Goldbach's comet: Difference between revisions
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=={{header|11l}}==
{{trans|Python}}
<syntaxhighlight lang="11l">
F is_prime(a)
I a == 2
R 1B
I a < 2 | a % 2 == 0
R 0B
L(i) (3 .. Int(sqrt(a))).step(2)
I a % i == 0
R 0B
R 1B
F g(n)
assert(n > 2 & n % 2 == 0, ‘n in goldbach function g(n) must be even’)
V count = 0
L(i) 1 .. n I/ 2
I is_prime(i) & is_prime(n - i)
count++
R count
print(‘The first 100 G numbers are:’)
V col = 1
L(n) (4.<204).step(2)
print(String(g(n)).ljust(4), end' I (col % 10 == 0) {"\n"} E ‘’)
col++
print("\nThe value of G(1000000) is "g(1'000'000))
</syntaxhighlight>
{{out}}
<pre>
The first 100 G numbers are:
1 1 1 2 1 2 2 2 2 3
3 3 2 3 2 4 4 2 3 4
3 4 5 4 3 5 3 4 6 3
5 6 2 5 6 5 5 7 4 5
8 5 4 9 4 5 7 3 6 8
5 6 8 6 7 10 6 6 12 4
5 10 3 7 9 6 5 8 7 8
11 6 5 12 4 8 11 5 8 10
5 6 13 9 6 11 7 7 14 6
8 13 5 8 11 7 9 13 8 9
The value of G(1000000) is 5402
</pre>
=={{header|ALGOL 68}}==
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) #
Line 94 ⟶ 143:
print( ( newline ) )
OD
END</
{{out}}
<pre>
Line 313 ⟶ 362:
=={{header|Arturo}}==
<
size select 2..n/2 'x ->
and? [prime? x][prime? n-x]
Line 330 ⟶ 379:
; write the CSV data to a file which we can then visualize
; via our preferred spreadsheet app
write "comet.csv" csv</
{{out}}
Line 349 ⟶ 398:
Here, you can find the result of the visualization - or the "Goldbach's comet": [https://i.ibb.co/JvLDRc0/Screenshot-2022-05-07-at-11-35-23.png 2D-chart of all G values up to 2000]
=={{header|AutoHotkey}}==
<syntaxhighlight lang="autohotkey">c := 0
while (c<100)
if (x := g(A_Index))
c++, result .= x (Mod(c, 10) ? "`t" : "`n")
MsgBox % result "`ng(1000000) : " g(1000000)
return
g(n, i:=1) {
if Mod(n, 2)
return false
while (++i <= n/2)
if (is_prime(i) && is_prime(n-i))
count++
return count
}
is_prime(N) {
Loop, % Floor(Sqrt(N))
if (A_Index > 1 && !Mod(N, A_Index))
Return false
Return true
}</syntaxhighlight>
{{out}}
<pre>1 1 1 2 1 2 2 2 2 3
3 3 2 3 2 4 4 2 3 4
3 4 5 4 3 5 3 4 6 3
5 6 2 5 6 5 5 7 4 5
8 5 4 9 4 5 7 3 6 8
5 6 8 6 7 10 6 6 12 4
5 10 3 7 9 6 5 8 7 8
11 6 5 12 4 8 11 5 8 10
5 6 13 9 6 11 7 7 14 6
8 13 5 8 11 7 9 13 8 9
g(1000000) : 5402</pre>
=={{header|AWK}}==
<syntaxhighlight lang="awk">
# syntax: GAWK -f GOLDBACHS_COMET.AWK
BEGIN {
print("The first 100 G numbers:")
for (n=4; n<=202; n+=2) {
printf("%4d%1s",g(n),++count%10?"":"\n")
}
n = 1000000
printf("\nG(%d): %d\n",n,g(n))
n = 4
printf("G(%d): %d\n",n,g(n))
n = 22
printf("G(%d): %d\n",n,g(n))
exit(0)
}
function g(n, count,i) {
if (n % 2 == 0) { # n must be even
for (i=2; i<=(1/2)*n; i++) {
if (is_prime(i) && is_prime(n-i)) {
count++
}
}
}
return(count)
}
function is_prime(n, d) {
d = 5
if (n < 2) { return(0) }
if (n % 2 == 0) { return(n == 2) }
if (n % 3 == 0) { return(n == 3) }
while (d*d <= n) {
if (n % d == 0) { return(0) }
d += 2
if (n % d == 0) { return(0) }
d += 4
}
return(1)
}
</syntaxhighlight>
{{out}}
<pre>
The first 100 G numbers:
1 1 1 2 1 2 2 2 2 3
3 3 2 3 2 4 4 2 3 4
3 4 5 4 3 5 3 4 6 3
5 6 2 5 6 5 5 7 4 5
8 5 4 9 4 5 7 3 6 8
5 6 8 6 7 10 6 6 12 4
5 10 3 7 9 6 5 8 7 8
11 6 5 12 4 8 11 5 8 10
5 6 13 9 6 11 7 7 14 6
8 13 5 8 11 7 9 13 8 9
G(1000000): 5402
G(4): 1
G(22): 3
</pre>
=={{Header|BASIC}}==
==={{header|BASIC256}}===
{{trans|FreeBASIC}}
<syntaxhighlight lang="vb">#arraybase 1
print "The first 100 G numbers are:"
col = 1
for n = 4 to 202 step 2
print rjust(string(g(n)), 4);
