Yeah, that should be be 3!(23)-1. The multiplicative group
of a prime order that extends to an additive group when the
extra (0) element is included. 137 and 139 are twin primes,
and their product is 138^2 - 1 = [3!(23)]^2.
Try that again. And it is NOT the experimental value!
The experimental value is (1-e)/137, where 0<e<<1.
I.e., a perturbation. Thanks for your post!