Meissel–Mertens constant: Difference between revisions
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<pre>MM = 0.261497</pre>
=={{header|C++}}==
<syntaxhighlight lang="c++">
#include <cmath>
#include <cstdint>
#include <iomanip>
#include <iostream>
#include <vector>
std::vector<double> list_prime_reciprocals(const int32_t& limit) {
const int32_t half_limit = ( limit % 2 == 0 ) ? limit / 2 : 1 + limit / 2;
std::vector<bool> composite(half_limit);
for ( int32_t i = 1, p = 3; i < half_limit; p += 2, ++i ) {
if ( ! composite[i] ) {
for ( int32_t a = i + p; a < half_limit; a = a + p ) {
composite[a] = true;
}
}
}
std::vector<double> result(composite.size());
result[0] = 0.5;
for ( int32_t i = 1, p = 3; i < half_limit; p += 2, ++i ) {
if ( ! composite[i] ) {
result.emplace_back(1.0 / p);
}
}
return result;
}
int main() {
std::vector<double> prime_reciprocals = list_prime_reciprocals(100'000'000);
const double euler = 0.577'215'664'901'532'861;
double sum = 0.0;
for ( double reciprocal : prime_reciprocals ) {
sum += reciprocal + log(1.0 - reciprocal);
}
const double meissel_mertens = euler + sum;
std::cout << "The Meissel-Mertens constant = " << std::setprecision(8) << meissel_mertens << std::endl;
}
</syntaxhighlight>
{{ out }}
<pre>
The Meissel-Mertens constant = 0.26149721
</pre>
=={{header|Delphi}}==
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{{out}}
<pre>MM = 0.2614972131057144</pre>
=={{header|EasyLang}}==
{{trans|BASIC256}}
<syntaxhighlight>
fastfunc isprim num .
if num mod 2 = 0
if num = 2
return 1
.
return 0
.
i = 3
while i <= sqrt num
if num mod i = 0
return 0
.
i += 2
.
return 1
.
func log x .
return log10 x / log10 2.7182818284590452354
.
euler = 0.5772156649
for x = 2 to 1e6
if isprim x = 1
m += log (1 - (1 / x)) + (1 / x)
.
.
numfmt 11 0
print "mm = " & euler + m
</syntaxhighlight>
{{out}}
<pre>
mm = 0.26149724673
</pre>
=={{header|FreeBASIC}}==
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import java.util.List;
public final class MeisselMertensConstant {
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double sum = 0.0;
for ( double reciprocal : primeReciprocals ) {
sum +=
}
final double
System.out.println(String.format("%s%.9f", "The Meissel-Mertens constant = ",
}
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sieve.set(2, aLimit + 1);
for ( int j = i * i; j <= aLimit; j += i ) {
sieve.clear(j);
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{{ out }}
<pre>
The Meissel-Mertens constant = 0.
</pre>
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@show meissel_mertens(100_000_000) # meissel_mertens(100000000) = 0.2614972128591237
</syntaxhighlight>
=={{header|Maxima}}==
<syntaxhighlight lang="maxima">
meissel_mertens:%gamma+lsum(log(1-(1/i))+(1/i),i,primes(2,10000000)),numer;
</syntaxhighlight>
{{out}}
<pre>
0.2614972157776471
</pre>
=={{header|Nim}}==
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{{libheader|ntheory}}
<syntaxhighlight lang="perl" line>use v5.36;
use ntheory
my $s;
say my $result = $s + .57721566490153286;</syntaxhighlight>
{{out}}
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<pre>
1: 0.262733140866
</pre>
=={{header|Sidef}}==
<syntaxhighlight lang="ruby">var sum = 0
1e7.each_prime {|p|
with (1f/p) {|t|
sum += (log(1 - t) + t)
}
}
say sum+Num.EulerGamma</syntaxhighlight>
{{out}}
<pre>
0.26149721577767111119422410228297206467931376306
</pre>
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{{libheader|Wren-fmt}}
It will be seen that this is converging to the correct answer though we'd need to add a lot more primes to obtain a valid 11th digit.
<syntaxhighlight lang="
import "./fmt" for Fmt
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{{libheader|Wren-gmp}}
This agrees with the Phix entry that the 1,000th digit after the decimal point is '8' after rounding (according to OEIS it's actually '7' but the next one is '7' also).
<syntaxhighlight lang="
import "./math" for Int
import "./fmt" for Fmt
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