Ramanujan primes/twins: Difference between revisions
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syntax highlighting fixup automation
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=={{header|F_Sharp|F#}}==
This task uses [http://www.rosettacode.org/wiki/Ramanujan_primes#F.23 Ramanujan primes (F#)]
<
// Twin Ramanujan primes. Nigel Galloway: September 9th., 2021
printfn $"There are %d{rP 1000000|>Seq.pairwise|>Seq.filter(fun(n,g)->n=g-2)|>Seq.length} twins in the first million Ramanujan primes"
</syntaxhighlight>
{{out}}
<pre>
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{{trans|Wren}}
{{libheader|Go-rcu}}
<
import (
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fmt.Println()
}
}</
{{out}}
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=={{header|Julia}}==
<
function rajpairs(N, verbose, interval = 2)
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rajpairs(100000, false)
@time rajpairs(1000000, true)
</
<pre>
There are 74973 twins in the first 1000000 Ramanujan primes.
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=={{header|Mathematica}}/{{header|Wolfram Language}}==
<
l = PrimePi[Range[35 10^6]] - PrimePi[Range[35 10^6]/2];
ramanujanprimes = GatherBy[Transpose[{Range[2, Length[l] + 1], l}], Last][[All, -1, 1]];
ramanujanprimes = Take[Sort@ramanujanprimes, 10^6];
Count[Differences[ramanujanprimes], 2]</
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<pre>74973</pre>
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{{trans|Go}}
We use Phix algorithm in its Go translation.
<
let t0 = now()
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main()
echo "\nElapsed time: ", (now() - t0).inMilliseconds, " ms"</
{{out}}
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Can't do better than the <code>ntheory</code> module.
{{libheader|ntheory}}
<
use warnings;
use ntheory <ramanujan_primes nth_ramanujan_prime>;
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printf "There are %s twins in the first %s Ramanujan primes.\n\n",
comma( scalar grep { $rp->[$_+1] == $rp->[$_]+2 } 0 .. $limit-2 ), comma $limit;
}</
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<pre>The 100,000th Ramanujan prime is 2,916,539
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Calculating pi(p) - pi(floor(pi/2) for all (normal) primes below that one millionth, and then
filtering them based on that list is significantly faster, and finally we can scan for twins.
<!--<
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">pi</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"There are %,d twins in the first %,d Ramanujan primes\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">twins</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">)})</span>
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)</span>
<!--</
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using a smaller limit:
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Timing is informational only. Will vary by system specs and load.
{{libheader|ntheory}}
<syntaxhighlight lang="raku"
use Lingua::EN::Numbers;
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}
say (now - INIT now).fmt('%.3f') ~ ' seconds';</
{{out}}
<pre>The 100,000th Ramanujan prime is 2,916,539
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<br>
As calculating the first 1 million Ramanujan primes individually is out of the question, we follow the Phix entry's clever strategy here which brings this task comfortably within our ambit.
<
import "/math" for Int, Math
import "/fmt" for Fmt
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Fmt.print("There are $,d twins in the first $,d Ramanujan primes.", twins, limit)
System.print("Took %(Math.toPlaces(System.clock -start, 2, 0)) seconds.\n")
}</
{{out}}
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