Akshay Venkatesh recently gave a nice public lecture at the IAS on the analogy between primes and knots.
The analogy involves a conversion factor, which is described in the talk as follows: given a 100 digit prime number, one digit of the number corresponds to "2.3 units of length of the tangle" (this appears at 26:00 in the talk).
My question is: what is the precise definition of this conversion factor and/or where can I read more about it?
Because the talk was a public lecture, the description given there was heuristic and references to the literature were not given.
