Find out the unit digit in product of all prime numbers in between 1 and 99999.

Options

A. 9
B. 7
C. 0
D. None of these

Answer

To find the unit digit in the product of all prime numbers between 1 and 99999, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Prime Numbers**:
The prime numbers between 1 and 99999 include 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, and many more up to 99999.

2. **Focus on the Unit Digit**:
We need to find the unit digit of the product of these prime numbers. The unit digit of a product is determined by the unit digits of the factors involved.

3. **Identify Key Prime Numbers**:
Notice that among the prime numbers, we have:
- The prime number **2** (unit digit = 2)
- The prime number **5** (unit digit = 5)

4. **Calculate the Product of Key Primes**:
When we multiply 2 and 5, we get:
\[ 2 \times 5 = 10 \]
The unit digit of 10 is **0**.

5. **Conclusion**:
Since the product of the prime numbers includes both 2 and 5, the overall product will have a unit digit of **0**. This is because any number multiplied by 10 will end with a unit digit of 0.

### Final Answer:
The unit digit in the product of all prime numbers between 1 and 99999 is **0**.