The easiest way to do this for integers is to use hexadecimal, provided that there isn't something like Int.maxInt(). The reason is this:
Max unsigned values
8-bit 0xFF
16-bit 0xFFFF
32-bit 0xFFFFFFFF
64-bit 0xFFFFFFFFFFFFFFFF
128-bit 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
Signed values, using 7F as the max signed value
8-bit 0x7F
16-bit 0x7FFF
32-bit 0x7FFFFFFF
64-bit 0x7FFFFFFFFFFFFFFF
Signed values, using 80 as the max signed value
8-bit 0x80
16-bit 0x8000
32-bit 0x80000000
64-bit 0x8000000000000000
How does this work? This is very similar to the binary tactic, and each hex digit is exactly 4 bits. Also, a lot of compilers support hex a lot better than they support binary.
F hex to binary: 1111
8 hex to binary: 1000
7 hex to binary: 0111
0 hex to binary: 0000
So 7F is equal to 01111111 / 7FFF is equal to 0111111111111111. Also, if you are using this for "insanely-high constant", 7F... is safe hex, but it's easy enough to try out 7F and 80 and just print them to your screen to see which one it is.
0x7FFF + 0x0001 = 0x8000, so your loss is only one number, so using 0x7F... usually isn't a bad tradeoff for more reliable code, especially once you start using 32-bits or more