if col mod 10 = 0 then print
col += 1
next n
print : print "G(1000000) = "; g(1000000)
end
function isPrime(v)
if v <= 1 then return False
for i = 2 to int(sqrt(v))
if v mod i = 0 then return False
next i
return True
end function
function g(n)
cont = 0
if n mod 2 = 0 then
for i = 2 to (1/2) * n
if isPrime(i) = 1 and isPrime(n - i) = 1 then cont += 1
next i
end if
return cont
end function</syntaxhighlight>
{{out}}
<pre>Similar to FreeBASIC entry.</pre>
==={{header|FreeBASIC}}===
<syntaxhighlight lang="freebasic">Function isPrime(Byval ValorEval As Uinteger) As Boolean
If ValorEval <= 1 Then Return False
For i As Integer = 2 To Int(Sqr(ValorEval))
If ValorEval Mod i = 0 Then Return False
Next i
Return True
End Function
Function g(n As Uinteger) As Uinteger
Dim As Uinteger i, count = 0
If (n Mod 2 = 0) Then 'n in goldbach function g(n) must be even
For i = 2 To (1/2) * n
If isPrime(i) And isPrime(n - i) Then count += 1
Next i
End If
Return count
End Function
Print "The first 100 G numbers are:"
Dim As Uinteger col = 1
For n As Uinteger = 4 To 202 Step 2
Print Using "####"; g(n);
If (col Mod 10 = 0) Then Print
col += 1
Next n
Print !"\nThe value of G(1000000) is "; g(1000000)
Sleep</syntaxhighlight>
{{out}}
<pre>The first 100 G numbers are:
1 1 1 2 1 2 2 2 2 3
3 3 2 3 2 4 4 2 3 4
3 4 5 4 3 5 3 4 6 3
5 6 2 5 6 5 5 7 4 5
8 5 4 9 4 5 7 3 6 8
5 6 8 6 7 10 6 6 12 4
5 10 3 7 9 6 5 8 7 8
11 6 5 12 4 8 11 5 8 10
5 6 13 9 6 11 7 7 14 6
8 13 5 8 11 7 9 13 8 9
The value of G(1000000) is 5402</pre>
==={{header|Gambas}}===
{{trans|FreeBASIC}}
<syntaxhighlight lang="vbnet">Use "isprime.bas"
Public Sub Main()
Print "The first 100 G numbers are:"
Dim n As Integer, col As Integer = 1
For n = 4 To 202 Step 2
Print Format$(Str(g(n)), "####");
If col Mod 10 = 0 Then Print
col += 1
Next
Print "\nG(1.000.000) = "; g(1000000)
End
Function g(n As Integer) As Integer
Dim i As Integer, count As Integer = 0
If n Mod 2 = 0 Then
For i = 2 To n \ 2 '(1/2) * n
If isPrime(i) And isPrime(n - i) Then count += 1
Next
End If
Return count
End Function</syntaxhighlight>
{{out}}
<pre>Same as FreeBASIC entry.</pre>
==={{Header|SmileBASIC}}===
(click the image to view full-size)
[[File:GoldbachsComet SmileBASIC 3DS screenshot.png|thumb]]
<syntaxhighlight lang="smilebasic">OPTION STRICT: OPTION DEFINT
VAR MAX_G = 4000, MAX_P = 1000000
VAR ROOT_MAX_P = FLOOR(SQR(MAX_P))
VAR HALF_MAX_G = MAX_G DIV 2
VAR G[MAX_G + 1], P[MAX_P + 1]
VAR I, J
CLS: GCLS
P[0] = FALSE: P[1] = 0: P[2] = TRUE
FOR I = 4 TO MAX_P STEP 2 P[I] = FALSE: NEXT
FOR I = 3 TO MAX_P STEP 2 P[I] = TRUE: NEXT
FOR I = 3 TO ROOT_MAX_P STEP 2
IF P[I] THEN
FOR J = I * I TO MAX_P STEP I
P[J] = FALSE
NEXT
ENDIF
NEXT
FOR I = 1 TO MAX_G G[I] = 0: NEXT
G[4] = 1 ' 4 is the only sum of 2 even primes
FOR I = 3 TO HALF_MAX_G STEP 2
IF P[I] THEN
INC G[I + 1]
FOR J = I + 2 TO MAX_G - 1
IF P[J] THEN
INC G[I + 1]
ENDIF
NEXT
ENDIF
NEXT
VAR C = 0
FOR I = 4 TO 202 STEP 2
PRINT FORMAT$("%3D", G[I]),
INC C
IF C == 10 THEN PRINT: C = 0: ENDIF
NEXT
VAR GM = 0
FOR I = 3 TO MAX_P DIV 2 STEP 2
IF P[I] THEN
IF P[MAX_P - I] THEN INC GM: ENDIF
ENDIF
NEXT
PRINT FORMAT$("G(%D): ", MAX_P); GM
FOR I = 2 TO MAX_G - 10 STEP 10
FOR J = 1 TO I + 8 STEP 2
GPSET I DIV 10, 240-G[J],RGB(255,255,255)
NEXT
NEXT</syntaxhighlight>
==={{header|uBasic/4tH}}===
{{trans|FreeBASIC}}
For performance reasons only '''g(100000)''' is calculated. The value "810" has been verified and is correct.
