Why is '397' used for ReSharper GetHashCode override?
Solution 1:
Probably because 397 is a prime of sufficient size to cause the result variable to overflow and mix the bits of the hash somewhat, providing a better distribution of hash codes. There's nothing particularly special about 397 that distinguishes it from other primes of the same magnitude.
Solution 2:
The hash that resharper uses looks like a variant of the FNV hash. FNV is frequently implemented with different primes. There's a discussion on the appropriate choice of primes for FNV here.