AMC8 2023

AMC8 2023 · Q4

AMC8 2023 · Q4. It mainly tests Casework, Primes & prime factorization.

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?

数字从 $1$ 到 $49$ 在一个正方形网格上以螺旋图案排列，从中心开始。下面网格中已填入了前几个数字。考虑将出现在阴影方块中的四个数字，这些方块与数字 $7$ 在同一条对角线上。其中有多少个是质数？

(A) \ 0 \ 0

(B) \ 1 \ 1

(D) \ 3 \ 3

(E) \ 4 \ 4

Answer

Correct choice: (D)

正确答案：（D）

Solution

We fill out the grid, as shown below: From the four numbers that appear in the shaded squares, $\boxed{\textbf{(D)}\ 3}$ of them are prime: $19,23,$ and $47.$

我们填完网格，如下所示：在阴影方块中出现的四个数字中，\boxed{\textbf{(D)}\ 3} 个是质数：$19,23,$ 和 $47$ 。

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