<syntaxhighlight lang="text">Print "The first 100 G numbers are:"
c = 1
For n = 4 To 202 Step 2
Print Using "___#"; FUNC(_g(n));
If (c % 10) = 0 Then Print
c = c + 1
Next
Print "\nThe value of G(100000) is "; FUNC(_g(100000))
End
_isPrime
Param (1)
Local (1)
If a@ < 2 Then Return (0)
For b@ = 2 To FUNC(_Sqrt(a@))
If (a@ % b@) = 0 Then Unloop: Return (0)
Next
Return (1)
_g
Param (1)
Local (2)
c@ = 0
If (a@ % 2) = 0 Then 'n in goldbach function g(n) must be even
For b@ = 2 To a@/2
If FUNC(_isPrime(b@)) * FUNC(_isPrime(a@ - b@)) Then c@ = c@ + 1
Next
EndIf
Return (c@)
_Sqrt
Param (1)
Local (3)
Let b@ = 1
Let c@ = 0
Do Until b@ > a@
Let b@ = b@ * 4
Loop
Do While b@ > 1
Let b@ = b@ / 4
Let d@ = a@ - c@ - b@
Let c@ = c@ / 2
If d@ > -1 Then
Let a@ = d@
Let c@ = c@ + b@
Endif
Loop
Return (c@)</syntaxhighlight>
{{out}}
<pre>The first 100 G numbers are:
1 1 1 2 1 2 2 2 2 3
3 3 2 3 2 4 4 2 3 4
3 4 5 4 3 5 3 4 6 3
5 6 2 5 6 5 5 7 4 5
8 5 4 9 4 5 7 3 6 8
5 6 8 6 7 10 6 6 12 4
5 10 3 7 9 6 5 8 7 8
11 6 5 12 4 8 11 5 8 10
5 6 13 9 6 11 7 7 14 6
8 13 5 8 11 7 9 13 8 9
The value of G(100000) is 810
0 OK, 0:210 </pre>
==={{header|Yabasic}}===
{{trans|FreeBASIC}}
<syntaxhighlight lang="vb">import isprime
print "The first 100 G numbers are:"
col = 1
for n = 4 to 202 step 2
print g(n) using ("####");
if mod(col, 10) = 0 print
col = col + 1
next n
print "\nG(1000000) = ", g(1000000)
end
sub g(n)
count = 0
if mod(n, 2) = 0 then
for i = 2 to (1/2) * n
if isPrime(i) and isPrime(n - i) count = count + 1
next i
fi
return count
end sub</syntaxhighlight>
{{out}}
<pre>Same as FreeBASIC entry.</pre>
=={{Header|C++}}==
<syntaxhighlight lang="c++">
#include <cmath>
#include <cstdint>
#include <iomanip>
#include <iostream>
#include <stdexcept>
#include <vector>
std::vector<bool> primes;
void initialise_primes(const int32_t& limit) {
primes.resize(limit);
for ( int32_t i = 2; i < limit; ++i ) {
primes[i] = true;
}
for ( int32_t n = 2; n < sqrt(limit); ++n ) {
for ( int32_t k = n * n; k < limit; k += n ) {
primes[k] = false;
}
}
}
int32_t goldbach_function(const int32_t& number) {
if ( number <= 2 || number % 2 == 1 ) {
throw std::invalid_argument("Argument must be even and greater than 2: " + std::to_string(number));
}
int32_t result = 0;
for ( int32_t i = 1; i <= number / 2; ++i ) {
if ( primes[i] && primes[number - i] ) {
result++;
}
}
return result;
}
int main() {
initialise_primes(2'000'000);
std::cout << "The first 100 Goldbach numbers:" << std::endl;
for ( int32_t n = 2; n < 102; ++n ) {
std::cout << std::setw(3) << goldbach_function(2 * n) << ( n % 10 == 1 ? "\n" : "" );
}
std::cout << "\n" << "The 1,000,000th Goldbach number = " << goldbach_function(1'000'000) << std::endl;
}
</syntaxhighlight>
{{ out }}
<pre>
The first 100 Goldbach numbers:
1 1 1 2 1 2 2 2 2 3
3 3 2 3 2 4 4 2 3 4
3 4 5 4 3 5 3 4 6 3
5 6 2 5 6 5 5 7 4 5
8 5 4 9 4 5 7 3 6 8
5 6 8 6 7 10 6 6 12 4
5 10 3 7 9 6 5 8 7 8
11 6 5 12 4 8 11 5 8 10
5 6 13 9 6 11 7 7 14 6
8 13 5 8 11 7 9 13 8 9
The 1,000,000th Goldbach number = 5402
</pre>
=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
<syntaxhighlight lang="Delphi">
function GetGoldbachCount(N: integer): integer;
{Count number of prime number combinations add up to N }
var I: integer;
begin
Result:=0;
{Look at all number pairs that add up to N}
{And see if they are prime}
for I:=1 to N div 2 do
if IsPrime(I) and IsPrime(N-I) then Inc(Result);
end;
procedure ShowGoldbachComet(Memo: TMemo);
{Show first 100 Goldback numbers}
var I,N,Cnt,C: integer;
var S: string;
begin
Cnt:=0; N:=2; S:='';
while true do
begin
C:=GetGoldbachCount(N);
if C>0 then
begin
Inc(Cnt);
S:=S+Format('%3d',[C]);
if (Cnt mod 10)=0 then S:=S+CRLF;
if Cnt>=100 then break;
end;
Inc(N,2);
end;
Memo.Lines.Add(S);
end;
</syntaxhighlight>
{{out}}
<pre>
1 1 1 2 1 2 2 2 2 3
3 3 2 3 2 4 4 2 3 4
3 4 5 4 3 5 3 4 6 3
5 6 2 5 6 5 5 7 4 5
8 5 4 9 4 5 7 3 6 8
5 6 8 6 7 10 6 6 12 4
5 10 3 7 9 6 5 8 7 8
11 6 5 12 4 8 11 5 8 10
5 6 13 9 6 11 7 7 14 6
8 13 5 8 11 7 9 13 8 9
Elapsed Time: 1.512 ms.
