7. Encode the letters $a \sim z$ as $(\mathbf{a}=1, \mathbf{b}=2, \ldots, \mathbf{z}=26)$, so that each English word (all letters in the word are considered lowercase) can have the product $\mathbf{p}$ of the encodings of all its letters calculated. For example, for the word good, the corresponding $\mathbf{p}$ value is $7 \times 15 \times 15 \times 4=6300$ (since $g=7, o=15, d=4$). If a composite number cannot be represented as the $\mathbf{p}$ value of any word (regardless of whether the word is meaningful), such a composite number is called a “zhonghuan number”. The smallest three-digit “zhonghuan number” is . $\qquad$
【Analysis】(Method one) To be a "middle ring number", the prime factors decomposed must include at least one prime factor greater than 26: The prime numbers greater than 26 are $29, 31, 37 \cdots, 29 \times 4 = 116$, which is definitely a middle ring number, so it is necessary to verify whether there are any middle ring numbers less than 107. At this point, it is found that 106 is the smallest one;
(Method two) The method used by most children, directly starting from the smallest three-digit composite number.
$100, 102, 104, 105, 106$, then it is found that 106 is the first one that meets the criteria, $106 = 2 \times 53$. So the answer is 106.