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UKMT Junior Mathematical Challenge, 2023

Number theory Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

When this prime number square is completed, the eight circles contain eight different primes, and each of the four sides has total 43. The diagram shows a square arrangement of eight circles, one at each corner and one at the midpoint of each side. The circle at the top-left has the value $13$ , the circle at the top-right has the value $23$ , and the circle at the bottom (second from left) has the value $29$ . What is the sum of the five missing primes?

(A) $51$ (B) $53$ (C) $55$ (D) $57$ (E) $59$

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