updated Readme

Signed-off-by: Matteo Muraca <mmuraca247@gmail.com>

README.md

@@ -1,13 +1,15 @@
 # Halo2 Playground
 
-This crate contains the implementation of a circuit that builds a
-Zero Knowledge Proof of the fact that the prover knows a solution
-to a given sudoku problem.
+This crate contains the implementation of two circuits that build a Zero Knowledge Proof:
+
+1. Given a public witness `b` that is a Sudoku board, the circuit is a proof that the prover knows a solution `s` for the Sudoku puzzle.
+2. Given a public witness `w` and a public constant `k`, the prover knows a secret witness such that `w = n * (n + 1) * (n + 2) * ... * (n + k)`. When `n = 1`, the circuit is a proof that `w` is a factorial number.
 
 We wrote this crate to get a first-hand feeling of the user friendlyness
 of the [Halo2](https://github.com/zcash/halo2) proving system.
 
 ## Running the tests
+
 To run the tests, run the command `cargo test --release`.
 The command `cargo test` works too, but in that case you may want
 to give your computer a couple of minutes to compute the test results.
@@ -17,12 +19,15 @@ The single circuits can be tested by matching the test name with `sudoku`, `perm
 The tests that match the `mock` pattern are written using the `MockProver` struct, while the others use the custom real-world provers.
 
 ### Running via Docker
+
 To run the tests via Docker, the simplest way is to use the image published by CI:
+
 ```bash
 docker run --rm --network host ghcr.io/libecciolabs/halo2-playground:main
 ```
 
 You can always build the docker image yourself:
+
 ```bash
 git clone https://github.com/LibeccioLabs/Halo2-Playground/
 docker build -t halo2-playground ./Halo2-Playground/
@@ -31,6 +36,7 @@ docker run --rm halo2-playground
 
 Since the Docker image will run `cargo test --release`, you can append any other flag, including a match for the tests you want to run.
 For example, to run only the tests in the `sudoku` module, you can run:
+
 ```bash
 docker run --rm halo2-playground sudoku
 ```