</pre>
=={{header|EasyLang}}==
{{trans|AWK}}
<syntaxhighlight lang="easylang">
func isprim n .
if n mod 2 = 0 and n > 2
return 0
.
i = 3
sq = sqrt n
while i <= sq
if n mod i = 0
return 0
.
i += 2
.
return 1
.
func goldbach n .
for i = 2 to n div 2
if isprim i = 1
cnt += isprim (n - i)
.
.
return cnt
.
numfmt 0 3
for n = 4 step 2 to 202
write goldbach n
if n mod 20 = 2
print ""
.
.
print goldbach 1000000
</syntaxhighlight>
=={{header|J}}==
Line 354 ⟶ 931:
Task implementation:
<
1 1 1 2 1 2 2 2 2 3
3 3 2 3 2 4 4 2 3 4
Line 364 ⟶ 941:
11 6 5 12 4 8 11 5 8 10
5 6 13 9 6 11 7 7 14 6
8 13 5 8 11 7 9 13 8 9</
And, for G(1e6):
<syntaxhighlight lang="j">
-:+/1 p: 1e6-p:i.p:inv 1e6
5402</
Explanation:
Line 383 ⟶ 960:
---
For G(1e6) that brute force approach becomes inefficient -- instead of about 2000
Instead, for G(1e6), we find all primes less than a million, subtract each from 1 million and count how many of the differences are prime and cut that in half. We cut that
=={{header|Java}}==
<syntaxhighlight lang="java">
import java.awt.Color;
import java.awt.Graphics;
import java.awt.image.BufferedImage;
import java.io.File;
import java.io.IOException;
import java.util.List;
import javax.imageio.ImageIO;
public final class GoldbachsComet {
public static void main(String[] aArgs) {
initialisePrimes(2_000_000);
System.out.println("The first 100 Goldbach numbers:");
for ( int n = 2; n < 102; n++ ) {
System.out.print(String.format("%3d%s", goldbachFunction(2 * n), ( n % 10 == 1 ? "\n" : "" )));
}
System.out.println();
System.out.println("The 1,000,000th Goldbach number = " + goldbachFunction(1_000_000));
createImage();
}
private static void createImage() {
final int width = 1040;
final int height = 860;
BufferedImage image = new BufferedImage(width, height, BufferedImage.TYPE_INT_RGB);
Graphics graphics = image.getGraphics();
graphics.setColor(Color.WHITE);
graphics.fillRect(0, 0, width, height);
List<Color> colours = List.of( Color.BLUE, Color.GREEN, Color.RED );
for ( int n = 2; n < 2002; n++ ) {
graphics.setColor(colours.get(n % 3));
graphics.fillOval(n / 2, height - 5 * goldbachFunction(2 * n), 10, 10);
}
try {
ImageIO.write(image, "png", new File("GoldbachsCometJava.png"));
} catch (IOException ioe) {
ioe.printStackTrace();
}
}
private static int goldbachFunction(int aNumber) {
if ( aNumber <= 2 || aNumber % 2 == 1 ) {
throw new AssertionError("Argument must be even and greater than 2: " + aNumber);
}
int result = 0;
for ( int i = 1; i <= aNumber / 2; i++ ) {
if ( primes[i] && primes[aNumber - i] ) {
result += 1;
}
}
return result;
}
private static void initialisePrimes(int aLimit) {
primes = new boolean[aLimit];
for ( int i = 2; i < aLimit; i++ ) {
primes[i] = true;
}
for ( int n = 2; n < Math.sqrt(aLimit); n++ ) {
for ( int k = n * n; k < aLimit; k += n ) {
primes[k] = false;
}
}
}
private static boolean[] primes;
}
</syntaxhighlight>
{{ out }}
[[Media:GoldbachsCometJava.png]]
<pre>
The first 100 Goldbach numbers:
1 1 1 2 1 2 2 2 2 3
3 3 2 3 2 4 4 2 3 4
3 4 5 4 3 5 3 4 6 3
5 6 2 5 6 5 5 7 4 5
8 5 4 9 4 5 7 3 6 8
5 6 8 6 7 10 6 6 12 4
5 10 3 7 9 6 5 8 7 8
11 6 5 12 4 8 11 5 8 10
5 6 13 9 6 11 7 7 14 6
8 13 5 8 11 7 9 13 8 9
The 1,000,000th Goldbach number = 5402
</pre>
=={{header|jq}}==
'''Works with jq and gojq, the C and Go implementations of jq.'''
'''Preliminaries'''
<syntaxhighlight lang=jq>
def count(s): reduce s as $_ (0; .+1);
def lpad($len): tostring | ($len - length) as $l | (" " * $l)[:$l] + .;
def nwise($n):
def n: if length <= $n then . else .[0:$n] , (.[$n:] | n) end;
n;
def is_prime:
. as $n
| if ($n < 2) then false
elif ($n % 2 == 0) then $n == 2
elif ($n % 3 == 0) then $n == 3
elif ($n % 5 == 0) then $n == 5
elif ($n % 7 == 0) then $n == 7
elif ($n % 11 == 0) then $n == 11
elif ($n % 13 == 0) then $n == 13
elif ($n % 17 == 0) then $n == 17
elif ($n % 19 == 0) then $n == 19
else
($n | sqrt) as $rt
| 23
| until( . > $rt or ($n % . == 0); .+2)
| . > $rt
end;
</syntaxhighlight>
'''The Tasks'''
<syntaxhighlight lang=jq>
# emit nothing if . is odd
def G:
select(. % 2 == 0)
| count( range(2; (./2)+1) as $i
| select(($i|is_prime) and ((.-$i)|is_prime)) );
def task1:
"The first 100 G numbers:",
([range(4; 203; 2) | G] | nwise(10) | map(lpad(4)) | join(" "));
def task($n):
$n, 4, 22
|"G(\(.)): \(G)";
task1, "", task(1000000)
</syntaxhighlight>
{{output}}
<pre>
The first 100 G numbers:
1 1 1 2 1 2 2 2 2 3
3 3 2 3 2 4 4 2 3 4
3 4 5 4 3 5 3 4 6 3
5 6 2 5 6 5 5 7 4 5
8 5 4 9 4 5 7 3 6 8
5 6 8 6 7 10 6 6 12 4
5 10 3 7 9 6 5 8 7 8
11 6 5 12 4 8 11 5 8 10
5 6 13 9 6 11 7 7 14 6
8 13 5 8 11 7 9 13 8 9
G(1000000): 5402
G(4): 1
G(22): 3
</pre>
=={{header|Julia}}==
Run in VS Code or REPL to view and save the plot.
