Find two different PRIME numbers whose sum is a composite number. Explain the DIVISIBILITY rule that proves the sum is composite
Let's consider two prime numbers, 3 and 5. The sum of these prime numbers is 3 + 5 = 8, which is a composite number.
The divisibility rule that proves the sum of 3 and 5 is composite is the divisibility rule for 2. According to this rule, a number is divisible by 2 if it ends in an even digit (0, 2, 4, 6, or 8).
In the case of the sum 3 + 5 = 8, we can see that 8 is divisible by 2 because it ends in an even digit (8). Therefore, following the divisibility rule for 2, we can conclude that the sum of 3 and 5 (8) is a composite number.
To find two different prime numbers whose sum is a composite number, we can consider the prime numbers 3 and 5.
The first PRIME number is 3.
The second PRIME number is 5.
Prime numbers have the property that they are only divisible by 1 and themselves. So, a number is prime if it has exactly two positive divisors.
Now let's calculate their sum:
3 + 5 = 8
To prove that 8 is a composite number, we can use the divisibility rule for 2. According to the rule, any number that is divisible by 2 is an even number and therefore composite.
In this case, since 8 is divisible by 2:
8 ÷ 2 = 4
4 is also divisible by 2, giving us:
4 ÷ 2 = 2
Since 2 is the smallest positive divisor of 4, we can conclude that 8 has more than two positive divisors (1, 2, 4, 8), and thus it is a composite number.
Therefore, the sum of the prime numbers 3 and 5 is a composite number (8).
To find two different prime numbers whose sum is a composite number, we can first identify the divisibility rule that proves the sum is composite.
The divisibility rule we need to consider is that any number greater than 1 can be divided evenly by 1 and itself. In other words, if a number can be divided evenly by a factor other than 1 and itself, then it is a composite number.
Now, let's find two different prime numbers whose sum is a composite number.
Step 1: Identify a prime number.
Let's take the prime number 2.
Step 2: Identify another prime number.
We need to choose another prime number different from 2. Let's consider 3.
Step 3: Find the sum of the two prime numbers.
Adding 2 and 3, we get 5.
Step 4: Check if the sum is a prime or composite number.
In this case, 5 is a prime number as it can only be divided evenly by 1 and itself. Therefore, the sum of 2 and 3 does not satisfy the requirement of being a composite number.
To find two different prime numbers whose sum is a composite number, we need to choose a different pair of prime numbers. Let's try again.
Step 1: Identify a prime number.
We'll choose the prime number 2.
Step 2: Identify another prime number.
This time, let's consider the prime number 5.
Step 3: Find the sum of the two prime numbers.
Adding 2 and 5, we get 7.
Step 4: Check if the sum is a prime or composite number.
In this case, 7 is also a prime number since it can only be divided evenly by 1 and itself. Hence, the sum of 2 and 5 is not a composite number.
Based on these attempts, we can see that it is not possible to find two different prime numbers whose sum is a composite number. This is because the sum of any two prime numbers will always result in a prime number.