implement PrimeHash game for plasma prime

[snjax]

PrimeHash game for Plasma Prime

We need to use the mapping between integers and prime numbers for some cases in Plasma Prime:

• calculating $H_{prime}$ for Wesolowski proof
• calculating prime numbers for each coin

Also, it will be useful if we can use it without any precomputations in lazy mode. I propose to use something like truebit protocol for deterministic mapping any uint256 number (excluding 0 and 1) to a prime number.

Let's determine $ Prime(I) := \max(n: 1 < n \leq I; n \in P) $.

We do not use any better computable subsets in the set of prime numbers, because it brings us additional work in the contract, as you can see below. $Prime(I)$ is not complicated to compute offchain for any 256bit I (not only PC but also cell phones are OK).

We can enumerate all plasma dust coins as $Prime(I*offset)$ and use not only $2^{40}$, but also $2^{50}$ or more dust coins and do not need to store the data anywhere.

Also we can use $PrimeHash(x) := Prime(keccak256(x))$ for $H_{prime}$ calculation.

For onchain cases let's use the game:

The game is simply generalizable for calculation with multiple prime numbers (it is enough to challenge one value to reject the calculation).