2022 AMC 10B Problems/Problem 13
Solution
Let the two primes be and
. We would have
and
Solution 2
Let the two primes be and
such that
and
By the difference of cubes formula,
Plugging in and
,
Through the givens, we can see that .
Thus,
Checking prime pairs near , we find that
The least prime greater than these two primes is
~BrandonZhang202415