do  -- find some Humble numbers - numbers with no prime factors above 7
    local maxHumble <const>, maxShownHumble <const> = 2048, 50
    local h, hCount      = {}, { [0] = 0, 0, 0, 0, 0, 0, 0 }
    local p2, p3, p5, p7 = 2, 3, 5, 7
    local last2, last3, last5, last7 = 1, 1, 1, 1
    -- 1 is the first humble number ( 2^0 * 3^0 * 5^0 * 7^0 ) and has 1 digit
    h[ 1 ], hCount[ 1 ]  = 1, 1
    io.write( "1" )
    for n = 2, maxHumble do
        -- the next humble number is the lowest of the next multiples of 2, 3, 5, 7
        local m = math.min( p2, p3, p5, p7 )
        h[ n ] = m
        if n <= maxShownHumble then io.write( " ", m ) end
        if m == p2 then last2 += 1  p2 = 2 * h[ last2 ] end
        if m == p3 then last3 += 1  p3 = 3 * h[ last3 ] end
        if m == p5 then last5 += 1  p5 = 5 * h[ last5 ] end
        if m == p7 then last7 += 1  p7 = 7 * h[ last7 ] end
        hCount[ ( m <        10 ) ? 1
              : ( m <       100 ) ? 2
              : ( m <     1_000 ) ? 3
              : ( m <    10_000 ) ? 4
              : ( m <   100_000 ) ? 5
              : ( m < 1_000_000 ) ? 6
              :                     0
              ] += 1
    end
    io.write( "\n" )
    for i = 1, 6 do
        io.write( string.format( "There are %4d Humble numbers with %d digits\n", hCount[ i ], i ) )
    end
end