For a prime $q$, let $\Phi_q(x) = x^{q-1} + x^{q-2} + \cdots + x + 1$. 
Find the sum of all primes $p$ such that $3 \le p \le 100$ and there exists an odd prime $q$ and a positive integer $N$ satisfying
\[\binom{N}{\Phi_q(p)} \equiv \binom{2\Phi_q(p)}{N} \not\equiv 0 \pmod{p}.\]

Let's think step by step and output the final answer within \boxed{}.
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