[Retros] A single integer N = a complete chess game

[Eric Angelini]

Hello RetroChess and Seq fans!
(crossposted to both groups in two separated mails)

Since Gödel's works we know we can assignate a unique integer to
almost anything (a 1000 words poetry, a Rothko painting, a walk
of Hamish Fulton, etc.) -- anything "with an end", of course.

[If I remember well the technique would use prime exponents:
N = a^2 * b^3 * c^5 * d^7 * e^11 * ... with a, b, c, d, e, ...
being "plys" http://en.wikipedia.org/wiki/Ply_(game_theory) ]

What would be the most "economical way" to assign a single number
to a complete chess game? I guess this number would be of googol-
length...

An easier (?) task would be to transform a _chess position_ into
a single integer (using X-FEN? http://en.wikipedia.org/wiki/X-FEN )

But I know that the retro-content of a position is very difficult
to encode (e.p and castling rights, for instance) -- so the task
of encoding a full game into a single integer (from the starting 
position onwards) might be simpler.

Sorry if this is old hat.

Best,
É.