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

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