this question is unprecedented: it's honestly the first question i've ever seen on which it's simply impossible to compute the actual answer choice within the time limit. in other words, this is the first, and only, problem i've ever seen on which you must use the 'ok, i know i can solve this one, but i won't bother' reasoning; on all other problems, that can be a nice way to save time, but it's not, strictly speaking, necessary, as it is here.

this is a really freaky problem, then; it will be interesting to see if it's just a one-off thing or if it portends a rising tide of problems requiring increasingly abstract reasoning.

--

in any case:

(2) must be sufficient, as there is obviously some fixed number of primes between 1 and 3912. we don't care what that number is, because it's clear that there's only one such number (the number of primes in a fixed range isn't about to change anytime soon).

(1) also sufficient: p is a prime number, so:
if p is the 100th prime, then there are 100 primes - viz., the first 100 primes - between 1 and p + 1.
if p is the 101th prime or later, then there are 101 or more primes, so that's no good.
if p is the 99th prime or earlier, then there are 99 or fewer primes; also no good.
therefore, p is the 100th prime.

answer = d

incidentally, the actual value of p is 541.