Second-pass fixed bugs:

16. oops exponent of 3 off by one
22. oops triple-negated the condition somewhere AND 11 | 2013 ergo 230 is ok
27. oops exponent of denominator (without the binomial coefficient) off by one

Waking-up-20-minutes-before-contest-deadline-induced-paranoia fixed bugs:

20. oops 407 isn't a prime

Unfixed bugs:

28. oops 31 + 1 = 32

And I didn't get 30 (I was all "hmm let's perform magic with the Galois group of this polynomial because obviously that's what people do with the last problem of contests" and never felt like bashing it for one second)

So, perfect score!