Find the next term in the pattern 7 : 11 : : 31 : ?

Concept: This is a number-based analogy in which each pair links a number to the very next prime number after it — the rule governing the pattern is "the second term is the next prime greater than the first term."

Application:

1. Check the first pair, 7 : 11 — 7 is prime; testing 8, 9, 10 (all composite) shows 11 is indeed the next prime after 7, confirming the rule.

2. Apply the same rule to 31 : ? — 31 is prime; test 32, 33, 34, 35, 36 in turn.

3. 32 = 2 × 16, 33 = 3 × 11, 34 = 2 × 17, 35 = 5 × 7, and 36 = 6 × 6 are all composite, so none of them is prime.

4. 37 has no factor other than 1 and itself, so 37 is the next prime number after 31.

Cross-check: among the given values, 33 (3 × 11), 39 (3 × 13), and 42 (2 × 3 × 7) are all composite, so only 37 satisfies the pattern's rule, confirming it as the next term.