That's a nice idea. I guess it's better to stay in primitive type range (to avoid long arithmetics), so we can "compress" up to 15 items into a single prime_product making it less than 2^64 - for English words should be just fine, I don't expect many words with 16 and more letters.

UPD: Sorry, "up to 15" is a wrong phrasing. I checked once how "prime factorial" fits into primitive, and first 15 primes can fit into long. So it's possible to handle even more symbols if it's smth like "aaaaaaa"64 times because it would be just 2^64