$30 \cdot 10$ The famous Goldbach's conjecture states that any even integer greater than 7 can be written as the sum of two distinct primes. Using this method to represent the even number 126, the largest difference between the two primes is
(A) 112.
(B) 100.
(C) 92.
(D) 88.
(E) 80.
(24th American High School Mathematics Examination, 1973)
[Solution] $p=13$ is the smallest prime number that makes $126-p$ also a prime number. Therefore, the largest difference is $113-13=100$.
Thus, the answer is $(B)$.
Note: The number 126 can be expressed as the sum of two prime numbers in ten ways:
$$
\begin{array}{l}
13+113, \quad 17+109, \quad 19+107, \quad 23+103, \quad 29+97, \quad 37+89, \\
43+83, \quad 47+79, \quad 53+73, \quad 59+67 .
\end{array}
$$