user
Task

Calculate Meissel–Mertens constant up to a precision your language can handle.

Motivation

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.

Example

We consider the finite sum of reciprocal natural numbers:

*1 + 1/2 + 1/3 + 1/4 + 1/5 ... 1/n*

this sum can be well approximated with:

*log(n) + E*

where *E* denotes Euler's constant: 0.57721...

*log(n)* denotes the natural logarithm of *n*.

Now consider the finite sum of reciprocal primes:

*1/2 + 1/3 + 1/5 + 1/7 + 1/11 ... 1/p*

this sum can be well approximated with:

*log( log(p) ) + M*

where *M* denotes Meissel-Mertens constant: 0.26149...

See
:   * Details in the Wikipedia article:  Meissel–Mertens constant
assistant
**Translation of**: FreeBASIC

```
# 20221011 Raku programming solution

my $s;
.is-prime and $s += log(1-1/$_)+1/$_ for 2 .. 10**8;
say $s + .57721566490153286

```

Output:

```
0.26149721310571383
```