@pxeger I'll add a comment once I post this

Allowing duplicates makes the challenge a bit easier, since you don't have to simplify the exponents. Basically without duplicates there are two parts to the program, one is the recursion part (factor to primes and recurse) and the other one is the simplification. If duplicates are allowed, then simplification is not necessary so the answers will be shorter. Personally I slightly prefer allowing duplicates, since the answers would be a bit more "focused". But I think if you allow duplicates then you should also allow a 0 exponent.

Are duplicate prime numbers allowed? (is 36 = 3#3 3#-1 or 36 = 3#1 3#1 valid?)

The base 10 logarithm feels a bit arbitrary. This also means that there are no heavy numbers if \$b>9\$

@Jitse Different distributions can have the same standard deviation. Perhaps you forgot to specify that the radius of the points should have a normal distribution?

@l4m2 Yes, that's right, I'll fix it

@l4m2 Yes, otherwise it wouldn't be turing complete.