A nerdy idea:
A C# class that quicly can supply a lot of primes (here limited to about the largest prime about 50G – as arrays with over 2G entries are not currently supported without splitting the arrays)
A struct that supports basic arithmetic for large accurately represented numbers in Q, by factorization into primes.
A test program that tries to find solutions for a!b!=c! with 1<a<b<c