<
using Plots
using Primes
Line 404 ⟶ 1,146:
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
Line 419 ⟶ 1,161:
The value of G(1000000) is 5402
</pre>
[[File:Jgoldbachplot.png]]
=={{header|Lua}}==
<syntaxhighlight lang="lua">function T(t) return setmetatable(t, {__index=table}) end
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
table.batch = function(t,n,f) for i=1,#t,n do local s=T{} for j=1,n do s[j]=t[i+j-1] end f(s) end return t end
function isprime(n)
if n < 2 then return false end
if n % 2 == 0 then return n==2 end
if n % 3 == 0 then return n==3 end
for f = 5, n^0.5, 6 do
if n%f==0 or n%(f+2)==0 then return false end
end
return true
end
function goldbach(n)
local count = 0
for i = 1, n/2 do
if isprime(i) and isprime(n-i) then
count = count + 1
end
end
return count
end
print("The first 100 G numbers:")
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)
print("G(1000000) = "..goldbach(1000000))</syntaxhighlight>
{{out}}
<pre>The first 100 G numbers:
1 1 1 2 1 2 2 2 2 3
3 3 2 3 2 4 4 2 3 4
3 4 5 4 3 5 3 4 6 3
5 6 2 5 6 5 5 7 4 5
8 5 4 9 4 5 7 3 6 8
5 6 8 6 7 10 6 6 12 4
5 10 3 7 9 6 5 8 7 8
11 6 5 12 4 8 11 5 8 10
5 6 13 9 6 11 7 7 14 6
8 13 5 8 11 7 9 13 8 9
G(1000000) = 5402</pre>
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">ClearAll[GoldbachFuncion]
GoldbachFuncion[e_Integer] := Module[{ps},
ps = Prime[Range[PrimePi[e/2]]];
Total[Boole[PrimeQ[e - ps]]]
]
Grid[Partition[GoldbachFuncion /@ Range[4, 220, 2], 10]]
GoldbachFuncion[10^6]
DiscretePlot[GoldbachFuncion[e], {e, 4, 2000}, Filling -> None]</syntaxhighlight>
{{out}}
<pre>1 1 1 2 1 2 2 2 2 3
3 3 2 3 2 4 4 2 3 4
3 4 5 4 3 5 3 4 6 3
5 6 2 5 6 5 5 7 4 5
8 5 4 9 4 5 7 3 6 8
5 6 8 6 7 10 6 6 12 4
5 10 3 7 9 6 5 8 7 8
11 6 5 12 4 8 11 5 8 10
5 6 13 9 6 11 7 7 14 6
8 13 5 8 11 7 9 13 8 9
5402
[graphical object showing Goldbach's comet]</pre>
=={{header|Nim}}==
{{libheader|nim-plotly}}
{{libheader|chroma}}
To display the Golbach’s comet, we use a library providing a Nim interface to “plotly”. The graph is displayed into a browser.
<syntaxhighlight lang="Nim">import std/[math, strformat, strutils, sugar]
import chroma, plotly
const
N1 = 100 # For part 1 of task.
N2 = 1_000_000 # For part 2 of task.
N3 = 2000 # For stretch part.
# Erathostenes sieve.
var isPrime: array[1..N1, bool]
for i in 2..N1: isPrime[i] = true
for n in 2..sqrt(N1.toFloat).int:
for k in countup(n * n, N1, n):
isPrime[k] = false
proc g(n: int): int =
## Goldbach function.
assert n > 2 and n mod 2 == 0, "“n” must be even and greater than 2."
for i in 1..(n div 2):
if isPrime[i] and isPrime[n - i]:
inc result
# Part 1.
echo &"First {N1} G numbers:"
var col = 1
for n in 2..N1:
stdout.write align($g( 2 * n), 3)
stdout.write if col mod 10 == 0: '\n' else: ' '
inc col
# Part 2.
echo &"\nG({N2}) = ", g(N2)
