens_constant Meissel–Mertens constant]
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<br /><br />
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