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