# Stretch part.
const Colors = collect(for name in ["red", "blue", "green"]: name.parseHtmlName())
var x, y: seq[float]
var colors: seq[Color]
for n in 2..N3:
x.add n.toFloat
y.add g(2 * n).toFloat
colors.add Colors[n mod 3]
let trace = Trace[float](type: Scatter, mode: Markers, marker: Marker[float](color: colors), xs: x, ys: y)
let layout = Layout(title: "Goldbach’s comet", width: 1200, height: 400)
Plot[float64](layout: layout, traces: @[trace]).show(removeTempFile = true)
</syntaxhighlight>
{{out}}
<pre>First 100 G numbers:
1 1 1 2 1 2 2 2 2 3
3 3 2 3 2 4 4 2 3 4
3 4 5 4 3 5 3 4 6 3
5 6 2 5 6 5 5 7 4 5
8 5 4 9 4 5 7 3 6 8
5 6 8 6 7 10 6 6 12 4
5 10 3 7 9 6 5 8 7 8
11 6 5 12 4 8 11 5 8 10
5 6 13 9 6 11 7 7 14 6
8 13 5 8 11 7 9 13 8 9
G(1000000) = 5402
</pre>
=={{header|Perl}}==
{{libheader|ntheory}}
<syntaxhighlight lang="perl">use strict;
use warnings;
use feature 'say';
use List::Util 'max';
use GD::Graph::bars;
use ntheory 'is_prime';
sub table { my $t = shift() * (my $c = 1 + max map {length} @_); ( sprintf( ('%'.$c.'s')x@_, @_) ) =~ s/.{1,$t}\K/\n/gr }
sub G {
my($n) = @_;
scalar grep { is_prime($_) and is_prime($n - $_) } 2 .. $n/2;
}
my @y;
push @y, G(2*$_ + 4) for my @x = 0..1999;
say $_ for table 10, @y;
printf "G $_: %d", G($_) for 1e6;
my @data = ( \@x, \@y);
my $graph = GD::Graph::bars->new(1200, 400);
$graph->set(
title => q/Goldbach's Comet/,
y_max_value => 170,
x_tick_number => 10,
r_margin => 10,
dclrs => [ 'blue' ],
) or die $graph->error;
my $gd = $graph->plot(\@data) or die $graph->error;
open my $fh, '>', 'goldbachs-comet.png';
binmode $fh;
print $fh $gd->png();
close $fh;</syntaxhighlight>
{{out}}
<pre> 1 1 1 2 1 2 2 2 2 3
3 3 2 3 2 4 4 2 3 4
3 4 5 4 3 5 3 4 6 3
5 6 2 5 6 5 5 7 4 5
8 5 4 9 4 5 7 3 6 8
5 6 8 6 7 10 6 6 12 4
5 10 3 7 9 6 5 8 7 8
11 6 5 12 4 8 11 5 8 10
5 6 13 9 6 11 7 7 14 6
8 13 5 8 11 7 9 13 8 9
G 1000000: 5402</pre>
Stretch goal: (offsite image) [https://github.com/SqrtNegInf/Rosettacode-Perl-Smoke/blob/master/ref/goldbachs-comet.png goldbachs-comet.png]
=={{header|Phix}}==
{{libheader|Phix/pGUI}}
{{libheader|Phix/online}}
You can run this online [http://phix.x10.mx/p2js/goldbach.htm here].
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #000080;font-style:italic;">--
-- demo\rosetta\Goldbachs_comet.exw
-- ================================
--
-- Note: this plots n/2 vs G(n) for n=6 to 4000 by 2, matching wp and
-- Algol 68, Python, and Raku. However, while not wrong, Arturo
-- and Wren apparently plot n vs G(n) for n=6 to 2000 by 2, so
-- should you spot any (very) minor differences, that'd be why.
--</span>
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #7060A8;">requires</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"1.0.2"</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">limit</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">4000</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">primes</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">get_primes_le</span><span style="color: #0000FF;">(</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">)[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">..$],</span>
<span style="color: #000000;">goldbach</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">reinstate</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">),{</span><span style="color: #000000;">4</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">primes</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">i</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">primes</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">primes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">primes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">></span><span style="color: #000000;">limit</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">goldbach</span><span style="color: #0000FF;">[</span><span style="color: #000000;">s</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">fhg</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">extract</span><span style="color: #0000FF;">(</span><span style="color: #000000;">goldbach</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">tagstart</span><span style="color: #0000FF;">(</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">))</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">fhgs</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">join_by</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fhg</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%2d"</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">gm</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1e6</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">get_primes_le</span><span style="color: #0000FF;">(</span><span style="color: #000000;">499999</span><span style="color: #0000FF;">)[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">..$]),</span><span style="color: #7060A8;">is_prime</span><span style="color: #0000FF;">))</span>
<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;">"The first 100 G values:\n%s\n\nG(1,000,000) = %,d\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">fhgs</span><span style="color: #0000FF;">,</span><span style="color: #000000;">gm</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">include</span> <span style="color: #000000;">pGUI</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
