[axelsvensson]

I feel like that would fail. The reason is that Gödel numbers are rather arbitrary, and will therefore be rather far from a form that insights can be gleaned from. They are a representation of a representation, using the fundamental theorem of arithmetic only as a trick to encode any string of symbols into one integer.

As an example of just how arbitrary Gödel numbers are, consider the expressions `((3*n)+1)` and `((n*3)+1)`. Those expressions are clearly equivalent, yet the Gödel numbers for those two expressions are wildly different, with a relation that is rather complex.

IIUC Gödel himself never "used" or analyzed Gödel numbers as such, only the idea that they could be constructed.

[koheripbal]

In your example, the Godel number works out to be the same when you multiply them out - but your underlying point is valid that the assignment of primes to variables and operators cannot be as arbitrary as Godel used them as.

...a better example is just "x 1". You could add that ad infinitum to any equation and it cannot change the meaning of the outputted Godel number. ...but remember that getting a different result does not mean the interpretation of the Godel number is different. For example, multiples of ten are also even. 64 and 9 are different numbers, but they are both perfect squares. ...and the goal is to find something descriptive of the resultant number - not the number itself.

...but that's one of the main areas to explore. There are different types of primes to experiment with to see if anything meaningful can be discovered.

[sdwr]

If you multiply it out, then it's just a regular number?

Your idea smells like wishful thinking.