To display all the prime numbers within a given range, you need to understand the definition of a prime number. A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. In other words, a prime number has only two distinct positive divisors: 1 and itself.
Let's determine the prime numbers within the range from 1 to 100.
1. Define the Range: We are considering all numbers between 1 and 100.
2. Prime Number Criteria:
- A number is prime if it is greater than 1.
- A number is prime if it is not divisible by any number other than 1 and itself.
3. Process to Find Prime Numbers:
- For each number in the range, check if it meets the criteria of a prime number.
- Numbers like 2, 3, 5, and 7 are familiar examples of prime numbers because they can only be divided evenly by 1 and themselves.
- Other numbers like 4, 6, 8, 9, etc., are not prime because they can be divided by additional numbers other than 1 and themselves (e.g., 6 can be divided by 2 and 3).
4. Steps to Check Each Number:
- Start with the first number in our range (2, since 1 is not a prime number).
- For each number, check divisibility from 2 up to the square root of the number (since if a number n is divisible by some number p, then n = p q and one of these factors must be less than or equal to the square root of n).
5. Example Breakdown:
- Look at the number 6:
- It is greater than 1.
- However, 6 can be divided by 2 and 3 (6 = 2 3), so it is not a prime number.
- Look at the number 37:
- It is greater than 1.
- When you check for divisors of 37, you notice it cannot be divided evenly by any number other than 1 and 37 itself, so it is a prime number.
Following these steps, the list of prime numbers between 1 and 100 are:
[tex]\[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97\][/tex]
This is the complete list of prime numbers within the range of 1 to 100.
