2023 AMC 8 Problems/Problem 4

The numbers from 1 to 49 are arranged in a spiral pattern on a square grid, beginning at the center. The first few numbers have been entered into the grid below. Consider the four numbers that will appear in the shaded squares, on the same diagonal as the number 7. How many of these four numbers are prime?

$\textbf{(A)}\ 0 \qquad \textbf{(B)}\ 1 \qquad \textbf{(C)}\ 2 \qquad \textbf{(D)}\ 3 \qquad \textbf{(E)}\ 4$

Solution 1

First, we fill out the entire grid. We find that the four numbers are $39,19,23,47$ . The numbers $19,23,$ and $47$ are prime, so there are $\boxed{\textbf{(D) }3}$ prime numbers.

~MathFun1000

Solution 2

Fill out the entire grid to count that there are $\boxed{\text{(D)}3}$ -apex304

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2023 AMC 8 Problems/Problem 4

Solution 1

Solution 2