<span style="color: #008080;">include</span> <span style="color: #000000;">IupGraph</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">get_data</span><span style="color: #0000FF;">(</span><span style="color: #004080;">Ihandle</span> <span style="color: #000080;font-style:italic;">/*graph*/</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{{</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">extract</span><span style="color: #0000FF;">(</span><span style="color: #000000;">goldbach</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">)),</span><span style="color: #004600;">CD_RED</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">extract</span><span style="color: #0000FF;">(</span><span style="color: #000000;">goldbach</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">)),</span><span style="color: #004600;">CD_BLUE</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">extract</span><span style="color: #0000FF;">(</span><span style="color: #000000;">goldbach</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">)),</span><span style="color: #004600;">CD_DARK_GREEN</span><span style="color: #0000FF;">}}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #7060A8;">IupOpen</span><span style="color: #0000FF;">()</span>
<span style="color: #004080;">Ihandle</span> <span style="color: #000000;">graph</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">IupGraph</span><span style="color: #0000FF;">(</span><span style="color: #000000;">get_data</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"RASTERSIZE=640x440,MARKSTYLE=PLUS"</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">IupSetAttributes</span><span style="color: #0000FF;">(</span><span style="color: #000000;">graph</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"XTICK=%d,XMIN=0,XMAX=%d"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">/</span><span style="color: #000000;">20</span><span style="color: #0000FF;">,</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">})</span>
<span style="color: #7060A8;">IupSetAttributes</span><span style="color: #0000FF;">(</span><span style="color: #000000;">graph</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"YTICK=20,YMIN=0,YMAX=%d"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">max</span><span style="color: #0000FF;">(</span><span style="color: #000000;">goldbach</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">20</span><span style="color: #0000FF;">})</span>
<span style="color: #004080;">Ihandle</span> <span style="color: #000000;">dlg</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupDialog</span><span style="color: #0000FF;">(</span><span style="color: #000000;">graph</span><span style="color: #0000FF;">,</span><span style="color: #008000;">`TITLE="Goldbach's comet",MINSIZE=400x300`</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">IupShow</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dlg</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()!=</span><span style="color: #004600;">JS</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">IupMainLoop</span><span style="color: #0000FF;">()</span>
<span style="color: #7060A8;">IupClose</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
The first 100 G values:
1 1 1 2 1 2 2 2 2 3
3 3 2 3 2 4 4 2 3 4
3 4 5 4 3 5 3 4 6 3
5 6 2 5 6 5 5 7 4 5
8 5 4 9 4 5 7 3 6 8
5 6 8 6 7 10 6 6 12 4
5 10 3 7 9 6 5 8 7 8
11 6 5 12 4 8 11 5 8 10
5 6 13 9 6 11 7 7 14 6
8 13 5 8 11 7 9 13 8 9
G(1,000,000) = 5,402
</pre>
=={{header|Picat}}==
<syntaxhighlight lang="picat">main =>
println("First 100 G numbers:"),
foreach({G,I} in zip(take([G: T in 1..300, G=g(T),G>0],100),1..100))
printf("%2d %s",G,cond(I mod 10 == 0,"\n",""))
end,
nl,
printf("G(1_000_000): %d\n", g(1_000_000)).
g(N) = cond((N > 2, N mod 2 == 0),
{1 : I in 1..N // 2,
prime(I),prime(N-I)}.len,
0).</syntaxhighlight>
{{out}}
<pre>First 100 G numbers:
1 1 1 2 1 2 2 2 2 3
3 3 2 3 2 4 4 2 3 4
3 4 5 4 3 5 3 4 6 3
5 6 2 5 6 5 5 7 4 5
8 5 4 9 4 5 7 3 6 8
5 6 8 6 7 10 6 6 12 4
5 10 3 7 9 6 5 8 7 8
11 6 5 12 4 8 11 5 8 10
5 6 13 9 6 11 7 7 14 6
8 13 5 8 11 7 9 13 8 9
G(1_000_000): 5402</pre>
=={{header|Python}}==
<
from sympy import isprime
Line 445 ⟶ 1,479:
colors = [["red", "blue", "green"][(i // 2) % 3] for i in x]
scatter([i // 2 for i in x], y, marker='.', color = colors)
show()</
<pre>
The first 100 G numbers are:
Line 461 ⟶ 1,495:
The value of G(1000000) is 5402
</pre>
[[File:PGoldbachplot.png]]
=={{header|Raku}}==
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]].)
<syntaxhighlight lang="raku"
# Task
Line 487 ⟶ 1,522:
values => [@y,],
).plot: :points;
</syntaxhighlight>
{{out}}
<pre>The first 100 G values:
Line 504 ⟶ 1,539:
'''Stretch goal:''' (offsite SVG image) [https://raw.githubusercontent.com/thundergnat/rc/master/img/Goldbachs-Comet-Raku.svg Goldbachs-Comet-Raku.svg]
=={{header|RPL}}==
{{works with|HP|49}}
« '''IF''' 2 MOD '''THEN'''
"GOLDB Error: Odd number" DOERR
'''ELSE'''
0
2 PICK3 2 / CEIL '''FOR''' j
'''IF''' j ISPRIME? '''THEN'''
'''IF''' OVER j - ISPRIME? '''THEN''' 1 + '''END'''
'''END'''
'''NEXT''' NIP
'''END'''
» '<span style="color:blue">GOLDB</span>' STO
« « n <span style="color:blue">GOLDB</span> » 'n' 4 202 2 SEQ
OBJ→ DROP { 10 10 } →ARRY
1000000 <span style="color:blue">GOLDB</span> "G(1000000)" →TAG
» '<span style="color:blue">TASK</span>' STO
{{out}}
<pre>
2: [[ 1 1 1 2 1 2 2 2 2 3 ]
[ 3 3 2 3 2 4 4 2 3 4 ]
[ 3 4 5 4 3 5 3 4 6 3 ]
[ 5 6 2 5 6 5 5 7 4 5 ]
[ 8 5 4 9 4 5 7 3 6 8 ]
[ 5 6 8 6 7 10 6 6 12 4 ]
[ 5 10 3 7 9 6 5 8 7 8 ]
[ 11 6 5 12 4 8 11 5 8 10 ]
[ 5 6 13 9 6 11 7 7 14 6 ]
[ 8 13 5 8 11 7 9 13 8 9 ]]
1: G(1000000): 5402
</pre>
=={{header|Ruby}}==
following the J comments, but only generating primes up-to half a million
<syntaxhighlight lang="ruby">require 'prime'
n = 100
puts "The first #{n} Godbach numbers are: "
sums = Prime.each(n*2 + 2).to_a[1..].repeated_combination(2).map(&:sum)
sums << 4
sums.sort.tally.values[...n].each_slice(10){|slice| puts "%4d"*slice.size % slice}
n = 1000000
puts "\nThe value of G(#{n}) is #{Prime.each(n/2).count{|pr| (n-pr).prime?} }."
