What is the product of the greatest prime number that is less than 50 and the smallest prime number that is greater than 50?

Answer

To solve the problem, we need to find the product of the greatest prime number that is less than 50 and the smallest prime number that is greater than 50. Let's break this down step by step.

### Step 1: Identify the greatest prime number less than 50.
- We will list the prime numbers less than 50:
- The prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.
- The greatest prime number in this list is **47**.

### Step 2: Identify the smallest prime number greater than 50.
- We will list the prime numbers greater than 50:
- The prime numbers are: 53, 59, 61, 67, ...
- The smallest prime number in this list is **53**.

### Step 3: Calculate the product of the two identified prime numbers.
- Now, we need to calculate the product of 47 and 53:
- \( 47 \times 53 \)

### Step 4: Perform the multiplication.
- We can break down the multiplication:
- \( 47 \times 53 = 2491 \)

### Final Answer:
The product of the greatest prime number less than 50 and the smallest prime number greater than 50 is **2491**.

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