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The number of prime number divisible by ...

The number of prime number divisible by 2 plus the number of prime number divisible by 3 is

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To solve the problem, we need to determine the number of prime numbers that are divisible by 2 and the number of prime numbers that are divisible by 3, and then sum these two counts. ### Step-by-Step Solution: 1. **Identify Prime Numbers Divisible by 2:** - A prime number is defined as a number greater than 1 that has no positive divisors other than 1 and itself. - The only even prime number is 2. All other even numbers are not prime because they can be divided by 2. - Therefore, the only prime number that is divisible by 2 is **2**. - Count: There is **1 prime number** divisible by 2. 2. **Identify Prime Numbers Divisible by 3:** - A prime number can only be divisible by 1 and itself. - The only prime number that is divisible by 3 is **3** itself. - Therefore, the only prime number that is divisible by 3 is **3**. - Count: There is **1 prime number** divisible by 3. 3. **Add the Counts:** - Now, we need to add the counts of prime numbers divisible by 2 and 3. - Count of prime numbers divisible by 2 = 1 - Count of prime numbers divisible by 3 = 1 - Total = 1 + 1 = **2**. ### Final Answer: The number of prime numbers divisible by 2 plus the number of prime numbers divisible by 3 is **2**.
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