</syntaxhighlight>
{{out}}
<pre>The first 100 Godbach numbers are:
1 1 1 2 1 2 2 2 2 3
3 3 2 3 2 4 4 2 3 4
3 4 5 4 3 5 3 4 6 3
5 6 2 5 6 5 5 7 4 5
8 5 4 9 4 5 7 3 6 8
5 6 8 6 7 10 6 6 12 4
5 10 3 7 9 6 5 8 7 8
11 6 5 12 4 8 11 5 8 10
5 6 13 9 6 11 7 7 14 6
8 13 5 8 11 7 9 13 8 9
The value of G(1000000) is 5402.
</pre>
=={{header|Rust}}==
<syntaxhighlight lang="rust">// [dependencies]
// primal = "0.3"
// plotters = "0.3.2"
use plotters::prelude::*;
fn goldbach(n: u64) -> u64 {
let mut p = 2;
let mut count = 0;
loop {
let q = n - p;
if q < p {
break;
}
if primal::is_prime(p) && primal::is_prime(q) {
count += 1;
}
if p == 2 {
p += 1;
} else {
p += 2;
}
}
count
}
fn goldbach_plot(filename: &str) -> Result<(), Box<dyn std::error::Error>> {
let gvalues : Vec<u64> = (1..=2000).map(|x| goldbach(2 * x + 2)).collect();
let mut gmax = *gvalues.iter().max().unwrap();
gmax = 10 * ((gmax + 9) / 10);
let root = SVGBackend::new(filename, (1000, 500)).into_drawing_area();
root.fill(&WHITE)?;
let mut chart = ChartBuilder::on(&root)
.x_label_area_size(20)
.y_label_area_size(20)
.margin(10)
.caption("Goldbach's Comet", ("sans-serif", 24).into_font())
.build_cartesian_2d(0usize..2000usize, 0u64..gmax)?;
chart
.configure_mesh()
.disable_x_mesh()
.disable_y_mesh()
.draw()?;
chart.draw_series(
gvalues
.iter()
.cloned()
.enumerate()
.map(|p| Circle::new(p, 2, BLUE.filled())),
)?;
Ok(())
}
fn main() {
println!("First 100 G numbers:");
for i in 1..=100 {
print!(
"{:2}{}",
goldbach(2 * i + 2),
if i % 10 == 0 { "\n" } else { " " }
);
}
println!("\nG(1000000) = {}", goldbach(1000000));
match goldbach_plot("goldbach.svg") {
Ok(()) => {}
Err(error) => eprintln!("Error: {}", error),
}
}</syntaxhighlight>
{{out}}
<pre>
First 100 G numbers:
1 1 1 2 1 2 2 2 2 3
3 3 2 3 2 4 4 2 3 4
3 4 5 4 3 5 3 4 6 3
5 6 2 5 6 5 5 7 4 5
8 5 4 9 4 5 7 3 6 8
5 6 8 6 7 10 6 6 12 4
5 10 3 7 9 6 5 8 7 8
11 6 5 12 4 8 11 5 8 10
5 6 13 9 6 11 7 7 14 6
8 13 5 8 11 7 9 13 8 9
G(1000000) = 5402
</pre>
[[Media:Goldbach's comet rust.svg]]
=={{header|Wren}}==
{{libheader|DOME}}
{{libheader|Wren-math}}
{{libheader|Wren-
{{libheader|Wren-fmt}}
{{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.
<syntaxhighlight lang="wren">import "dome" for Window
import "graphics" for Canvas, Color
import "./math2" for Int
import "./iterate" for Stepped
import "./fmt" for Fmt
import "
var limit =
var primes = Int.primeSieve(limit-1).skip(1).toList
var goldbach = {4: 1}
Line 541 ⟶ 1,739:
System.print("\nG(1000000) = %(gm)")
var Red = []
var Blue = []
var Green = []
// create lists for the first 2000 G values for plotting by DOME.
for(e in Stepped.new(4..limit, 2)) {
var c = e % 6
var n = e/2 - 1
if (c == 0) {
Red.add([n, goldbach[e]])
} else if (c == 2) {
Blue.add([n, goldbach[e]])
} else {
Green.add([n, goldbach[e]])
}
}
class Main {
construct new() {
Window.title = "Goldbach's comet"
Canvas.resize(1000, 600)
Window.resize(1000, 600)
Canvas.cls(Color.white)
var axes = Axes.new(100, 500, 800, 400, 0..2000, 0..200)
axes.draw(Color.black, 2)
var xMarks = Stepped.new(0..2000, 200)
var yMarks = Stepped.new(0..200, 20)
axes.mark(xMarks, yMarks, Color.black, 2)
var xMarks2 = Stepped.new(0..2000, 400)
var yMarks2 = Stepped.new(0..200, 40)
axes.label(xMarks2, yMarks2, Color.black, 2, Color.black)
axes.plot(Red, Color.red, "+")
axes.plot(Blue, Color.blue, "+")
axes.plot(Green, Color.green, "+")
}
init() {}
update() {}
draw(alpha) {}
}
var Game = Main.new()</syntaxhighlight>
{{out}}
Line 567 ⟶ 1,802:
=={{header|XPL0}}==
<syntaxhighlight lang="xpl0">
func IsPrime(N); \Return 'true' if N is prime
int N, I;
Line 610 ⟶ 1,845:
Text(0, "G(1,000,000) = "); IntOut(0, G(1_000_000));
CrLf(0);
]</
{{out}}
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