Yes, by definition, all prime numbers are prime.
Understanding Prime Numbers
Prime numbers are a fundamental concept in mathematics. According to the reference, they are:
- Natural numbers (positive whole numbers greater than 0).
- Greater than 1.
- Divisible only by 1 and themselves. This means they have exactly two factors: 1 and the number itself.
Key Characteristics of Prime Numbers
Here's a breakdown of what makes a number prime:
- No other divisors: A prime number cannot be divided evenly by any other whole number besides 1 and itself.
- Examples: 2, 3, 5, 7, 11, 13, and so on are all prime numbers.
- 1 is not prime: The number 1 is explicitly excluded from the set of prime numbers, as it only has one factor.
Examples and Insights
Let's look at some examples:
- 2: This is the smallest prime number. Its only factors are 1 and 2.
- 4: This is not a prime number because it is divisible by 1, 2, and 4.
- 7: This is a prime number. Its only factors are 1 and 7.
- 15: This is not a prime number because it's divisible by 1, 3, 5, and 15.
In essence, the definition of a prime number means that if a number is identified as a prime number, it must fulfill all the criteria of being prime. Therefore, all prime numbers are inherently prime by definition.
