Goldbach's comet: Difference between revisions

Generates an ASCII-Art scatter plot - the vertical axis is n/10 and the hotizontal is G(n).

{{libheader|ALGOL 68-primes}}

# of prime pairs that sum to n, n even and > 2 #

# generates an ASCII scatter plot of G(n) up to G(2000) #

print( ( newline ) )

OD

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<pre>

=={{header|Arturo}}==

 

size select 2..n/2 'x ->

and? [prime? x][prime? n-x]

; write the CSV data to a file which we can then visualize

; via our preferred spreadsheet app

 

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=={{header|AutoHotkey}}==

while (c<100)

if (x := g(A_Index))

Return false

Return true

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<pre>1 1 1 2 1 2 2 2 2 3

g(1000000) : 5402</pre>

=={{header|AWK}}==

# syntax: GAWK -f GOLDBACHS_COMET.AWK

BEGIN {

return(1)

}

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<pre>

 

=={{header|FreeBASIC}}==

If ValorEval <= 1 Then Return False

For i As Integer = 2 To Int(Sqr(ValorEval))

 

Print !"\nThe value of G(1000000) is "; g(1000000)

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<pre>The first 100 G numbers are:

Task implementation:

 

1 1 1 2 1 2 2 2 2 3

3 3 2 3 2 4 4 2 3 4

11 6 5 12 4 8 11 5 8 10

5 6 13 9 6 11 7 7 14 6

 

And, for G(1e6):

-:+/1 p: 1e6-p:i.p:inv 1e6

 

Explanation:

=={{header|Julia}}==

Run in VS Code or REPL to view and save the plot.

using Plots

using Primes

y = map(g, 2x)

scatter(x, y, markerstrokewidth = 0, color = ["red", "blue", "green"][mod1.(x, 3)])

The first 100 G numbers are:

1 1 1 2 1 2 2 2 2 3

 

=={{header|Lua}}==

table.range = function(t,n) local s=T{} for i=1,n do s[i]=i end return s end

table.map = function(t,f) local s=T{} for i=1,#t do s[i]=f(t[i]) end return s end

g = T{}:range(100):map(function(n) return goldbach(2+n*2) end)

g:map(function(n) return string.format("%2d ",n) end):batch(10,function(t) print(t:concat()) end)

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<pre>The first 100 G numbers:

 

=={{header|Mathematica}}/{{header|Wolfram Language}}==

GoldbachFuncion[e_Integer] := Module[{ps},

ps = Prime[Range[PrimePi[e/2]]];

Grid[Partition[GoldbachFuncion /@ Range[4, 220, 2], 10]]

GoldbachFuncion[10^6]

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<pre>1 1 1 2 1 2 2 2 2 3

=={{header|Perl}}==

{{libheader|ntheory}}

use warnings;

use feature 'say';

binmode $fh;

print $fh $gd->png();

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<pre> 1 1 1 2 1 2 2 2 2 3

{{libheader|Phix/online}}

You can run this online [http://phix.x10.mx/p2js/goldbach.htm here].

<span style="color: #000080;font-style:italic;">--

-- demo\rosetta\Goldbachs_comet.exw

<span style="color: #7060A8;">IupClose</span><span style="color: #0000FF;">()</span>

<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>

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<pre>

 

=={{header|Picat}}==

println("First 100 G numbers:"),

foreach({G,I} in zip(take([G: T in 1..300, G=g(T),G>0],100),1..100))

{1 : I in 1..N // 2,

prime(I),prime(N-I)}.len,

 

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=={{header|Python}}==

from sympy import isprime

 

colors = [["red", "blue", "green"][(i // 2) % 3] for i in x]

scatter([i // 2 for i in x], y, marker='.', color = colors)

<pre>

The first 100 G numbers are:

For the stretch, actually generates a plot, doesn't just calculate values to be plotted by a third party application. Deviates slightly from the stretch goal, plots the first two thousand defined values rather than the values up to two thousand that happen to be defined. (More closely matches the [[wp:Goldbach's_comet|wikipedia example image]].)

 

 

# Task

values => [@y,],

).plot: :points;

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<pre>The first 100 G values:

 

=={{header|Rust}}==

// primal = "0.3"

// plotters = "0.3.2"

Err(error) => eprintln!("Error: {}", error),

}

 

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{{trans|FreeBASIC}}

For performance reasons only '''g(100000)''' is calculated. The value "810" has been verified and is correct.

c = 1

 

Loop

 

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<pre>The first 100 G numbers are:

{{libheader|Wren-plot}}

This follows the Raku example in plotting the first two thousand G values rather than the values up to G(2000) in order to produce an image something like the image in the Wikipedia article.

import "graphics" for Canvas, Color

import "./math2" for Int

}

 

 

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=={{header|XPL0}}==

func IsPrime(N); \Return 'true' if N is prime

int N, I;

Text(0, "G(1,000,000) = "); IntOut(0, G(1_000_000));

CrLf(0);

 

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