A number is Beprisque if it is the only natural number between a prime number and a perfect square (e.g. 10 is Beprisque but 12 is not). The number of two-digit Beprisque numbers (including 10) is
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
A number is Beprisque if it is the only natural number between a prime number and a perfect square (e.g. 10 is Beprisque but 12 is not). The number of two-digit Beprisque numbers (including 10) is
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

## Solution

We start with the observation that it is necessary to consider only the odd perfect squares and the integers adjacent to them. It is not necessary to consider the even perfect squares because if we add 2 or subtract 2 from an even number the result is even and it is required by the conditions set out in the question that this number be prime. Considering then the odd perfect squares we have: $\{9,(10,11\}$, $\{23,(44), 25,26,27\},\{47,48,49,50,51\},\{79,80,81,82,83\}$.

The Beprisque numbers are those that are circled.

ANSWER: (E)