Data update

Task/Goldbachs-comet/Pluto/goldbachs-comet-1.pluto

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+do  -- Goldbach's comet, translation of Lua
+
+    local int = require( "int" )      -- RC Pluto integer library, inc. prime utilities
+
+    local function goldbach( n : number ) : number
+        local count = 0
+        for i = 1, n // 2 do
+            if int.isprime( i ) and int.isprime( n - i ) then
+                ++ count
+            end
+        end
+        return count
+    end
+
+    print( "The first 100 G numbers:" )
+    print( range( 100 ):map( | n | -> string.format( "%2d"..if n % 10 == 0 then "\n" else " " end
+                                                   , goldbach( 2 + n * 2 )
+                                                   )
+                           )
+                       :concat( "" )
+         )
+    print( $"G(1000000) = { goldbach( 1_000_000 ) }" )
+end

Task/Goldbachs-comet/Pluto/goldbachs-comet-2.pluto

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+do  -- create a bitmap of Goldbach's Comet
+
+    local int = require( "int" )      -- RC Pluto integer library, inc. prime utilities
+    require( "bitmap" )               -- RC bitmap library
+
+    local bmp = bitmap.of( 400, 240, color.black, "Goldbachs_comet_Pluto" )
+
+    local maxG <const>, maxP <const> = 4000, 1_000_000
+    local rootMaxP <const>, halfMaxG <const> = math.floor( math.sqrt( maxP ) ), maxG // 2
+
+    local prime <const> = int.arecomps( maxP ):map( | v | -> not v ) -- sieve the primes to maxP
+
+    local G <const> = {}                                       -- construct a table of G numbers
+    for i = 1, maxG do G[ i ] = 0 end
+    G[ 4 ] = 1                                             -- 4 is the only sum of 2 even primes
+    for i = 3, halfMaxG, 2 do
+        if prime[ i ] then
+            G[ i + i ] += 1
+            for j = i + 2, maxG - i do
+                if prime[ j ] then
+                    G[ i + j ] += 1
+                end
+            end
+        end
+    end
+    -- print the first few G numbers to the bitmap - 8x8 charaxters
+    local c, tx, ty = 0, 2, 2
+    for i = 4, 202, 2 do
+        c += 1
+        bmp:text( string.format( "%3d", G[ i ] ), tx, ty, color.white, 1 )
+        if c % 10 != 0 then
+            tx += 24
+        else
+            tx, ty = 2, ty + 10
+        end
+    end
+    local Gm = 0
+    for i = 3, maxP // 2, 2 do
+        if prime[ i ] then
+            if prime[ maxP - i ] then Gm += 1 end
+        end
+    end
+    -- print G(1_000_000) to the bitmap
+    bmp:text( string.format( "G(%d): %d", maxP, Gm ), 2, ty + 10, color.white, 1 )
+    for i = 2, maxG - 10, 10 do
+        local maxY = 0
+        local x <const> = i // 10
+        for j = i, i + 8, 2 do
+            if G[ j ] > 0 then
+                local y <const> = 240 - G[ j ]
+                bmp:set( x, y, switch bmp:get( x, y ) do
+                                      case color.black  -> color.orange
+                                      case color.orange -> color.yellow
+                                      default           -> color.white
+                               end
+                       )
+                if y > maxY then maxY = y end
+            end
+        end
+        -- we're going to save it as a png, so convert from BGR to RGb
+        for j = 1, maxY do
+            local bgr <const> = bmp:get( x, j )
+            if bgr != color.black then
+                bmp:set( x, j, bmp.flipColor( bgr ) )
+            end
+        end
+    end
+    bmp:view( true )
+end